Southwest Rafters Case 2:Case 1: Capital Budgeting Cash Flows and Capital Budgeting Techniques Create a data sheet (or section) and link calculations to the data so that if the data is updated the calculations automatically update. 1) Calculate the Initial Cash Outlay and Annual Capital Budgeting Cash Flow for years 1 thru 5 for both alternatives. 2) Discuss the ethical implications of this business. Might there be a difference between these two alternatives? 3) Calculate the Payback Period, Net Present Value and Internal Rate of Return for both alternatives based on your Initial Cash Outlay and Capital Budgeting Cash Flows. 4) Calculate NPV and IRR if cash flows increase at an estimated 6% annual rate. 5) What discount rate would leave them indifferent between the two alternatives? 6) What does the discount rate in #5 imply about the growth rate needed to make the Buenaventura better than the Green? 7) What is the probability of negative NPV both in the case of perfect serial correlation and in the case of independence of cash flows for both alternatives? Assume no growth and a $5,000 standard deviation of annual cash flow for both alternatives. 8) Calculate Accounting (Profit) and Cash Breakeven Points (average number of clients per trip) and the Degree of Operating Leverage for both alternatives for year 1. Treat all revenue as variable. Treat all expenses as fixed except the client portion of transportation and food and the administrative cost. Include externalities. If you spreadsheet is functional BEP is easy! 9) Could either alternative have Multiple Internal Rates of Return? Explain 10) Discuss the option values associated with these alternatives. Is there a difference between them? 11) Which alternative do you recommend for Southwest Rafters? Defend your choice using the results from the other questions. Assume that the assumptions are reasonable.

Southwest Rafters Case 2:Case 1: Capital Budgeting Cash Flows and Capital Budgeting Techniques Create a data sheet (or section) and link calculations to the data so that if the data is updated the calculations automatically update. 1) Calculate the Initial Cash Outlay and Annual Capital Budgeting Cash Flow for years 1 thru 5 for both alternatives. 2) Discuss the ethical implications of this business. Might there be a difference between these two alternatives? 3) Calculate the Payback Period, Net Present Value and Internal Rate of Return for both alternatives based on your Initial Cash Outlay and Capital Budgeting Cash Flows. 4) Calculate NPV and IRR if cash flows increase at an estimated 6% annual rate. 5) What discount rate would leave them indifferent between the two alternatives? 6) What does the discount rate in #5 imply about the growth rate needed to make the Buenaventura better than the Green? 7) What is the probability of negative NPV both in the case of perfect serial correlation and in the case of independence of cash flows for both alternatives? Assume no growth and a $5,000 standard deviation of annual cash flow for both alternatives. 8) Calculate Accounting (Profit) and Cash Breakeven Points (average number of clients per trip) and the Degree of Operating Leverage for both alternatives for year 1. Treat all revenue as variable. Treat all expenses as fixed except the client portion of transportation and food and the administrative cost. Include externalities. If you spreadsheet is functional BEP is easy! 9) Could either alternative have Multiple Internal Rates of Return? Explain 10) Discuss the option values associated with these alternatives. Is there a difference between them? 11) Which alternative do you recommend for Southwest Rafters? Defend your choice using the results from the other questions. Assume that the assumptions are reasonable.

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Activation of this hormone increases blood pressure by causing the blood vessels to constrict and the kidneys to retain more water. Question 5 options: neuropeptide Y adrenocorticotropic hormone hypothalamic-pituitary-adrenal axis antidiuretic hormone

Activation of this hormone increases blood pressure by causing the blood vessels to constrict and the kidneys to retain more water. Question 5 options: neuropeptide Y adrenocorticotropic hormone hypothalamic-pituitary-adrenal axis antidiuretic hormone

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When discussing homeostasis in body temperature, it is NOT true to state that the body responds to Select one: a. heat by stimulating sweat release. b. heat by constricting the blood vessels in the skin. c. cold by contracting the arrector pili muscles. d. cold by contracting skeletal muscles causing shivering. e. cold by rerouting blood away from the skin.

When discussing homeostasis in body temperature, it is NOT true to state that the body responds to Select one: a. heat by stimulating sweat release. b. heat by constricting the blood vessels in the skin. c. cold by contracting the arrector pili muscles. d. cold by contracting skeletal muscles causing shivering. e. cold by rerouting blood away from the skin.

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A block with mass m =7.1 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.23 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.4 m/s. The block oscillates on the spring without friction. 1) What is the spring constant of the spring? N/m You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. 2) What is the oscillation frequency? Hz You currently have 2 submissions for this question. Only 10 submission are allowed. You can make 8 more submissions for this question. 3) After t = 0.37 s what is the speed of the block? m/s You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. 4) What is the magnitude of the maximum acceleration of the block? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) At t = 0.37 s what is the magnitude of the net force on the block? N You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) Where is the potential energy of the system the greatest? At the highest point of the oscillation. At the new equilibrium position of the oscillation. At the lowest point of the oscillation. You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 7) Below is some space to write notes on this problem A 5.2-kg object on a frictionless horizontal surface is attached to one end of a horizontal spring that has a force constantk = 717 N/m. The spring is stretched 7.9 cm from equilibrium and released. 1) (a) What is the frequency of the motion? Hz You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 2) (b) What is the period of the motion? s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) (c) What is the amplitude of the motion? cm You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) (d) What is the maximum speed of the motion? m/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) (e) What is the maximum acceleration of the motion? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) (f) When does the object first reach its equilibrium position? s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 7) (h) What is its acceleration at this time? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 1) An 86 kg person steps into a car of mass 2437 kg, causing it to sink 2.35 cm on its springs. Assuming no damping, with what frequency will the car and passenger vibrate on the springs? Hz You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 1) A 0.117-kg block is suspended from a spring. When a small pebble of mass 30 g is placed on the block, the spring stretches an additional 5.1 cm. With the pebble on the block, the block oscillates with an amplitude of 12 cm. Find the maximum amplitude of oscillation at which the pebble will remain in contact with the block. Block and Spring SHM ________________________________________ At t = 0 a block with mass M = 5 kg moves with a velocity v = 2 m/s at position xo = -.33 m from the equilibrium position of the spring. The block is attached to a massless spring of spring constant k = 61.2 N/m and slides on a frictionless surface. At what time will the block next pass x = 0, the place where the spring is unstretched? t1 = seconds You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. A simple pendulum with mass m = 1.9 kg and length L = 2.39 m hangs from the ceiling. It is pulled back to an small angle of θ = 9.9° from the vertical and released at t = 0. 1) What is the period of oscillation? s You currently have 2 submissions for this question. Only 10 submission are allowed. You can make 8 more submissions for this question. 2) What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0? N You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) What is the maximum speed of the pendulum? m/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) What is the angular displacement at t = 3.5 s? (give the answer as a negative angle if the angle is to the left of the vertical) ° You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) What is the magnitude of the tangential acceleration as the pendulum passes through the equilibrium position? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) What is the magnitude of the radial acceleration as the pendulum passes through the equilibrium position? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 7) Which of the following would change the frequency of oscillation of this simple pendulum? increasing the mass decreasing the initial angular displacement increasing the length hanging the pendulum in an elevator accelerating downward You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 8) Below is some space to write notes on this problem 1) If the period of a 74-cm-long simple pendulum is 1.72 s, what is the value of g at the location of the pendulum? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. Torsion Pendulum • 1 • 2 • 3 • 4 • 5 A torsion pendulum is made from a disk of mass m = 6.6 kg and radius R = 0.66 m. A force of F = 44.8 N exerted on the edge of the disk rotates the disk 1/4 of a revolution from equilibrium. 1) What is the torsion constant of this pendulum? N-m/rad You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 2) What is the minimum torque needed to rotate the pendulum a full revolution from equilibrium? N-m You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) What is the angular frequency of oscillation of this torsion pendulum? rad/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) Which of the following would change the period of oscillation of this torsion pendulum? increasing the mass decreasing the initial angular displacement replacing the disk with a sphere of equal mass and radius hanging the pendulum in an elevator accelerating downward You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 5) Below is some space to write notes on this problem You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. Physical Pendulum ________________________________________ A rigid rod of length L= 1 m and mass M = 2.5 kg is attached to a pivot mounted d = 0.17 m from one end. The rod can rotate in the vertical plane, and is influenced by gravity. What is the period for small oscillations of the pendulum shown? T = seconds A circular hoop of radius 57 cm is hung on a narrow horizontal rod and allowed to swing in the plane of the hoop. What is the period of its oscillation, assuming that the amplitude is small? s 1) You are given a wooden rod 68 cm long and asked to drill a small diameter hole in it so that when pivoted about the the hole the period of the pendulum will be a minimum. How far from the center should you drill the hole? cm

