Describe the Maxwell model with the aid of sketches. What are its strengths and limitations?

Describe the Maxwell model with the aid of sketches. What are its strengths and limitations?

Maxwell Model             In the Maxwell model, the material is … Read More...
PHY-102: Energy and Circular Motion Exercises Complete the following exercises. 1. A rifle with a longer barrel can fire bullets with a larger velocity than a rifle with a shorter barrel. a. Explain this using the impulse-momentum theorem. b. Explain this using the work-energy theorem 2. Use physics terms to explain the benefits of crumple zones in modern cars. 3. When a gun is fired at the shooting range, the gun recoils (moves backward). Explain this using the law of conservation of momentum. 4. Rank the following in terms of increasing inertia: A. A 10,000 kg train car at rest B. A 100 kg person running at 5 m/s C. A 1200 kg car going 15 m/s D. A 15 kg meteor going at a speed of 1000 m/s 5. Rank the following in terms of increasing momentum: A. A 10,000 kg train car at rest B. A 100 kg person running at 5 m/s C. A 1200 kg car going 15 m/s D. A 15 kg meteor going at a speed of 1000 m/s 6. Rank the following in terms of increasing kinetic energy: A. A 1200 kg car going 15 m/s B. A 10,000 kg train car at rest C. A 15 kg meteor going at a speed of 1000 m/s D. A 100 kg person running at 5 m/s 7. Ben (55 kg) is standing on very slippery ice when Junior (25 kg) bumps into him. Junior was moving at a speed of 8 m/s before the collision and Ben and Junior embrace after the collision. Find the speed of Ben and Junior as they move across the ice after the collision. Give the answer in m/s. Describe the work you did to get the answer. 8. Identical marbles are released from the same height on each of the following four frictionless ramps. Compare the speed of the marbles at the end of each ramp. Explain your reasoning. 9. A force of only 150 N can lift a 600 N sack of flour to a height of 0.50 m when using a lever as shown in the diagram below. a. Find the work done on the sack of flour (in J). b. Find the distance you must push with the 150 N force on the left side (in m). c. Briefly explain the benefit of using a lever to lift a heavy object. 10. Rank the following in terms of increasing power. A. Doing 100 J of work in 10 seconds. B. Doing 100 J of work in 5 seconds. C. Doing 200 J of work in 5 seconds. D. Doing 400 J of work in 30 seconds. 11. A student lifts a 25 kg mass a vertical distance of 1.6 m in a time of 2.0 seconds. a. Find the force needed to lift the mass (in N). b. Find the work done by the student (in J). c. Find the power exerted by the student (in W). 12. A satellite is put into an orbit at a distance from the center of the Earth equal to twice the distance from the center of the Earth to the surface. If the satellite had a weight at the surface of 4000 N, what is the force of gravity (weight) of the satellite when it is in its orbit? Give your answer in newtons, N. 13. Consider a satellite in a circular orbit around the Earth. a. Why is it important to give a satellite a horizontal speed when placing it in orbit? b. What will happen if the horizontal speed is too small? c. What will happen if the horizontal speed is too large? 14. If you drop an object from a distance of 1 meter above the ground, where would it fall to the ground in the shortest time: Atop Mt. Everest or in New York? 15. Why do the astronauts aboard the space station appear to be weightless? 16. Why do the passengers on a high-flying airplane not appear weightless, similar to the astronauts on the space station? 17. A ranger needs to capture a monkey hanging on a tree branch. The ranger aims his dart gun directly at the monkey and fires the tranquilizer dart. However, the monkey lets go of the branch at exactly the same time as the ranger fires the dart. Will the monkey get hit or will it avoid the dart? The remaining questions are multiple-choice questions: 18. Compared to its weight on Earth, a 5 kg object on the moon will weigh A. the same amount. B. less. C. more. 19. Compared to its mass on Earth, a 5 kg object on the moon will have A. the same mass. B. less mass. C. more mass. 20. The reason padded dashboards are used in cars is that they A. look nice and feel good. B. decrease the impulse in a collision. C. increase the force of impact in a collision. D. decrease the momentum of a collision. E. increase the time of impact in a collision. 