A block with mass m =7.1 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.23 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.4 m/s. The block oscillates on the spring without friction. 1) What is the spring constant of the spring? N/m You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. 2) What is the oscillation frequency? Hz You currently have 2 submissions for this question. Only 10 submission are allowed. You can make 8 more submissions for this question. 3) After t = 0.37 s what is the speed of the block? m/s You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. 4) What is the magnitude of the maximum acceleration of the block? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) At t = 0.37 s what is the magnitude of the net force on the block? N You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) Where is the potential energy of the system the greatest? At the highest point of the oscillation. At the new equilibrium position of the oscillation. At the lowest point of the oscillation. You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 7) Below is some space to write notes on this problem A 5.2-kg object on a frictionless horizontal surface is attached to one end of a horizontal spring that has a force constantk = 717 N/m. The spring is stretched 7.9 cm from equilibrium and released. 1) (a) What is the frequency of the motion? Hz You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 2) (b) What is the period of the motion? s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) (c) What is the amplitude of the motion? cm You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) (d) What is the maximum speed of the motion? m/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) (e) What is the maximum acceleration of the motion? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) (f) When does the object first reach its equilibrium position? s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 7) (h) What is its acceleration at this time? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 1) An 86 kg person steps into a car of mass 2437 kg, causing it to sink 2.35 cm on its springs. Assuming no damping, with what frequency will the car and passenger vibrate on the springs? Hz You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 1) A 0.117-kg block is suspended from a spring. When a small pebble of mass 30 g is placed on the block, the spring stretches an additional 5.1 cm. With the pebble on the block, the block oscillates with an amplitude of 12 cm. Find the maximum amplitude of oscillation at which the pebble will remain in contact with the block. Block and Spring SHM ________________________________________ At t = 0 a block with mass M = 5 kg moves with a velocity v = 2 m/s at position xo = -.33 m from the equilibrium position of the spring. The block is attached to a massless spring of spring constant k = 61.2 N/m and slides on a frictionless surface. At what time will the block next pass x = 0, the place where the spring is unstretched? t1 = seconds You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. A simple pendulum with mass m = 1.9 kg and length L = 2.39 m hangs from the ceiling. It is pulled back to an small angle of θ = 9.9° from the vertical and released at t = 0. 1) What is the period of oscillation? s You currently have 2 submissions for this question. Only 10 submission are allowed. You can make 8 more submissions for this question. 2) What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0? N You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) What is the maximum speed of the pendulum? m/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) What is the angular displacement at t = 3.5 s? (give the answer as a negative angle if the angle is to the left of the vertical) ° You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) What is the magnitude of the tangential acceleration as the pendulum passes through the equilibrium position? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) What is the magnitude of the radial acceleration as the pendulum passes through the equilibrium position? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 7) Which of the following would change the frequency of oscillation of this simple pendulum? increasing the mass decreasing the initial angular displacement increasing the length hanging the pendulum in an elevator accelerating downward You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 8) Below is some space to write notes on this problem 1) If the period of a 74-cm-long simple pendulum is 1.72 s, what is the value of g at the location of the pendulum? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. Torsion Pendulum • 1 • 2 • 3 • 4 • 5 A torsion pendulum is made from a disk of mass m = 6.6 kg and radius R = 0.66 m. A force of F = 44.8 N exerted on the edge of the disk rotates the disk 1/4 of a revolution from equilibrium. 1) What is the torsion constant of this pendulum? N-m/rad You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 2) What is the minimum torque needed to rotate the pendulum a full revolution from equilibrium? N-m You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) What is the angular frequency of oscillation of this torsion pendulum? rad/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) Which of the following would change the period of oscillation of this torsion pendulum? increasing the mass decreasing the initial angular displacement replacing the disk with a sphere of equal mass and radius hanging the pendulum in an elevator accelerating downward You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 5) Below is some space to write notes on this problem You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. Physical Pendulum ________________________________________ A rigid rod of length L= 1 m and mass M = 2.5 kg is attached to a pivot mounted d = 0.17 m from one end. The rod can rotate in the vertical plane, and is influenced by gravity. What is the period for small oscillations of the pendulum shown? T = seconds A circular hoop of radius 57 cm is hung on a narrow horizontal rod and allowed to swing in the plane of the hoop. What is the period of its oscillation, assuming that the amplitude is small? s 1) You are given a wooden rod 68 cm long and asked to drill a small diameter hole in it so that when pivoted about the the hole the period of the pendulum will be a minimum. How far from the center should you drill the hole? cm

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Chapter 03 Reading Questions Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Chapter 3 Reading Quiz Question 1 Part A Isotopes of an element differ from each other by the _____. ANSWER: Correct Chapter 3 Reading Quiz Question 2 Part A Which one of the following statements about pH is correct? ANSWER: Correct Lemon juice is an acid. Chapter 3 Reading Quiz Question 17 Part A In which form are water molecules most closely bonded to each other? ANSWER: number of electrons number of neutrons types of electrons number of protons Stomach acid has more OH- ions than H+ ions. Baking soda has more H+ ions than OH- ions. Lemon juice has more H+ ions than OH- ions. Seawater is slightly acidic. Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 9 5/21/2014 7:58 PM Correct Chapter 3 Reading Quiz Question 16 Part A Which one of the following is a molecule but NOT a compound? ANSWER: Correct Oxygen is a molecule made up of just one element. Therefore, it is not a compound. Chapter 3 Reading Quiz Question 3 Part A Which one of the following is a carbohydrate and one of Earth’s most abundant organic molecule? ANSWER: Correct equally closely bonded in water vapor and ice solid ice forming part of an Antarctic sheet liquid water a few degrees above the freezing point water vapor above a boiling pot of water CH4 O2 CO2 H2O oil protein cellulose DNA Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 9 5/21/2014 7:58 PM Chapter 3 Reading Quiz Question 4 Part A Which one of the following is a protein that functions as a catalyst? ANSWER: Correct Chapter 3 Reading Quiz Question 18 Part A The process of translation involves the use of _____. ANSWER: Chapter 3 Reading Quiz Question 5 Part A The cooling effect of sweating best represents _____. ANSWER: glucose cellulose enzyme RNA proteins to make lipids lipids to make carbohydrates carbohydrates to make proteins nucleic acids to make proteins latent heat transfer conduction radiation convection Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 9 5/21/2014 7:58 PM Correct Chapter 3 Reading Quiz Question 6 Part A When plants use sunlight in photosynthesis, the plants are using a form of _____. ANSWER: Correct Chapter 3 Reading Quiz Question 8 Part A Which of the following converts mass to energy? ANSWER: Correct Chapter 3 Reading Quiz Question 19 Part A When a windmill turns to generate electricity, the amount of kinetic energy input _____. ANSWER: chemical energy in sunlight nuclear fission electromagnetic radiation conduction conduction the breaking of chemical bonds nuclear fission photosynthesis Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 9 5/21/2014 7:58 PM Correct Chapter 3 Reading Quiz Question 20 Part A Which of the following best represents kinetic energy? ANSWER: Correct Chapter 3 Reading Quiz Question 21 Part A Which of the following processes reduces entropy? ANSWER: Correct Chapter 3 Reading Quiz Question 9 is unrelated to the amount of electrical energy produced is more than the amount of electrical energy produced equals the amount of electrical energy produced is less than the amount of electrical energy produced a charged battery gunpowder in a bullet the energy in the wax molecules of a candle a hot burner on a stove burning gasoline in an automobile engine photosynthesis in a leaf a person walking up a flight of stairs cell respiration in a leaf Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 9 5/21/2014 7:58 PM Part A Which one of the following planets is a gas giant? ANSWER: Correct Chapter 3 Reading Quiz Question 10 Part A What is the main driving force that causes Earth’s tectonic plates to drift? ANSWER: Correct Chapter 3 Reading Quiz Question 23 Part A In which of the following locations would you expect to find large quantities of young rocks? ANSWER: Venus Jupiter Mars Mercury Heat from Earth’s core causes the mantle rock to circulate. The weight of the tectonic plates causes them to sink and melt. Currents of magma from the core of Earth circulate just beneath the tectonic plates. Electromagnetic radiation from the sun heats the tectonic plates, causing them to expand. the Appalachian Mountains the Himalayas deep in the central parts of India the Mid-Atlantic Ridge Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 9 5/21/2014 7:58 PM Chapter 3 Reading Quiz Question 12 Part A The oxygen-rich atmosphere of Earth is mainly the result of _____. ANSWER: Correct Chapter 3 Reading Quiz Question 13 Part A A scientist working on the chemical reactions in the ozone layer is studying the _____. ANSWER: Correct Chapter 3 Reading Quiz Question 24 Part A The total amount of moisture in the air is highest when relative humidity is _____. ANSWER: volcanic activity chemical reactions between the early Earth atmosphere and iron photosynthetic organisms erosion of rocks into soil troposphere thermosphere stratosphere mesosphere Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 9 5/21/2014 7:58 PM Chapter 3 Reading Quiz Question 15 Part A You are enjoying a spring day but expect a storm to arrive soon . As the storm arrives and the rain begins to fall, you notice that the temperature drops dramatically. Most likely, you have just experienced the arrival of a _____. ANSWER: Correct Chapter 3 Reading Quiz Question 25 Part A Every day tremendous amounts of the sun’s energy strikes Earth. Why doesn’t Earth overheat? ANSWER: Correct Earth’s energy budget is balanced. Over the course of a year, the energy input is equal to the energy output. Chapter 3 Reading Quiz Question 7 low and temperatures are low high and temperatures are high high and temperatures are low low and temperatures are high cold front Hadley cell intertropical convergence stratospheric event The energy is ultimately radiated back to space. Much of the heat melts rocks, forming lava deep inside of Earth. Most of the energy is used in photosynthesis to help plants grow and survive. The energy mostly is absorbed in various weather systems. Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 8 of 9 5/21/2014 7:58 PM Part A How many calories are required to heat up 1,000 grams of liquid water (about 1 liter) from 20 °C to 70 °C? ANSWER: Correct Chapter 3 Reading Quiz Question 14 Part A Hadley cells near the Equator consist of _____. ANSWER: Correct Score Summary: Your score on this assignment is 85.5%. You received 19.67 out of a possible total of 23 points. 100 1,000 5,000 50,000 rising dry air associated with deserts and falling moist air that produces precipitation and rainforests rising moist air that produces precipitation and rainforests, and falling dry air associated with deserts warm, moist air rising up the sides of mountains and cool, dry air descending on the leeward sides cool, dry air rising up the sides of mountains and warm, moist air descending on the leeward sides Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 9 of 9 5/21/2014 7:58 PM

Chapter 03 Reading Questions Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Chapter 3 Reading Quiz Question 1 Part A Isotopes of an element differ from each other by the _____. ANSWER: Correct Chapter 3 Reading Quiz Question 2 Part A Which one of the following statements about pH is correct? ANSWER: Correct Lemon juice is an acid. Chapter 3 Reading Quiz Question 17 Part A In which form are water molecules most closely bonded to each other? ANSWER: number of electrons number of neutrons types of electrons number of protons Stomach acid has more OH- ions than H+ ions. Baking soda has more H+ ions than OH- ions. Lemon juice has more H+ ions than OH- ions. Seawater is slightly acidic. Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 9 5/21/2014 7:58 PM Correct Chapter 3 Reading Quiz Question 16 Part A Which one of the following is a molecule but NOT a compound? ANSWER: Correct Oxygen is a molecule made up of just one element. Therefore, it is not a compound. Chapter 3 Reading Quiz Question 3 Part A Which one of the following is a carbohydrate and one of Earth’s most abundant organic molecule? ANSWER: Correct equally closely bonded in water vapor and ice solid ice forming part of an Antarctic sheet liquid water a few degrees above the freezing point water vapor above a boiling pot of water CH4 O2 CO2 H2O oil protein cellulose DNA Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 9 5/21/2014 7:58 PM Chapter 3 Reading Quiz Question 4 Part A Which one of the following is a protein that functions as a catalyst? ANSWER: Correct Chapter 3 Reading Quiz Question 18 Part A The process of translation involves the use of _____. ANSWER: Chapter 3 Reading Quiz Question 5 Part A The cooling effect of sweating best represents _____. ANSWER: glucose cellulose enzyme RNA proteins to make lipids lipids to make carbohydrates carbohydrates to make proteins nucleic acids to make proteins latent heat transfer conduction radiation convection Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 9 5/21/2014 7:58 PM Correct Chapter 3 Reading Quiz Question 6 Part A When plants use sunlight in photosynthesis, the plants are using a form of _____. ANSWER: Correct Chapter 3 Reading Quiz Question 8 Part A Which of the following converts mass to energy? ANSWER: Correct Chapter 3 Reading Quiz Question 19 Part A When a windmill turns to generate electricity, the amount of kinetic energy input _____. ANSWER: chemical energy in sunlight nuclear fission electromagnetic radiation conduction conduction the breaking of chemical bonds nuclear fission photosynthesis Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 9 5/21/2014 7:58 PM Correct Chapter 3 Reading Quiz Question 20 Part A Which of the following best represents kinetic energy? ANSWER: Correct Chapter 3 Reading Quiz Question 21 Part A Which of the following processes reduces entropy? ANSWER: Correct Chapter 3 Reading Quiz Question 9 is unrelated to the amount of electrical energy produced is more than the amount of electrical energy produced equals the amount of electrical energy produced is less than the amount of electrical energy produced a charged battery gunpowder in a bullet the energy in the wax molecules of a candle a hot burner on a stove burning gasoline in an automobile engine photosynthesis in a leaf a person walking up a flight of stairs cell respiration in a leaf Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 9 5/21/2014 7:58 PM Part A Which one of the following planets is a gas giant? ANSWER: Correct Chapter 3 Reading Quiz Question 10 Part A What is the main driving force that causes Earth’s tectonic plates to drift? ANSWER: Correct Chapter 3 Reading Quiz Question 23 Part A In which of the following locations would you expect to find large quantities of young rocks? ANSWER: Venus Jupiter Mars Mercury Heat from Earth’s core causes the mantle rock to circulate. The weight of the tectonic plates causes them to sink and melt. Currents of magma from the core of Earth circulate just beneath the tectonic plates. Electromagnetic radiation from the sun heats the tectonic plates, causing them to expand. the Appalachian Mountains the Himalayas deep in the central parts of India the Mid-Atlantic Ridge Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 9 5/21/2014 7:58 PM Chapter 3 Reading Quiz Question 12 Part A The oxygen-rich atmosphere of Earth is mainly the result of _____. ANSWER: Correct Chapter 3 Reading Quiz Question 13 Part A A scientist working on the chemical reactions in the ozone layer is studying the _____. ANSWER: Correct Chapter 3 Reading Quiz Question 24 Part A The total amount of moisture in the air is highest when relative humidity is _____. ANSWER: volcanic activity chemical reactions between the early Earth atmosphere and iron photosynthetic organisms erosion of rocks into soil troposphere thermosphere stratosphere mesosphere Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 9 5/21/2014 7:58 PM Chapter 3 Reading Quiz Question 15 Part A You are enjoying a spring day but expect a storm to arrive soon . As the storm arrives and the rain begins to fall, you notice that the temperature drops dramatically. Most likely, you have just experienced the arrival of a _____. ANSWER: Correct Chapter 3 Reading Quiz Question 25 Part A Every day tremendous amounts of the sun’s energy strikes Earth. Why doesn’t Earth overheat? ANSWER: Correct Earth’s energy budget is balanced. Over the course of a year, the energy input is equal to the energy output. Chapter 3 Reading Quiz Question 7 low and temperatures are low high and temperatures are high high and temperatures are low low and temperatures are high cold front Hadley cell intertropical convergence stratospheric event The energy is ultimately radiated back to space. Much of the heat melts rocks, forming lava deep inside of Earth. Most of the energy is used in photosynthesis to help plants grow and survive. The energy mostly is absorbed in various weather systems. Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 8 of 9 5/21/2014 7:58 PM Part A How many calories are required to heat up 1,000 grams of liquid water (about 1 liter) from 20 °C to 70 °C? ANSWER: Correct Chapter 3 Reading Quiz Question 14 Part A Hadley cells near the Equator consist of _____. ANSWER: Correct Score Summary: Your score on this assignment is 85.5%. You received 19.67 out of a possible total of 23 points. 100 1,000 5,000 50,000 rising dry air associated with deserts and falling moist air that produces precipitation and rainforests rising moist air that produces precipitation and rainforests, and falling dry air associated with deserts warm, moist air rising up the sides of mountains and cool, dry air descending on the leeward sides cool, dry air rising up the sides of mountains and warm, moist air descending on the leeward sides Chapter 03 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 9 of 9 5/21/2014 7:58 PM

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http://www.constitution.org/mac/prince17.htm How does Machiavelli feel about cruelty versus clemency? A. Machiavelli equates clemency with being loved and cruelty with being despised, and suggests that being despised is acceptable. B. Machiavelli suggests that cruelty doesn’t always result in being despised and winning the love of your subjects is the most important thing. C. Machiavelli says that cruelty, when applied in a prudent manner, will be held in more esteem than too much mercy. D. Cruelty and clemency are identical; being merciful to one person means that you must be cruel to another. E. Clemency is equated with happiness, and a happy set of subjects is the ultimate goal of a successful leader. What is the difference between hatred and fear? A. Fear makes people respect you. Hatred makes them work against you. B. Fear and hatred follow one another. If you create fear you will eventually create hatred. All leaders should avoid this. C. Hatred from external powers breeds nationalism within your country, causing people to fear external powers. D. Fear and hatred are opposites. E. Hatred follows love; fear follows clemency. http://www.constitution.org/mac/prince23.htm According to Machiavelli, what is a flatterer? A. Someone who wants to lavish gifts upon you in exchange for power. B. An external power that wants to ally with you. C. Someone who will tell you what you think rather than giving their own opinion. D. Someone who tests your opinions against their own to make a good argument. E. An external power that wants to make strong trade alliances to weaken you over time. According to Machiavelli, what is the best way to seek truth from advisers? A. Advisors should present any complaints to you as a group. B. Advisors should be called upon when the leader has a question, otherwise they are to remain silent. C. An advisor should involve the public, allowing them to call the leader to court to listen to their opinions. D. The leader should listen carefully to one private advisor with whom he always disagrees. E. Machiavelli thinks that advisors are not helpful because they will always try to flatter their leader.

http://www.constitution.org/mac/prince17.htm How does Machiavelli feel about cruelty versus clemency? A. Machiavelli equates clemency with being loved and cruelty with being despised, and suggests that being despised is acceptable. B. Machiavelli suggests that cruelty doesn’t always result in being despised and winning the love of your subjects is the most important thing. C. Machiavelli says that cruelty, when applied in a prudent manner, will be held in more esteem than too much mercy. D. Cruelty and clemency are identical; being merciful to one person means that you must be cruel to another. E. Clemency is equated with happiness, and a happy set of subjects is the ultimate goal of a successful leader. What is the difference between hatred and fear? A. Fear makes people respect you. Hatred makes them work against you. B. Fear and hatred follow one another. If you create fear you will eventually create hatred. All leaders should avoid this. C. Hatred from external powers breeds nationalism within your country, causing people to fear external powers. D. Fear and hatred are opposites. E. Hatred follows love; fear follows clemency. http://www.constitution.org/mac/prince23.htm According to Machiavelli, what is a flatterer? A. Someone who wants to lavish gifts upon you in exchange for power. B. An external power that wants to ally with you. C. Someone who will tell you what you think rather than giving their own opinion. D. Someone who tests your opinions against their own to make a good argument. E. An external power that wants to make strong trade alliances to weaken you over time. According to Machiavelli, what is the best way to seek truth from advisers? A. Advisors should present any complaints to you as a group. B. Advisors should be called upon when the leader has a question, otherwise they are to remain silent. C. An advisor should involve the public, allowing them to call the leader to court to listen to their opinions. D. The leader should listen carefully to one private advisor with whom he always disagrees. E. Machiavelli thinks that advisors are not helpful because they will always try to flatter their leader.