21. Suppose you are standing on a frozen lake where there is no friction between your feet and the ice. What can you do to get off the lake? A. Bend over touching the ice in front of you and then bring you feet to your hands. B. Walk very slowly on tiptoe. C. Get on your hands and knees and crawl off the ice. D. Throw something in the direction opposite to the way you want to go. 22. A car travels in a circle with constant speed. Which of the following is true? A. The net force on the car is zero because the car is not accelerating. B. The net force on the car is directed forward, in the direction of travel. C. The net force on the car is directed inward, toward the center of the curve. D. The net force on the car is directed outward, away from the center of the curve. 23. A job is done slowly, and an identical job is done quickly. Which of the following is true? a. They require the same amount of force, but different amounts of work. b. They require the same amount of work, but different amounts of power. c. They require the same amounts of power, but different amounts of work. d. They require the same amounts of work, but different amounts of energy. 24. How many joules of work are done on a box when a force of 60 N pushes it 5 m in 3 seconds? a. 300 J b. 12 J c. 100 J d. 36 J e. 4 J 25. A 1 kg cart moving with a speed of 3 m/s collides with a 2 kg cart at rest. If the carts stick together after the collision, with what speed will they move after the collision? a. 3 m/s b. 1.5 m/s c. 1 m/s d. 2 m/s

PHY-102: Energy and Circular Motion Exercises Complete the following exercises. 1. A rifle with a longer barrel can fire bullets with a larger velocity than a rifle with a shorter barrel. a. Explain this using the impulse-momentum theorem. b. Explain this using the work-energy theorem 2. Use physics terms to explain the benefits of crumple zones in modern cars. 3. When a gun is fired at the shooting range, the gun recoils (moves backward). Explain this using the law of conservation of momentum. 4. Rank the following in terms of increasing inertia: A. A 10,000 kg train car at rest B. A 100 kg person running at 5 m/s C. A 1200 kg car going 15 m/s D. A 15 kg meteor going at a speed of 1000 m/s 5. Rank the following in terms of increasing momentum: A. A 10,000 kg train car at rest B. A 100 kg person running at 5 m/s C. A 1200 kg car going 15 m/s D. A 15 kg meteor going at a speed of 1000 m/s 6. Rank the following in terms of increasing kinetic energy: A. A 1200 kg car going 15 m/s B. A 10,000 kg train car at rest C. A 15 kg meteor going at a speed of 1000 m/s D. A 100 kg person running at 5 m/s 7. Ben (55 kg) is standing on very slippery ice when Junior (25 kg) bumps into him. Junior was moving at a speed of 8 m/s before the collision and Ben and Junior embrace after the collision. Find the speed of Ben and Junior as they move across the ice after the collision. Give the answer in m/s. Describe the work you did to get the answer. 8. Identical marbles are released from the same height on each of the following four frictionless ramps. Compare the speed of the marbles at the end of each ramp. Explain your reasoning. 9. A force of only 150 N can lift a 600 N sack of flour to a height of 0.50 m when using a lever as shown in the diagram below. a. Find the work done on the sack of flour (in J). b. Find the distance you must push with the 150 N force on the left side (in m). c. Briefly explain the benefit of using a lever to lift a heavy object. 10. Rank the following in terms of increasing power. A. Doing 100 J of work in 10 seconds. B. Doing 100 J of work in 5 seconds. C. Doing 200 J of work in 5 seconds. D. Doing 400 J of work in 30 seconds. 11. A student lifts a 25 kg mass a vertical distance of 1.6 m in a time of 2.0 seconds. a. Find the force needed to lift the mass (in N). b. Find the work done by the student (in J). c. Find the power exerted by the student (in W). 