http://www.constitution.org/mac/prince17.htm   How does Machiavelli feel about cruelty versus clemency? … Read More...
Assignment 4 Due: 11:59pm on Wednesday, February 26, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy ± Two Forces Acting at a Point Two forces, and , act at a point. has a magnitude of 9.80 and is directed at an angle of 56.0 above the negative x axis in the second quadrant. has a magnitude of 5.20 and is directed at an angle of 54.1 below the negative x axis in the third quadrant. Part A What is the x component of the resultant force? Express your answer in newtons. Hint 1. How to approach the problem The resultant force is defined as the vector sum of all forces. Thus, its x component is the sum of the x components of the forces, and its y component is the sum of the y components of the forces. Hint 2. Find the x component of Find the x component of . Express your answer in newtons. Hint 1. Components of a vector Consider a vector that forms an angle with the positive x axis. The x and y components of are, respectively, and , where is the magnitude of the vector. Note that and if , and if . F 1 F  2 F  1 N  F  2 N  F 1 F  1 A  A Ax = Acos  Ay = Asin  A Ax < 0 Ay > 0  <  <  2 Ax < 0 Ay < 0  <  < 3 2 Hint 2. Find the direction of is directed at an angle of 56.0 above the x axis in the second quadrant. When you calculate the components of , however, the direction of the force is commonly expressed in terms of the angle that the vector representing the force forms with the positive x axis. What is the angle that forms with the positive x axis? Select an answer from the following list, where 56.0 . ANSWER: ANSWER: Hint 3. Find the x component of Find the x component of . Express your answer in newtons. Hint 1. Components of a vector Consider a vector that forms an angle with the positive x axis. The x and y components of are, respectively, and , where is the magnitude of the vector. Note that and if , F 1 F 1  F  1 F  1  =   180 −  180 +  90 +  -5.48 N F 2 F  2 A  A Ax = Acos  Ay = Asin  A Ax < 0 Ay > 0  <  <  2 Typesetting math: 100% and if . Hint 2. Find the direction of is directed at an angle of 54.1 below the x axis in the third quadrant. When you calculate the components of , however, the direction of the force is commonly expressed in terms of the angle that the vector representing the force forms with the positive x axis. What is the angle that forms with the positive x axis? Select an answer from the following list, where 54.1 . ANSWER: ANSWER: ANSWER: Correct Part B What is the y component of the resultant force? Express your answer in newtons. Ax < 0 Ay <  <  < 3 2 F 2 F 2  F 2 F  2  =   180 −   − 180 −90 −  -3.05 N -8.53 N Typesetting math: 100% Hint 1. How to approach the problem Follow the same procedure that you used in Part A to find the x component of the resultant force, though now calculate the y components of the two forces. Hint 2. Find the y component of Find the y component of . Express your answer in newtons. Hint 1. Components of a vector Consider a vector that forms an angle with the positive x axis. The x and y components of are, respectively, and , where is the magnitude of the vector. Note that and if , and if . ANSWER: Hint 3. Find the y component of Find the y component of . Express your answer in newtons. Hint 1. Components of a vector F 1 F  1 A  A Ax = Acos  Ay = Asin  A Ax < 0 Ay > 0  <  <  2 Ax < 0 Ay < 0  <  < 3 2 8.12 N F 2 F  2 Typesetting math: 100% Consider a vector that forms an angle with the positive x axis. The x and y components of are, respectively, and , where is the magnitude of the vector. Note that and if , and if . ANSWER: ANSWER: Correct Part C What is the magnitude of the resultant force? Express your answer in newtons. Hint 1. Magnitude of a vector Consider a vector , whose components are and . The magnitude of is . A  A Ax = Acos  Ay = Asin  A Ax < 0 Ay > 0  <  <  2 Ax < 0 Ay < 0  <  < 3 2 -4.21 N 3.91 N A Ax Ay A A = A + 2 x A2 y −−−−−−−  Typesetting math: 100% ANSWER: Correct Enhanced EOC: Problem 5.9 The figure shows acceleration-versus-force graphs for two objects pulled by rubber bands. You may want to review ( pages 127 - 130) . For help with math skills, you may want to review: Finding the Slope of a Line from a Graph Part A What is the mass ratio ? Express your answer using two significant figures. 9.38 N m1 m2 Typesetting math: 100% Hint 1. How to approach the problem How are the acceleration and the force on an object related to its mass? How is the slope of each line in the figure related to each object's mass? For each line, what two points are easy to measure accurately to determine the slope of line? How is the slope determined from the x and y coordinates of the two points you chose for each line? ANSWER: Correct A World-Class Sprinter World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude . Part A How much horizontal force must a sprinter of mass 54 exert on the starting blocks to produce this acceleration? Express your answer in newtons using two significant figures. Hint 1. Newton's 2nd law of motion According to Newton's 2nd law of motion, if a net external force acts on a body, the body accelerates, and the net force is equal to the mass of the body times the acceleration of the body: . ANSWER: = 0.36 m1 m2 15 m/s2 F kg Fnet m a Fnet = ma F = 810 N Typesetting math: 100% Correct Part B Which body exerts the force that propels the sprinter, the blocks or the sprinter? Hint 1. How to approach the question To start moving forward, sprinters push backward on the starting blocks with their feet. Newton's 3rd law tells you that the blocks exert a force on the sprinter of the same magnitude, but opposite in direction. ANSWER: Correct To start moving forward, sprinters push backward on the starting blocks with their feet. As a reaction, the blocks push forward on their feet with a force of the same magnitude. This external force accelerates the sprinter forward. Problem 5.12 The figure shows an acceleration-versus-force graph for a 600 object. the blocks the sprinter g Typesetting math: 100% Part A What must equal in order for the graph to be correct? Express your answer with the appropriate units. ANSWER: Correct Part B What must equal in order for the graph to be correct? Express your answer with the appropriate units. ANSWER: Correct Free-Body Diagrams Learning Goal: To gain practice drawing free-body diagrams Whenever you face a problem involving forces, always start with a free-body diagram. a1 a1 = 1.67 m s2 a2 a2 = 3.33 m s2 Typesetting math: 100% To draw a free-body diagram use the following steps: Isolate the object of interest. It is customary to represent the object of interest as a point 1. in your diagram. Identify all the forces acting on the object and their directions. Do not include forces acting on other objects in the problem. Also, do not include quantities, such as velocities and accelerations, that are not forces. 2. Draw the vectors for each force acting on your object of interest. When possible, the length of the force vectors you draw should represent the relative magnitudes of the forces acting on the object. 3. In most problems, after you have drawn the free-body diagrams, you will explicitly label your coordinate axes and directions. Always make the object of interest the origin of your coordinate system. Then you will need to divide the forces into x and y components, sum the x and y forces, and apply Newton's first or second law. In this problem you will only draw the free-body diagram. Suppose that you are asked to solve the following problem: Chadwick is pushing a piano across a level floor (see the figure). The piano can slide across the floor without friction. If Chadwick applies a horizontal force to the piano, what is the piano's acceleration? To solve this problem you should start by drawing a free-body diagram. Part A Determine the object of interest for the situation described in the problem introduction. Hint 1. How to approach the problem You should first think about the question you are trying to answer: What is the acceleration of the piano? The object of interest in this situation will be the object whose acceleration you are asked to find. ANSWER: Typesetting math: 100% Correct Part B Identify the forces acting on the object of interest. From the list below, select the forces that act on the piano. Check all that apply. ANSWER: Correct Now that you have identified the forces acting on the piano, you should draw the free-body diagram. Draw the length of your vectors to represent the relative magnitudes of the forces, but you don't need to worry about the exact scale. You won't have the exact value of all of the forces until you finish solving the problem. To maximize your learning, you should draw the diagram yourself before looking at the choices in the next part. You are on your honor to do so. Part C For this situation you should draw a free-body diagram for the floor. Chadwick. the piano. acceleration of the piano gravitational force acting on the piano (piano's weight) speed of the piano gravitational force acting on Chadwick (Chadwick's weight) force of the floor on the piano (normal force) force of the piano on the floor force of Chadwick on the piano force of the piano pushing on Chadwick Typesetting math: 100% Select the choice that best matches the free-body diagram you have drawn for the piano. Hint 1. Determine the directions and relative magnitudes of the forces Which of the following statements best describes the correct directions and relative magnitudes of the forces involved? ANSWER: ANSWER: The normal force and weight are both upward and the pushing force is horizontal. The normal force and weight are both downward and the pushing force is horizontal. The normal force is upward, the weight is downward, and the pushing force is horizontal. The normal force has a greater magnitude than the weight. The normal force is upward, the weight is downward, and the pushing force is horizontal. The normal force and weight have the same magnitude. The normal force is upward, the weight is downward, and the pushing force is horizontal. The normal force has a smaller magnitude than the weight. Typesetting math: 100% Typesetting math: 100% Correct If you were actually going to solve this problem rather than just draw the free-body diagram, you would need to define the coordinate system. Choose the position of the piano as the origin. In this case it is simplest to let the y axis point vertically upward and the x axis point horizontally to the right, in the direction of the acceleration. Chadwick now needs to push the piano up a ramp and into a moving van. at left. The ramp is frictionless. Is Chadwick strong enough to push the piano up the ramp alone or must he get help? To solve this problem you should start by drawing a free-body diagram. Part D Determine the object of interest for this situation. ANSWER: Correct Now draw the free-body diagram of the piano in this new situation. Follow the same sequence of steps that you followed for the first situation. Again draw your diagram before you look at the choices For this situation, you should draw a free-body diagram for the ramp. Chadwick. the piano. Typesetting math: 100% below. Part E Which diagram accurately represents the free-body diagram for the piano? ANSWER: Typesetting math: 100% Typesetting math: 100% Correct In working problems like this one that involve an incline, it is most often easiest to select a coordinate system that is not vertical and horizontal. Instead, choose the x axis so that it is parallel to the incline and choose the y axis so that it is perpendicular to the incline. Problem 5.18 The figure shows two of the three forces acting on an object in equilibrium. Part A Redraw the diagram, showing all three forces. Label the third force . Draw the force vector starting at the black dot. The location and orientation of the vector will be graded. The length of the vector will not be graded. ANSWER: F  3 Typesetting math: 100% Correct Problem 5.25 An ice hockey puck glides across frictionless ice. Part A Identify all forces acting on the object. ANSWER: Typesetting math: 100% Correct Part B Draw a free-body diagram of the ice hockey puck. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: Normal force ; Gravity Normal force ; Gravity ; Kinetic friction Tension ; Weight Thrust ; Gravity n F  G n F  G fk  T  w Fthrust  F  G Typesetting math: 100% Correct Problem 5.26 Your physics textbook is sliding to the right across the table. Part A Identify all forces acting on the object. ANSWER: Typesetting math: 100% Correct Part B Draw a free-body diagram of the object. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: Weight ; Kinetic friction Thrust ; Kinetic friction Normal force ; Weight ; Kinetic friction Normal force ; Weight ; Static friction w fk  Fthrust  fk  n w fk  n w fs  Typesetting math: 100% Correct Enhanced EOC: Problem 5.35 A constant force is applied to an object, causing the object to accelerate at 13 . You may want to review ( pages 127 - 130) . For help with math skills, you may want to review: Proportions I Proportions II Part A m/s2 Typesetting math: 100% What will the acceleration be if the force is halved? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the acceleration of an object related to its mass and the force applied? Expressing the acceleration in terms of the force and mass, what happens to the acceleration if the force is halved but the mass remains the same? ANSWER: Correct Part B What will the acceleration be if the object's mass is halved? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the acceleration of an object related to its mass and the force applied? Expressing the acceleration in terms of the force and mass, what happens to the acceleration if the mass is halved but the force remains the same? ANSWER: Correct Part C a = 6.50 m s2 a = 26.0 m s2 Typesetting math: 100% What will the acceleration be if the force and the object's mass are both halved? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the acceleration of an object related to its mass and the force applied? Expressing the acceleration in terms of the force and mass, what happens to the acceleration if both the force and mass are reduced by a factor of two? ANSWER: Correct Part D What will the acceleration be if the force is halved and the object's mass is doubled? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the acceleration of an object related to its mass and the force applied? Expressing the acceleration in terms of the force and mass, what happens to the acceleration if the force is decreased by a factor of two and the mass is increased by a factor of two? Check your answer by choosing numerical values of the force and mass, and then halve the force and double the mass. ANSWER: Correct a = 13.0 m s2 a = 3.25 m s2 Typesetting math: 100% Problem 5.44 A rocket is being launched straight up. Air resistance is not negligible. Part A Which of the following is the correct motion diagram for the situation described above? Enter the letter that corresponds with the best answer. ANSWER: Correct Part B Draw a free-body diagram. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: Typesetting math: 100% Correct Score Summary: Your score on this assignment is 99.7%. You received 63.82 out of a possible total of 64 points. Typesetting math: 100%

Assignment 4 Due: 11:59pm on Wednesday, February 26, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy ± Two Forces Acting at a Point Two forces, and , act at a point. has a magnitude of 9.80 and is directed at an angle of 56.0 above the negative x axis in the second quadrant. has a magnitude of 5.20 and is directed at an angle of 54.1 below the negative x axis in the third quadrant. Part A What is the x component of the resultant force? Express your answer in newtons. Hint 1. How to approach the problem The resultant force is defined as the vector sum of all forces. Thus, its x component is the sum of the x components of the forces, and its y component is the sum of the y components of the forces. Hint 2. Find the x component of Find the x component of . Express your answer in newtons. Hint 1. Components of a vector Consider a vector that forms an angle with the positive x axis. The x and y components of are, respectively, and , where is the magnitude of the vector. Note that and if , and if . F 1 F  2 F  1 N  F  2 N  F 1 F  1 A  A Ax = Acos  Ay = Asin  A Ax < 0 Ay > 0  <  <  2 Ax < 0 Ay < 0  <  < 3 2 Hint 2. Find the direction of is directed at an angle of 56.0 above the x axis in the second quadrant. When you calculate the components of , however, the direction of the force is commonly expressed in terms of the angle that the vector representing the force forms with the positive x axis. What is the angle that forms with the positive x axis? Select an answer from the following list, where 56.0 . ANSWER: ANSWER: Hint 3. Find the x component of Find the x component of . Express your answer in newtons. Hint 1. Components of a vector Consider a vector that forms an angle with the positive x axis. The x and y components of are, respectively, and , where is the magnitude of the vector. Note that and if , F 1 F 1  F  1 F  1  =   180 −  180 +  90 +  -5.48 N F 2 F  2 A  A Ax = Acos  Ay = Asin  A Ax < 0 Ay > 0  <  <  2 Typesetting math: 100% and if . Hint 2. Find the direction of is directed at an angle of 54.1 below the x axis in the third quadrant. When you calculate the components of , however, the direction of the force is commonly expressed in terms of the angle that the vector representing the force forms with the positive x axis. What is the angle that forms with the positive x axis? Select an answer from the following list, where 54.1 . ANSWER: ANSWER: ANSWER: Correct Part B What is the y component of the resultant force? Express your answer in newtons. Ax < 0 Ay <  <  < 3 2 F 2 F 2  F 2 F  2  =   180 −   − 180 −90 −  -3.05 N -8.53 N Typesetting math: 100% Hint 1. How to approach the problem Follow the same procedure that you used in Part A to find the x component of the resultant force, though now calculate the y components of the two forces. Hint 2. Find the y component of Find the y component of . Express your answer in newtons. Hint 1. Components of a vector Consider a vector that forms an angle with the positive x axis. The x and y components of are, respectively, and , where is the magnitude of the vector. Note that and if , and if . ANSWER: Hint 3. Find the y component of Find the y component of . Express your answer in newtons. Hint 1. Components of a vector F 1 F  1 A  A Ax = Acos  Ay = Asin  A Ax < 0 Ay > 0  <  <  2 Ax < 0 Ay < 0  <  < 3 2 8.12 N F 2 F  2 Typesetting math: 100% Consider a vector that forms an angle with the positive x axis. The x and y components of are, respectively, and , where is the magnitude of the vector. Note that and if , and if . ANSWER: ANSWER: Correct Part C What is the magnitude of the resultant force? Express your answer in newtons. Hint 1. Magnitude of a vector Consider a vector , whose components are and . The magnitude of is . A  A Ax = Acos  Ay = Asin  A Ax < 0 Ay > 0  <  <  2 Ax < 0 Ay < 0  <  < 3 2 -4.21 N 3.91 N A Ax Ay A A = A + 2 x A2 y −−−−−−−  Typesetting math: 100% ANSWER: Correct Enhanced EOC: Problem 5.9 The figure shows acceleration-versus-force graphs for two objects pulled by rubber bands. You may want to review ( pages 127 - 130) . For help with math skills, you may want to review: Finding the Slope of a Line from a Graph Part A What is the mass ratio ? Express your answer using two significant figures. 9.38 N m1 m2 Typesetting math: 100% Hint 1. How to approach the problem How are the acceleration and the force on an object related to its mass? How is the slope of each line in the figure related to each object's mass? For each line, what two points are easy to measure accurately to determine the slope of line? How is the slope determined from the x and y coordinates of the two points you chose for each line? ANSWER: Correct A World-Class Sprinter World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude . Part A How much horizontal force must a sprinter of mass 54 exert on the starting blocks to produce this acceleration? Express your answer in newtons using two significant figures. Hint 1. Newton's 2nd law of motion According to Newton's 2nd law of motion, if a net external force acts on a body, the body accelerates, and the net force is equal to the mass of the body times the acceleration of the body: . ANSWER: = 0.36 m1 m2 15 m/s2 F kg Fnet m a Fnet = ma F = 810 N Typesetting math: 100% Correct Part B Which body exerts the force that propels the sprinter, the blocks or the sprinter? Hint 1. How to approach the question To start moving forward, sprinters push backward on the starting blocks with their feet. Newton's 3rd law tells you that the blocks exert a force on the sprinter of the same magnitude, but opposite in direction. ANSWER: Correct To start moving forward, sprinters push backward on the starting blocks with their feet. As a reaction, the blocks push forward on their feet with a force of the same magnitude. This external force accelerates the sprinter forward. Problem 5.12 The figure shows an acceleration-versus-force graph for a 600 object. the blocks the sprinter g Typesetting math: 100% Part A What must equal in order for the graph to be correct? Express your answer with the appropriate units. ANSWER: Correct Part B What must equal in order for the graph to be correct? Express your answer with the appropriate units. ANSWER: Correct Free-Body Diagrams Learning Goal: To gain practice drawing free-body diagrams Whenever you face a problem involving forces, always start with a free-body diagram. a1 a1 = 1.67 m s2 a2 a2 = 3.33 m s2 Typesetting math: 100% To draw a free-body diagram use the following steps: Isolate the object of interest. It is customary to represent the object of interest as a point 1. in your diagram. Identify all the forces acting on the object and their directions. Do not include forces acting on other objects in the problem. Also, do not include quantities, such as velocities and accelerations, that are not forces. 2. Draw the vectors for each force acting on your object of interest. When possible, the length of the force vectors you draw should represent the relative magnitudes of the forces acting on the object. 3. In most problems, after you have drawn the free-body diagrams, you will explicitly label your coordinate axes and directions. Always make the object of interest the origin of your coordinate system. Then you will need to divide the forces into x and y components, sum the x and y forces, and apply Newton's first or second law. In this problem you will only draw the free-body diagram. Suppose that you are asked to solve the following problem: Chadwick is pushing a piano across a level floor (see the figure). The piano can slide across the floor without friction. If Chadwick applies a horizontal force to the piano, what is the piano's acceleration? To solve this problem you should start by drawing a free-body diagram. Part A Determine the object of interest for the situation described in the problem introduction. Hint 1. How to approach the problem You should first think about the question you are trying to answer: What is the acceleration of the piano? The object of interest in this situation will be the object whose acceleration you are asked to find. ANSWER: Typesetting math: 100% Correct Part B Identify the forces acting on the object of interest. From the list below, select the forces that act on the piano. Check all that apply. ANSWER: Correct Now that you have identified the forces acting on the piano, you should draw the free-body diagram. Draw the length of your vectors to represent the relative magnitudes of the forces, but you don't need to worry about the exact scale. You won't have the exact value of all of the forces until you finish solving the problem. To maximize your learning, you should draw the diagram yourself before looking at the choices in the next part. You are on your honor to do so. Part C For this situation you should draw a free-body diagram for the floor. Chadwick. the piano. acceleration of the piano gravitational force acting on the piano (piano's weight) speed of the piano gravitational force acting on Chadwick (Chadwick's weight) force of the floor on the piano (normal force) force of the piano on the floor force of Chadwick on the piano force of the piano pushing on Chadwick Typesetting math: 100% Select the choice that best matches the free-body diagram you have drawn for the piano. Hint 1. Determine the directions and relative magnitudes of the forces Which of the following statements best describes the correct directions and relative magnitudes of the forces involved? ANSWER: ANSWER: The normal force and weight are both upward and the pushing force is horizontal. The normal force and weight are both downward and the pushing force is horizontal. The normal force is upward, the weight is downward, and the pushing force is horizontal. The normal force has a greater magnitude than the weight. The normal force is upward, the weight is downward, and the pushing force is horizontal. The normal force and weight have the same magnitude. The normal force is upward, the weight is downward, and the pushing force is horizontal. The normal force has a smaller magnitude than the weight. Typesetting math: 100% Typesetting math: 100% Correct If you were actually going to solve this problem rather than just draw the free-body diagram, you would need to define the coordinate system. Choose the position of the piano as the origin. In this case it is simplest to let the y axis point vertically upward and the x axis point horizontally to the right, in the direction of the acceleration. Chadwick now needs to push the piano up a ramp and into a moving van. at left. The ramp is frictionless. Is Chadwick strong enough to push the piano up the ramp alone or must he get help? To solve this problem you should start by drawing a free-body diagram. Part D Determine the object of interest for this situation. ANSWER: Correct Now draw the free-body diagram of the piano in this new situation. Follow the same sequence of steps that you followed for the first situation. Again draw your diagram before you look at the choices For this situation, you should draw a free-body diagram for the ramp. Chadwick. the piano. Typesetting math: 100% below. Part E Which diagram accurately represents the free-body diagram for the piano? ANSWER: Typesetting math: 100% Typesetting math: 100% Correct In working problems like this one that involve an incline, it is most often easiest to select a coordinate system that is not vertical and horizontal. Instead, choose the x axis so that it is parallel to the incline and choose the y axis so that it is perpendicular to the incline. Problem 5.18 The figure shows two of the three forces acting on an object in equilibrium. Part A Redraw the diagram, showing all three forces. Label the third force . Draw the force vector starting at the black dot. The location and orientation of the vector will be graded. The length of the vector will not be graded. ANSWER: F  3 Typesetting math: 100% Correct Problem 5.25 An ice hockey puck glides across frictionless ice. Part A Identify all forces acting on the object. ANSWER: Typesetting math: 100% Correct Part B Draw a free-body diagram of the ice hockey puck. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: Normal force ; Gravity Normal force ; Gravity ; Kinetic friction Tension ; Weight Thrust ; Gravity n F  G n F  G fk  T  w Fthrust  F  G Typesetting math: 100% Correct Problem 5.26 Your physics textbook is sliding to the right across the table. Part A Identify all forces acting on the object. ANSWER: Typesetting math: 100% Correct Part B Draw a free-body diagram of the object. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: Weight ; Kinetic friction Thrust ; Kinetic friction Normal force ; Weight ; Kinetic friction Normal force ; Weight ; Static friction w fk  Fthrust  fk  n w fk  n w fs  Typesetting math: 100% Correct Enhanced EOC: Problem 5.35 A constant force is applied to an object, causing the object to accelerate at 13 . You may want to review ( pages 127 - 130) . For help with math skills, you may want to review: Proportions I Proportions II Part A m/s2 Typesetting math: 100% What will the acceleration be if the force is halved? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the acceleration of an object related to its mass and the force applied? Expressing the acceleration in terms of the force and mass, what happens to the acceleration if the force is halved but the mass remains the same? ANSWER: Correct Part B What will the acceleration be if the object's mass is halved? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the acceleration of an object related to its mass and the force applied? Expressing the acceleration in terms of the force and mass, what happens to the acceleration if the mass is halved but the force remains the same? ANSWER: Correct Part C a = 6.50 m s2 a = 26.0 m s2 Typesetting math: 100% What will the acceleration be if the force and the object's mass are both halved? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the acceleration of an object related to its mass and the force applied? Expressing the acceleration in terms of the force and mass, what happens to the acceleration if both the force and mass are reduced by a factor of two? ANSWER: Correct Part D What will the acceleration be if the force is halved and the object's mass is doubled? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the acceleration of an object related to its mass and the force applied? Expressing the acceleration in terms of the force and mass, what happens to the acceleration if the force is decreased by a factor of two and the mass is increased by a factor of two? Check your answer by choosing numerical values of the force and mass, and then halve the force and double the mass. ANSWER: Correct a = 13.0 m s2 a = 3.25 m s2 Typesetting math: 100% Problem 5.44 A rocket is being launched straight up. Air resistance is not negligible. Part A Which of the following is the correct motion diagram for the situation described above? Enter the letter that corresponds with the best answer. ANSWER: Correct Part B Draw a free-body diagram. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: Typesetting math: 100% Correct Score Summary: Your score on this assignment is 99.7%. You received 63.82 out of a possible total of 64 points. Typesetting math: 100%