12. A satellite is put into an orbit at a distance from the center of the Earth equal to twice the distance from the center of the Earth to the surface. If the satellite had a weight at the surface of 4000 N, what is the force of gravity (weight) of the satellite when it is in its orbit? Give your answer in newtons, N. 13. Consider a satellite in a circular orbit around the Earth. a. Why is it important to give a satellite a horizontal speed when placing it in orbit? b. What will happen if the horizontal speed is too small? c. What will happen if the horizontal speed is too large? 14. If you drop an object from a distance of 1 meter above the ground, where would it fall to the ground in the shortest time: Atop Mt. Everest or in New York? 15. Why do the astronauts aboard the space station appear to be weightless? 16. Why do the passengers on a high-flying airplane not appear weightless, similar to the astronauts on the space station? 17. A ranger needs to capture a monkey hanging on a tree branch. The ranger aims his dart gun directly at the monkey and fires the tranquilizer dart. However, the monkey lets go of the branch at exactly the same time as the ranger fires the dart. Will the monkey get hit or will it avoid the dart? The remaining questions are multiple-choice questions: 18. Compared to its weight on Earth, a 5 kg object on the moon will weigh A. the same amount. B. less. C. more. 19. Compared to its mass on Earth, a 5 kg object on the moon will have A. the same mass. B. less mass. C. more mass. 20. The reason padded dashboards are used in cars is that they A. look nice and feel good. B. decrease the impulse in a collision. C. increase the force of impact in a collision. D. decrease the momentum of a collision. E. increase the time of impact in a collision. 21. Suppose you are standing on a frozen lake where there is no friction between your feet and the ice. What can you do to get off the lake? A. Bend over touching the ice in front of you and then bring you feet to your hands. B. Walk very slowly on tiptoe. C. Get on your hands and knees and crawl off the ice. D. Throw something in the direction opposite to the way you want to go. 22. A car travels in a circle with constant speed. Which of the following is true? A. The net force on the car is zero because the car is not accelerating. B. The net force on the car is directed forward, in the direction of travel. C. The net force on the car is directed inward, toward the center of the curve. D. The net force on the car is directed outward, away from the center of the curve. 23. A job is done slowly, and an identical job is done quickly. Which of the following is true? a. They require the same amount of force, but different amounts of work. b. They require the same amount of work, but different amounts of power. c. They require the same amounts of power, but different amounts of work. d. They require the same amounts of work, but different amounts of energy. 24. How many joules of work are done on a box when a force of 60 N pushes it 5 m in 3 seconds? a. 300 J b. 12 J c. 100 J d. 36 J e. 4 J 25. A 1 kg cart moving with a speed of 3 m/s collides with a 2 kg cart at rest. If the carts stick together after the collision, with what speed will they move after the collision? a. 3 m/s b. 1.5 m/s c. 1 m/s d. 2 m/s

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The graph shown below depicts the relationship between concentration and time for the following chemical reaction: The slope of this line is equal to __________. A) k B) -1/k C) ln[A]o D) -k E) 1/k

The graph shown below depicts the relationship between concentration and time for the following chemical reaction: The slope of this line is equal to __________. A) k B) -1/k C) ln[A]o D) -k E) 1/k

D) -k
Fund A accumulates at a rate of 9 % convertible monthly. Fund B accumulates with force of interest of dt=t/25 for all t. At time t = 0, $ 1 is deposited in each fund. The positive time, in years, that the two funds are equal is denoted by T. Calculate T.

Fund A accumulates at a rate of 9 % convertible monthly. Fund B accumulates with force of interest of dt=t/25 for all t. At time t = 0, $ 1 is deposited in each fund. The positive time, in years, that the two funds are equal is denoted by T. Calculate T.