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Assignment 11 Due: 11:59pm on Wednesday, April 30, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 13.2 The gravitational force of a star on orbiting planet 1 is . Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force . Part A What is the ratio ? ANSWER: Correct Conceptual Question 13.3 A 1500 satellite and a 2200 satellite follow exactly the same orbit around the earth. Part A What is the ratio of the force on the first satellite to that on the second satellite? ANSWER: Correct F1 F2 F1 F2 = 2 F1 F2 kg kg F1 F2 = 0.682 F1 F2 Part B What is the ratio of the acceleration of the first satellite to that of the second satellite? ANSWER: Correct Problem 13.2 The centers of a 15.0 lead ball and a 90.0 lead ball are separated by 9.00 . Part A What gravitational force does each exert on the other? Express your answer with the appropriate units. ANSWER: Correct Part B What is the ratio of this gravitational force to the weight of the 90.0 ball? ANSWER: a1 a2 = 1 a1 a2 kg g cm 1.11×10−8 N g 1.26×10−8 Correct Problem 13.6 The space shuttle orbits 310 above the surface of the earth. Part A What is the gravitational force on a 7.5 sphere inside the space shuttle? Express your answer with the appropriate units. ANSWER: Correct ± A Satellite in Orbit A satellite used in a cellular telephone network has a mass of 2310 and is in a circular orbit at a height of 650 above the surface of the earth. Part A What is the gravitational force on the satellite? Take the gravitational constant to be = 6.67×10−11 , the mass of the earth to be = 5.97×1024 , and the radius of the Earth to be = 6.38×106 . Express your answer in newtons. Hint 1. How to approach the problem Use the equation for the law of gravitation to calculate the force on the satellite. Be careful about the units when performing the calculations. km kg Fe on s = 67.0 N kg km Fgrav G N m2/kg2 me kg re m Hint 2. Law of gravitation According to Newton’s law of gravitation, , where is the gravitational constant, and are the masses of the two objects, and is the distance between the centers of mass of the two objects. Hint 3. Calculate the distance between the centers of mass What is the distance from the center of mass of the satellite to the center of mass of the earth? Express your answer in meters. ANSWER: ANSWER: Correct Part B What fraction is this of the satellite’s weight at the surface of the earth? Take the free-fall acceleration at the surface of the earth to be = 9.80 . Hint 1. How to approach the problem All you need to do is to take the ratio of the gravitational force on the satellite to the weight of the satellite at ground level. There are two ways to do this, depending on how you define the force of gravity at the surface of the earth. ANSWER: F = Gm1m2/r2 G m1 m2 r r = 7.03×10r 6 m = 1.86×10Fgrav 4 N g m/s2 0.824 Correct Although it is easy to find the weight of the satellite using the constant acceleration due to gravity, it is instructional to consider the weight calculated using the law of gravitation: . Dividing the gravitational force on the satellite by , we find that the ratio of the forces due to the earth’s gravity is simply the square of the ratio of the earth’s radius to the sum of the earth’s radius and the height of the orbit of the satellite above the earth, . This will also be the fraction of the weight of, say, an astronaut in an orbit at the same altitude. Notice that an astronaut’s weight is never zero. When people speak of “weightlessness” in space, what they really mean is “free fall.” Problem 13.8 Part A What is the free-fall acceleration at the surface of the moon? Express your answer with the appropriate units. ANSWER: Correct Part B What is the free-fall acceleration at the surface of the Jupiter? Express your answer with the appropriate units. ANSWER: Correct w = G m/ me r2e Fgrav = Gmem/(re + h)2 w [re/(re + h)]2 gmoon = 1.62 m s2 gJupiter = 25.9 m s2 Enhanced EOC: Problem 13.14 A rocket is launched straight up from the earth’s surface at a speed of 1.90×104 . You may want to review ( pages 362 – 365) . For help with math skills, you may want to review: Mathematical Expressions Involving Squares Part A What is its speed when it is very far away from the earth? Express your answer with the appropriate units. Hint 1. How to approach the problem What is conserved in this problem? What is the rocket’s initial kinetic energy in terms of its unknown mass, ? What is the rocket’s initial gravitational potential energy in terms of its unknown mass, ? When the rocket is very far away from the Earth, what is its gravitational potential energy? Using conservation of energy, what is the rocket’s kinetic energy when it is very far away from the Earth? Therefore, what is the rocket’s velocity when it is very far away from the Earth? ANSWER: Correct Problem 13.13 Part A m/s m m 1.54×104 ms What is the escape speed from Venus? Express your answer with the appropriate units. ANSWER: Correct Problem 13.17 The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 4.2 earth years. Part A What is the asteroid’s orbital radius? Express your answer with the appropriate units. ANSWER: Correct Part B What is the asteroid’s orbital speed? Express your answer with the appropriate units. ANSWER: vescape = 10.4 km s = 3.89×1011 R m = 1.85×104 v ms Correct Problem 13.32 Part A At what height above the earth is the acceleration due to gravity 15.0% of its value at the surface? Express your answer with the appropriate units. ANSWER: Correct Part B What is the speed of a satellite orbiting at that height? Express your answer with the appropriate units. ANSWER: Correct Problem 13.36 Two meteoroids are heading for earth. Their speeds as they cross the moon’s orbit are 2 . 1.01×107 m 4920 ms km/s Part A The first meteoroid is heading straight for earth. What is its speed of impact? Express your answer with the appropriate units. ANSWER: Correct Part B The second misses the earth by 5500 . What is its speed at its closest point? Express your answer with the appropriate units. ANSWER: Incorrect; Try Again Problem 14.2 An air-track glider attached to a spring oscillates between the 11.0 mark and the 67.0 mark on the track. The glider completes 11.0 oscillations in 32.0 . Part A What is the period of the oscillations? Express your answer with the appropriate units. v1 = 11.3 km s km v2 = cm cm s ANSWER: Correct Part B What is the frequency of the oscillations? Express your answer with the appropriate units. ANSWER: Correct Part C What is the angular frequency of the oscillations? Express your answer with the appropriate units. ANSWER: Correct Part D What is the amplitude? Express your answer with the appropriate units. 2.91 s 0.344 Hz 2.16 rad s ANSWER: Correct Part E What is the maximum speed of the glider? Express your answer with the appropriate units. ANSWER: Correct Good Vibes: Introduction to Oscillations Learning Goal: To learn the basic terminology and relationships among the main characteristics of simple harmonic motion. Motion that repeats itself over and over is called periodic motion. There are many examples of periodic motion: the earth revolving around the sun, an elastic ball bouncing up and down, or a block attached to a spring oscillating back and forth. The last example differs from the first two, in that it represents a special kind of periodic motion called simple harmonic motion. The conditions that lead to simple harmonic motion are as follows: There must be a position of stable equilibrium. There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object’s displacement from its equilibrium position. Mathematically, the restoring force is given by , where is the displacement from equilibrium and is a constant that depends on the properties of the oscillating system. The resistive forces in the system must be reasonably small. In this problem, we will introduce some of the basic quantities that describe oscillations and the relationships among them. Consider a block of mass attached to a spring with force constant , as shown in the figure. The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at . If the 28.0 cm 60.5 cms F  F = −kx x k m k x = 0 block is pulled to the right a distance and then released, will be the amplitude of the resulting oscillations. Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block. Part A After the block is released from , it will ANSWER: Correct As the block begins its motion to the left, it accelerates. Although the restoring force decreases as the block approaches equilibrium, it still pulls the block to the left, so by the time the equilibrium position is reached, the block has gained some speed. It will, therefore, pass the equilibrium position and keep moving, compressing the spring. The spring will now be pushing the block to the right, and the block will slow down, temporarily coming to rest at . After is reached, the block will begin its motion to the right, pushed by the spring. The block will pass the equilibrium position and continue until it reaches , completing one cycle of motion. The motion will then repeat; if, as we’ve assumed, there is no friction, the motion will repeat indefinitely. The time it takes the block to complete one cycle is called the period. Usually, the period is denoted and is measured in seconds. The frequency, denoted , is the number of cycles that are completed per unit of time: . In SI units, is measured in inverse seconds, or hertz ( ). A A x = A remain at rest. move to the left until it reaches equilibrium and stop there. move to the left until it reaches and stop there. move to the left until it reaches and then begin to move to the right. x = −A x = −A x = −A x = −A x = A T f f = 1/T f Hz Part B If the period is doubled, the frequency is ANSWER: Correct Part C An oscillating object takes 0.10 to complete one cycle; that is, its period is 0.10 . What is its frequency ? Express your answer in hertz. ANSWER: Correct unchanged. doubled. halved. s s f f = 10 Hz Part D If the frequency is 40 , what is the period ? Express your answer in seconds. ANSWER: Correct The following questions refer to the figure that graphically depicts the oscillations of the block on the spring. Note that the vertical axis represents the x coordinate of the oscillating object, and the horizontal axis represents time. Part E Which points on the x axis are located a distance from the equilibrium position? ANSWER: Hz T T = 0.025 s A Correct Part F Suppose that the period is . Which of the following points on the t axis are separated by the time interval ? ANSWER: Correct Now assume for the remaining Parts G – J, that the x coordinate of point R is 0.12 and the t coordinate of point K is 0.0050 . Part G What is the period ? Express your answer in seconds. Hint 1. How to approach the problem In moving from the point to the point K, what fraction of a full wavelength is covered? Call that fraction . Then you can set . Dividing by the fraction will give the R only Q only both R and Q T T K and L K and M K and P L and N M and P m s T t = 0 a aT = 0.005 s a period . ANSWER: Correct Part H How much time does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement? Express your answer in seconds. ANSWER: Correct Part I What distance does the object cover during one period of oscillation? Express your answer in meters. ANSWER: Correct Part J What distance does the object cover between the moments labeled K and N on the graph? T T = 0.02 s t t = 0.01 s d d = 0.48 m d Express your answer in meters. ANSWER: Correct Problem 14.4 Part A What is the amplitude of the oscillation shown in the figure? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct d = 0.36 m A = 20.0 cm Part B What is the frequency of this oscillation? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the phase constant? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.10 An air-track glider attached to a spring oscillates with a period of 1.50 . At the glider is 4.60 left of the equilibrium position and moving to the right at 33.4 . Part A What is the phase constant? Express your answer to three significant figures and include the appropriate units. ANSWER: f = 0.25 Hz 0 = -60 % s t = 0 s cm cm/s 0 = -2.09 rad Correct Part B What is the phase at ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part C What is the phase at ? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part D What is the phase at ? Express your answer to three significant figures and include the appropriate units. ANSWER: t = 0.5 s  = 0 rad t = 1.0 s  = 2.09 rad t = 1.5 s  = 4.19 rad Correct Problem 14.12 A 140 air-track glider is attached to a spring. The glider is pushed in 12.2 and released. A student with a stopwatch finds that 14.0 oscillations take 19.0 . Part A What is the spring constant? Express your answer with the appropriate units. ANSWER: Correct Problem 14.14 The position of a 50 g oscillating mass is given by , where is in s. If necessary, round your answers to three significant figures. Determine: Part A The amplitude. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct g cm s 3.00 Nm x(t) = (2.0 cm)cos(10t − /4) t 2.00 cm Part B The period. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part C The spring constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part D The phase constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct 0.628 s 5.00 Nm -0.785 rad Part E The initial coordinate of the mass. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part F The initial velocity. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part G The maximum speed. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct 1.41 cm 14.1 cms 20.0 cms Part H The total energy. Express your answer to one decimal place and include the appropriate units. ANSWER: Correct Part I The velocity at . Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 14.17 A spring with spring constant 16 hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 4.0 and released. The ball makes 35 oscillations in 18 seconds. You may want to review ( pages 389 – 391) . For help with math skills, you may want to review: Differentiation of Trigonometric Functions Part A What is its the mass of the ball? 1.0 mJ t = 0.40 s 1.46 cms N/m cm s Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the period of oscillation? What is the angular frequency of the oscillations? How is the angular frequency related to the mass and spring constant? What is the mass? ANSWER: Correct Part B What is its maximum speed? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the amplitude of the oscillations? How is the maximum speed related to the amplitude of the oscillations and the angular frequency? ANSWER: Correct Changing the Period of a Pendulum m = 110 g vmax = 49 cms A simple pendulum consisting of a bob of mass attached to a string of length swings with a period . Part A If the bob’s mass is doubled, approximately what will the pendulum’s new period be? Hint 1. Period of a simple pendulum The period of a simple pendulum of length is given by , where is the acceleration due to gravity. ANSWER: Correct Part B If the pendulum is brought on the moon where the gravitational acceleration is about , approximately what will its period now be? Hint 1. How to approach the problem Recall the formula of the period of a simple pendulum. Since the gravitational acceleration appears in the denominator, the period must increase when the gravitational acceleration decreases. m L T T L T = 2 Lg −−  g T/2 T ‘2T 2T g/6 ANSWER: Correct Part C If the pendulum is taken into the orbiting space station what will happen to the bob? Hint 1. How to approach the problem Recall that the oscillations of a simple pendulum occur when a pendulum bob is raised above its equilibrium position and let go, causing the pendulum bob to fall. The gravitational force acts to bring the bob back to its equilibrium position. In the space station, the earth’s gravity acts on both the station and everything inside it, giving them the same acceleration. These objects are said to be in free fall. ANSWER: Correct In the space station, where all objects undergo the same acceleration due to the earth’s gravity, the tension in the string is zero and the bob does not fall relative to the point to which the string is attached. T/6 T/’6 ‘6T 6T It will continue to oscillate in a vertical plane with the same period. It will no longer oscillate because there is no gravity in space. It will no longer oscillate because both the pendulum and the point to which it is attached are in free fall. It will oscillate much faster with a period that approaches zero. Problem 14.20 A 175 ball is tied to a string. It is pulled to an angle of 8.0 and released to swing as a pendulum. A student with a stopwatch finds that 15 oscillations take 13 . Part A How long is the string? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.22 Part A What is the length of a pendulum whose period on the moon matches the period of a 2.1- -long pendulum on the earth? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.42 An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk ( = 0.17 ) driven back and forth in SHM at by an electromagnetic coil. g % s L = 19 cm m lmoon = 0.35 m m g 1.0 MHz Part A The maximum restoring force that can be applied to the disk without breaking it is 4.4×104 . What is the maximum oscillation amplitude that won’t rupture the disk? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the disk’s maximum speed at this amplitude? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 94.2%. You received 135.71 out of a possible total of 144 points. N amax = 6.6 μm vmax = 41 ms