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Assignment 9 Due: 11:59pm on Friday, April 11, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Problem 11.2 Part A Evaluate the dot product if and . Express your answer using two significant figures. ANSWER: Correct Part B Evaluate the dot product if and . Express your answer using two significant figures. ANSWER: Correct Problem 11.4  A B = 5 − 6 A i ^ j ^ = −9 − 5 B i ^ j ^ A  B  = -15  A B = −5 + 9 A i ^ j ^ = 5 + 6 B i ^ j ^ A  B  = 29 Part A What is the angle between vectors and if and ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part B What is the angle between vectors and if and ? Express your answer as an integer and include the appropriate units. ANSWER: Correct ± All Work and No Play Learning Goal: To be able to calculate work done by a constant force directed at different angles relative to displacement If an object undergoes displacement while being acted upon by a force (or several forces), it is said that work is being done on the object. If the object is moving in a straight line and the displacement and the force are known, the work done by the force can be calculated as , where is the work done by force on the object that undergoes displacement directed at angle relative to .  A B A = 2 + 5 ı ^  ^ B = −2 − 4 ı ^  ^  = 175  A B A = −6 + 2 ı ^  ^ B = − − 3 ı ^  ^  = 90 W =  = cos  F  s  F   s  W F  s  F  Note that depending on the value of , the work done can be positive, negative, or zero. In this problem, you will practice calculating work done on an object moving in a straight line. The first series of questions is related to the accompanying figure. Part A What can be said about the sign of the work done by the force ? ANSWER: Correct When , the cosine of is zero, and therefore the work done is zero. Part B cos  F  1 It is positive. It is negative. It is zero. There is not enough information to answer the question.  = 90  What can be said about the work done by force ? ANSWER: Correct When , is positive, and so the work done is positive. Part C The work done by force is ANSWER: Correct When , is negative, and so the work done is negative. Part D The work done by force is ANSWER: F  2 It is positive. It is negative. It is zero. 0 <  < 90 cos  F  3 positive negative zero 90 <  < 180 cos  F  4 Correct Part E The work done by force is ANSWER: Correct positive negative zero F  5 positive negative zero Part F The work done by force is ANSWER: Correct Part G The work done by force is ANSWER: Correct In the next series of questions, you will use the formula to calculate the work done by various forces on an object that moves 160 meters to the right. F  6 positive negative zero F  7 positive negative zero W =  = cos  F  s  F   s  Part H Find the work done by the 18-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Part I Find the work done by the 30-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Part J Find the work done by the 12-newton force. Use two significant figures in your answer. Express your answer in joules. W W = 2900 J W W = 4200 J W ANSWER: Correct Part K Find the work done by the 15-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Introduction to Potential Energy Learning Goal: Understand that conservative forces can be removed from the work integral by incorporating them into a new form of energy called potential energy that must be added to the kinetic energy to get the total mechanical energy. The first part of this problem contains short-answer questions that review the work-energy theorem. In the second part we introduce the concept of potential energy. But for now, please answer in terms of the work-energy theorem. Work-Energy Theorem The work-energy theorem states , where is the work done by all forces that act on the object, and and are the initial and final kinetic energies, respectively. Part A The work-energy theorem states that a force acting on a particle as it moves over a ______ changes the ______ energy of the particle if the force has a component parallel to the motion. W = -1900 J W W = -1800 J Kf = Ki + Wall Wall Ki Kf Choose the best answer to fill in the blanks above: ANSWER: Correct It is important that the force have a component acting in the direction of motion. For example, if a ball is attached to a string and whirled in uniform circular motion, the string does apply a force to the ball, but since the string's force is always perpendicular to the motion it does no work and cannot change the kinetic energy of the ball. Part B To calculate the change in energy, you must know the force as a function of _______. The work done by the force causes the energy change. Choose the best