Assignment 11 Due: 11:59pm on Wednesday, April 30, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 13.2 The gravitational force of a star on orbiting planet 1 is . Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force . Part A What is the ratio ? ANSWER: Correct Conceptual Question 13.3 A 1500 satellite and a 2200 satellite follow exactly the same orbit around the earth. Part A What is the ratio of the force on the first satellite to that on the second satellite? ANSWER: Correct F1 F2 F1 F2 = 2 F1 F2 kg kg F1 F2 = 0.682 F1 F2 Part B What is the ratio of the acceleration of the first satellite to that of the second satellite? ANSWER: Correct Problem 13.2 The centers of a 15.0 lead ball and a 90.0 lead ball are separated by 9.00 . Part A What gravitational force does each exert on the other? Express your answer with the appropriate units. ANSWER: Correct Part B What is the ratio of this gravitational force to the weight of the 90.0 ball? ANSWER: a1 a2 = 1 a1 a2 kg g cm 1.11×10−8 N g 1.26×10−8 Correct Problem 13.6 The space shuttle orbits 310 above the surface of the earth. Part A What is the gravitational force on a 7.5 sphere inside the space shuttle? Express your answer with the appropriate units. ANSWER: Correct ± A Satellite in Orbit A satellite used in a cellular telephone network has a mass of 2310 and is in a circular orbit at a height of 650 above the surface of the earth. Part A What is the gravitational force on the satellite? Take the gravitational constant to be = 6.67×10−11 , the mass of the earth to be = 5.97×1024 , and the radius of the Earth to be = 6.38×106 . Express your answer in newtons. Hint 1. How to approach the problem Use the equation for the law of gravitation to calculate the force on the satellite. Be careful about the units when performing the calculations. km kg Fe on s = 67.0 N kg km Fgrav G N m2/kg2 me kg re m Hint 2. Law of gravitation According to Newton’s law of gravitation, , where is the gravitational constant, and are the masses of the two objects, and is the distance between the centers of mass of the two objects. Hint 3. Calculate the distance between the centers of mass What is the distance from the center of mass of the satellite to the center of mass of the earth? Express your answer in meters. ANSWER: ANSWER: Correct Part B What fraction is this of the satellite’s weight at the surface of the earth? Take the free-fall acceleration at the surface of the earth to be = 9.80 . Hint 1. How to approach the problem All you need to do is to take the ratio of the gravitational force on the satellite to the weight of the satellite at ground level. There are two ways to do this, depending on how you define the force of gravity at the surface of the earth. ANSWER: F = Gm1m2/r2 G m1 m2 r r = 7.03×10r 6 m = 1.86×10Fgrav 4 N g m/s2 0.824 Correct Although it is easy to find the weight of the satellite using the constant acceleration due to gravity, it is instructional to consider the weight calculated using the law of gravitation: . Dividing the gravitational force on the satellite by , we find that the ratio of the forces due to the earth’s gravity is simply the square of the ratio of the earth’s radius to the sum of the earth’s radius and the height of the orbit of the satellite above the earth, . This will also be the fraction of the weight of, say, an astronaut in an orbit at the same altitude. Notice that an astronaut’s weight is never zero. When people speak of “weightlessness” in space, what they really mean is “free fall.” Problem 13.8 Part A What is the free-fall acceleration at the surface of the moon? Express your answer with the appropriate units. ANSWER: Correct Part B What is the free-fall acceleration at the surface of the Jupiter? Express your answer with the appropriate units. ANSWER: Correct w = G m/ me r2e Fgrav = Gmem/(re + h)2 w [re/(re + h)]2 gmoon = 1.62 m s2 gJupiter = 25.9 m s2 Enhanced EOC: Problem 13.14 A rocket is launched straight up from the earth’s surface at a speed of 1.90×104 . You may want to review ( pages 362 – 365) . For help with math skills, you may want to review: Mathematical Expressions Involving Squares Part A What is its speed when it is very far away from the earth? Express your answer with the appropriate units. Hint 1. How to approach the problem What is conserved in this problem? What is the rocket’s initial kinetic energy in terms of its unknown mass, ? What is the rocket’s initial gravitational potential energy in terms of its unknown mass, ? When the rocket is very far away from the Earth, what is its gravitational potential energy? Using conservation of energy, what is the rocket’s kinetic energy when it is very far away from the Earth? Therefore, what is the rocket’s velocity when it is very far away from the Earth? ANSWER: Correct Problem 13.13 Part A m/s m m 1.54×104 ms What is the escape speed from Venus? Express your answer with the appropriate units. ANSWER: Correct Problem 13.17 The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 4.2 earth years. Part A What is the asteroid’s orbital radius? Express your answer with the appropriate units. ANSWER: Correct Part B What is the asteroid’s orbital speed? Express your answer with the appropriate units. ANSWER: vescape = 10.4 km s = 3.89×1011 R m = 1.85×104 v ms Correct Problem 13.32 Part A At what height above the earth is the acceleration due to gravity 15.0% of its value at the surface? Express your answer with the appropriate units. ANSWER: Correct Part B What is the speed of a satellite orbiting at that height? Express your answer with the appropriate units. ANSWER: Correct Problem 13.36 Two meteoroids are heading for earth. Their speeds as they cross the moon’s orbit are 2 . 1.01×107 m 4920 ms km/s Part A The first meteoroid is heading straight for earth. What is its speed of impact? Express your answer with the appropriate units. ANSWER: Correct Part B The second misses the earth by 5500 . What is its speed at its closest point? Express your answer with the appropriate units. ANSWER: Incorrect; Try Again Problem 14.2 An air-track glider attached to a spring oscillates between the 11.0 mark and the 67.0 mark on the track. The glider completes 11.0 oscillations in 32.0 . Part A What is the period of the oscillations? Express your answer with the appropriate units. v1 = 11.3 km s km v2 = cm cm s ANSWER: Correct Part B What is the frequency of the oscillations? Express your answer with the appropriate units. ANSWER: Correct Part C What is the angular frequency of the oscillations? Express your answer with the appropriate units. ANSWER: Correct Part D What is the amplitude? Express your answer with the appropriate units. 2.91 s 0.344 Hz 2.16 rad s ANSWER: Correct Part E What is the maximum speed of the glider? Express your answer with the appropriate units. ANSWER: Correct Good Vibes: Introduction to Oscillations Learning Goal: To learn the basic terminology and relationships among the main characteristics of simple harmonic motion. Motion that repeats itself over and over is called periodic motion. There are many examples of periodic motion: the earth revolving around the sun, an elastic ball bouncing up and down, or a block attached to a spring oscillating back and forth. The last example differs from the first two, in that it represents a special kind of periodic motion called simple harmonic motion. The conditions that lead to simple harmonic motion are as follows: There must be a position of stable equilibrium. There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object’s displacement from its equilibrium position. Mathematically, the restoring force is given by , where is the displacement from equilibrium and is a constant that depends on the properties of the oscillating system. The resistive forces in the system must be reasonably small. In this problem, we will introduce some of the basic quantities that describe oscillations and the relationships among them. Consider a block of mass attached to a spring with force constant , as shown in the figure. The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at . If the 28.0 cm 60.5 cms F  F = −kx x k m k x = 0 block is pulled to the right a distance and then released, will be the amplitude of the resulting oscillations. Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block. Part A After the block is released from , it will ANSWER: Correct As the block begins its motion to the left, it accelerates. Although the restoring force decreases as the block approaches equilibrium, it still pulls the block to the left, so by the time the equilibrium position is reached, the block has gained some speed. It will, therefore, pass the equilibrium position and keep moving, compressing the spring. The spring will now be pushing the block to the right, and the block will slow down, temporarily coming to rest at . After is reached, the block will begin its motion to the right, pushed by the spring. The block will pass the equilibrium position and continue until it reaches , completing one cycle of motion. The motion will then repeat; if, as we’ve assumed, there is no friction, the motion will repeat indefinitely. The time it takes the block to complete one cycle is called the period. Usually, the period is denoted and is measured in seconds. The frequency, denoted , is the number of cycles that are completed per unit of time: . In SI units, is measured in inverse seconds, or hertz ( ). A A x = A remain at rest. move to the left until it reaches equilibrium and stop there. move to the left until it reaches and stop there. move to the left until it reaches and then begin to move to the right. x = −A x = −A x = −A x = −A x = A T f f = 1/T f Hz Part B If the period is doubled, the frequency is ANSWER: Correct Part C An oscillating object takes 0.10 to complete one cycle; that is, its period is 0.10 . What is its frequency ? Express your answer in hertz. ANSWER: Correct unchanged. doubled. halved. s s f f = 10 Hz Part D If the frequency is 40 , what is the period ? Express your answer in seconds. ANSWER: Correct The following questions refer to the figure that graphically depicts the oscillations of the block on the spring. Note that the vertical axis represents the x coordinate of the oscillating object, and the horizontal axis represents time. Part E Which points on the x axis are located a distance from the equilibrium position? ANSWER: Hz T T = 0.025 s A Correct Part F Suppose that the period is . Which of the following points on the t axis are separated by the time interval ? ANSWER: Correct Now assume for the remaining Parts G – J, that the x coordinate of point R is 0.12 and the t coordinate of point K is 0.0050 . Part G What is the period ? Express your answer in seconds. Hint 1. How to approach the problem In moving from the point to the point K, what fraction of a full wavelength is covered? Call that fraction . Then you can set . Dividing by the fraction will give the R only Q only both R and Q T T K and L K and M K and P L and N M and P m s T t = 0 a aT = 0.005 s a period . ANSWER: Correct Part H How much time does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement? Express your answer in seconds. ANSWER: Correct Part I What distance does the object cover during one period of oscillation? Express your answer in meters. ANSWER: Correct Part J What distance does the object cover between the moments labeled K and N on the graph? T T = 0.02 s t t = 0.01 s d d = 0.48 m d Express your answer in meters. ANSWER: Correct Problem 14.4 Part A What is the amplitude of the oscillation shown in the figure? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct d = 0.36 m A = 20.0 cm Part B What is the frequency of this oscillation? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the phase constant? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.10 An air-track glider attached to a spring oscillates with a period of 1.50 . At the glider is 4.60 left of the equilibrium position and moving to the right at 33.4 . Part A What is the phase constant? Express your answer to three significant figures and include the appropriate units. ANSWER: f = 0.25 Hz 0 = -60 % s t = 0 s cm cm/s 0 = -2.09 rad Correct Part B What is the phase at ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part C What is the phase at ? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part D What is the phase at ? Express your answer to three significant figures and include the appropriate units. ANSWER: t = 0.5 s  = 0 rad t = 1.0 s  = 2.09 rad t = 1.5 s  = 4.19 rad Correct Problem 14.12 A 140 air-track glider is attached to a spring. The glider is pushed in 12.2 and released. A student with a stopwatch finds that 14.0 oscillations take 19.0 . Part A What is the spring constant? Express your answer with the appropriate units. ANSWER: Correct Problem 14.14 The position of a 50 g oscillating mass is given by , where is in s. If necessary, round your answers to three significant figures. Determine: Part A The amplitude. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct g cm s 3.00 Nm x(t) = (2.0 cm)cos(10t − /4) t 2.00 cm Part B The period. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part C The spring constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part D The phase constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct 0.628 s 5.00 Nm -0.785 rad Part E The initial coordinate of the mass. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part F The initial velocity. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part G The maximum speed. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct 1.41 cm 14.1 cms 20.0 cms Part H The total energy. Express your answer to one decimal place and include the appropriate units. ANSWER: Correct Part I The velocity at . Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 14.17 A spring with spring constant 16 hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 4.0 and released. The ball makes 35 oscillations in 18 seconds. You may want to review ( pages 389 – 391) . For help with math skills, you may want to review: Differentiation of Trigonometric Functions Part A What is its the mass of the ball? 1.0 mJ t = 0.40 s 1.46 cms N/m cm s Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the period of oscillation? What is the angular frequency of the oscillations? How is the angular frequency related to the mass and spring constant? What is the mass? ANSWER: Correct Part B What is its maximum speed? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the amplitude of the oscillations? How is the maximum speed related to the amplitude of the oscillations and the angular frequency? ANSWER: Correct Changing the Period of a Pendulum m = 110 g vmax = 49 cms A simple pendulum consisting of a bob of mass attached to a string of length swings with a period . Part A If the bob’s mass is doubled, approximately what will the pendulum’s new period be? Hint 1. Period of a simple pendulum The period of a simple pendulum of length is given by , where is the acceleration due to gravity. ANSWER: Correct Part B If the pendulum is brought on the moon where the gravitational acceleration is about , approximately what will its period now be? Hint 1. How to approach the problem Recall the formula of the period of a simple pendulum. Since the gravitational acceleration appears in the denominator, the period must increase when the gravitational acceleration decreases. m L T T L T = 2 Lg −−  g T/2 T ‘2T 2T g/6 ANSWER: Correct Part C If the pendulum is taken into the orbiting space station what will happen to the bob? Hint 1. How to approach the problem Recall that the oscillations of a simple pendulum occur when a pendulum bob is raised above its equilibrium position and let go, causing the pendulum bob to fall. The gravitational force acts to bring the bob back to its equilibrium position. In the space station, the earth’s gravity acts on both the station and everything inside it, giving them the same acceleration. These objects are said to be in free fall. ANSWER: Correct In the space station, where all objects undergo the same acceleration due to the earth’s gravity, the tension in the string is zero and the bob does not fall relative to the point to which the string is attached. T/6 T/’6 ‘6T 6T It will continue to oscillate in a vertical plane with the same period. It will no longer oscillate because there is no gravity in space. It will no longer oscillate because both the pendulum and the point to which it is attached are in free fall. It will oscillate much faster with a period that approaches zero. Problem 14.20 A 175 ball is tied to a string. It is pulled to an angle of 8.0 and released to swing as a pendulum. A student with a stopwatch finds that 15 oscillations take 13 . Part A How long is the string? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.22 Part A What is the length of a pendulum whose period on the moon matches the period of a 2.1- -long pendulum on the earth? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.42 An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk ( = 0.17 ) driven back and forth in SHM at by an electromagnetic coil. g % s L = 19 cm m lmoon = 0.35 m m g 1.0 MHz Part A The maximum restoring force that can be applied to the disk without breaking it is 4.4×104 . What is the maximum oscillation amplitude that won’t rupture the disk? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the disk’s maximum speed at this amplitude? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 94.2%. You received 135.71 out of a possible total of 144 points. N amax = 6.6 μm vmax = 41 ms

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