answer to fill in the blank above: ANSWER: Correct Part C To illustrate the work-energy concept, consider the case of a stone falling from to under the influence of gravity. Using the work-energy concept, we say that work is done by the gravitational _____, resulting in an increase of the ______ energy of the stone. Choose the best answer to fill in the blanks above: distance / potential distance / kinetic vertical displacement / potential none of the above acceleration work distance potential energy xi xf ANSWER: Correct Potential Energy You should read about potential energy in your text before answering the following questions. Potential energy is a concept that builds on the work-energy theorem, enlarging the concept of energy in the most physically useful way. The key aspect that allows for potential energy is the existence of conservative forces, forces for which the work done on an object does not depend on the path of the object, only the initial and final positions of the object. The gravitational force is conservative; the frictional force is not. The change in potential energy is the negative of the work done by conservative forces. Hence considering the initial and final potential energies is equivalent to calculating the work done by the conservative forces. When potential energy is used, it replaces the work done by the associated conservative force. Then only the work due to nonconservative forces needs to be calculated. In summary, when using the concept of potential energy, only nonconservative forces contribute to the work, which now changes the total energy: , where and are the final and initial potential energies, and is the work due only to nonconservative forces. Now, we will revisit the falling stone example using the concept of potential energy. Part D Rather than ascribing the increased kinetic energy of the stone to the work of gravity, we now (when using potential energy rather than work-energy) say that the increased kinetic energy comes from the ______ of the _______ energy. Choose the best answer to fill in the blanks above: ANSWER: force / kinetic potential energy / potential force / potential potential energy / kinetic Kf + Uf = Ef = Wnc + Ei = Wnc + Ki + Ui Uf Ui Wnc Correct Part E This process happens in such a way that total mechanical energy, equal to the ______ of the kinetic and potential energies, is _______. Choose the best answer to fill in the blanks above: ANSWER: Correct Problem 11.7 Part A How much work is done by the force 2.2 6.6 on a particle that moves through displacement 3.9 Express your answer to two significant figures and include the appropriate units. ANSWER: work / potential force / kinetic change / potential sum / conserved sum / zero sum / not conserved difference / conserved F  = (− + i ^ ) N j ^ ! = r m i ^ Correct Part B How much work is done by the force 2.2 6.6 on a particle that moves through displacement 3.9 Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.10 A 1.8 book is lying on a 0.80- -high table. You pick it up and place it on a bookshelf 2.27 above the floor. Part A How much work does gravity do on the book? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B W = -8.6 J F  = (− + i ^ ) N j ^ ! = r m? j ^ W = 26 J kg m m Wg = -26 J How much work does your hand do on the book? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.12 The three ropes shown in the bird's-eye view of the figure are used to drag a crate 3.3 across the floor. Part A How much work is done by each of the three forces? Express your answers using two significant figures. Enter your answers numerically separated by commas. ANSWER: WH = 26 J m W1 , W2 , W3 = 1.9,1.2,-2.1 kJ Correct Enhanced EOC: Problem 11.16 A 1.2 particle moving along the x-axis experiences the force shown in the figure. The particle's velocity is 4.6 at . You may want to review ( pages 286 - 287) . For help with math skills, you may want to review: The Definite Integral Part A What is its velocity at ? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the work–kinetic energy theorem? What is the kinetic energy at ? How is the work done in going from to related to force shown in the graph? Using the work–kinetic energy theorem, what is the kinetic energy at ? What is the velocity at ? ANSWER: kg m/s x = 0m x = 2m x = 0 m x = 0 m x = 2 m x = 2 m x = 2 m Correct Part B What is its velocity at ? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the work–kinetic energy theorem? What is the kinetic energy at ? How is the work done in going from to related to force shown in the graph? Can the work be negative? Using the work–kinetic energy theorem, what is the kinetic energy at ? What is the velocity at ? ANSWER: Correct Work on a Sliding Block A block of weight sits on a frictionless inclined plane, which makes an angle with respect to the horizontal, as shown. A force of magnitude , applied parallel to the incline, pulls the block up the plane at constant speed. v = 6.2 ms x = 4m x = 0 m x = 0 m x = 4 m x = 4 m x = 4 m v = 4.6 ms w  F Part A The block moves a distance up the incline. The block does not stop after moving this distance but continues to move with constant speed. What is the total work done on the block by all forces? (Include only the work done after the block has started moving, not the work needed to start the block moving from rest.) Express your answer in terms of given quantities. Hint 1. What physical principle to use To find the total work done on the block, use the work-energy theorem: . Hint 2. Find the change in kinetic energy What is the change in the kinetic energy of the block, from the moment it starts moving until it has been pulled a distance ? Remember that the block is pulled at constant speed. Hint 1. Consider kinetic energy If the block's speed does not change, its kinetic energy cannot change. ANSWER: ANSWER: L Wtot Wtot = Kf − Ki L Kf − Ki = 0 Wtot = 0 Correct Part B What is , the work done on the block by the force of gravity as the block moves a distance up the incline? Express the work done by gravity in terms of the weight and any other quantities given in the problem introduction. Hint 1. Force diagram Hint 2. Force of gravity component What is the component of the force of gravity in the direction of the block's displacement (along the inclined plane)? Express your answer in terms of and . Hint 1. Relative direction of the force and the motion Remember that the force of gravity acts down the plane, whereas the block's displacement is directed up the plane. ANSWER: Wg L w w  ANSWER: Correct Part C What is , the work done on the block by the applied force as the block moves a distance up the incline? Express your answer in terms of and other given quantities. Hint 1. How to find the work done by a constant force Remember that the work done on an object by a particular force is the integral of the dot product of the force and the instantaneous displacement of the object, over the path followed by the object. In this case, since the force is constant and the path is a straight segment of length up the inclined plane, the dot product becomes simple multiplication. ANSWER: Correct Part D What is , the work done on the block by the normal force as the block moves a distance up the inclined plane? Express your answer in terms of given quantities. Hint 1. First step in computing the work Fg|| = −wsin() Wg = −wLsin() WF F L F L WF = FL Wnormal L The work done by the normal force is equal to the dot product of the force vector and the block's displacement vector. The normal force and the block's displacement vector are perpendicular. Therefore, what is their dot product? ANSWER: ANSWER: Correct Problem 11.20 A particle moving along the -axis has the potential energy , where is in . Part A What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. N  L = 0 Wnormal = 0 y U = 3.2y3 J y m y y = 0 m Fy = 0 N y y = 1 m ANSWER: Correct Part C What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.28 A cable with 25.0 of tension pulls straight up on a 1.08 block that is initially at rest. Part A What is the block's speed after being lifted 2.40 ? Solve this problem using work and energy. Express your answer with the appropriate units. ANSWER: Correct Fy = -9.6 N y y = 2 m Fy = -38 N N kg m vf = 8.00 ms Problem 11.29 Part A How much work does an elevator motor do to lift a 1500 elevator a height of 110 ? Express your answer with the appropriate units. ANSWER: Correct Part B How much power must the motor supply to do this in 50 at constant speed? Express your answer with the appropriate units. ANSWER: Correct Problem 11.32 How many energy is consumed by a 1.20 hair dryer used for 10.0 and a 11.0 night light left on for 16.0 ? Part A Hair dryer: Express your answer with the appropriate units. kg m Wext = 1.62×106 J s = 3.23×104 P W kW min W hr ANSWER: Correct Part B Night light: Express your answer with the appropriate units. ANSWER: Correct Problem 11.42 A 2500 elevator accelerates upward at 1.20 for 10.0 , starting from rest. Part A How much work does gravity do on the elevator? Express your answer with the appropriate units. ANSWER: Correct W = 7.20×105 J = 6.34×105 W J kg m/s2 m −2.45×105 J Part B How much work does the tension in the elevator cable do on the elevator? Express your answer with the appropriate units. ANSWER: Correct Part C Use the work-kinetic energy theorem to find the kinetic energy of the elevator as it reaches 10.0 . Express your answer with the appropriate units. ANSWER: Correct Part D What is the speed of the elevator as it reaches 10.0 ? Express your answer with the appropriate units. ANSWER: Correct 2.75×105 J m 3.00×104 J m 4.90 ms Problem 11.47 A horizontal spring with spring constant 130 is compressed 17 and used to launch a 2.4 box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface is 0.15. Part A Use work and energy to find how far the box slides across the rough surface before stopping. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.49 Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward slope and a large coefficient of rolling friction as the truck tires sink into the gravel brings the truck safely to a halt. Suppose a gravel ramp slopes upward at 6.0 and the coefficient of rolling friction is 0.45. Part A Use work and energy to find the length of a ramp that will stop a 15,000 truck that enters the ramp at 30 . Express your answer to two significant figures and include the appropriate units. ANSWER: Correct N/m cm kg l = 53 cm kg m/s l = 83 m Problem 11.51 Use work and energy to find an expression for the speed of the block in the following figure just before it hits the floor. Part A Find an expression for the speed of the block if the coefficient of kinetic friction for the block on the table is . Express your answer in terms of the variables , , , , and free fall acceleration . ANSWER: Part B Find an expression for the speed of the block if the table is frictionless. Express your answer in terms of the variables , , , and free fall acceleration . ANSWER: μk M m h μk g v = M m h g Problem 11.57 The spring shown in the figure is compressed 60 and used to launch a 100 physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the incline is 0.12 . Part A What is the student's speed just after losing contact with the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How far up the incline does the student go? Express your answer to two significant figures and include the appropriate units. ANSWER: v = cm kg 30 v = 17 ms Correct Score Summary: Your score on this assignment is 93.6%. You received 112.37 out of a possible total of 120 points. !s = 41 m

Assignment 9 Due: 11:59pm on Friday, April 11, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Problem 11.2 Part A Evaluate the dot product if and . Express your answer using two significant figures. ANSWER: Correct Part B Evaluate the dot product if and . Express your answer using two significant figures. ANSWER: Correct Problem 11.4  A B = 5 − 6 A i ^ j ^ = −9 − 5 B i ^ j ^ A  B  = -15  A B = −5 + 9 A i ^ j ^ = 5 + 6 B i ^ j ^ A  B  = 29 Part A What is the angle between vectors and if and ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part B What is the angle between vectors and if and ? Express your answer as an integer and include the appropriate units. ANSWER: Correct ± All Work and No Play Learning Goal: To be able to calculate work done by a constant force directed at different angles relative to displacement If an object undergoes displacement while being acted upon by a force (or several forces), it is said that work is being done on the object. If the object is moving in a straight line and the displacement and the force are known, the work done by the force can be calculated as , where is the work done by force on the object that undergoes displacement directed at angle relative to .  A B A = 2 + 5 ı ^  ^ B = −2 − 4 ı ^  ^  = 175  A B A = −6 + 2 ı ^  ^ B = − − 3 ı ^  ^  = 90 W =  = cos  F  s  F   s  W F  s  F  Note that depending on the value of , the work done can be positive, negative, or zero. In this problem, you will practice calculating work done on an object moving in a straight line. The first series of questions is related to the accompanying figure. Part A What can be said about the sign of the work done by the force ? ANSWER: Correct When , the cosine of is zero, and therefore the work done is zero. Part B cos  F  1 It is positive. It is negative. It is zero. There is not enough information to answer the question.  = 90  What can be said about the work done by force ? ANSWER: Correct When , is positive, and so the work done is positive. Part C The work done by force is ANSWER: Correct When , is negative, and so the work done is negative. Part D The work done by force is ANSWER: F  2 It is positive. It is negative. It is zero. 0 <  < 90 cos  F  3 positive negative zero 90 <  < 180 cos  F  4 Correct Part E The work done by force is ANSWER: Correct positive negative zero F  5 positive negative zero Part F The work done by force is ANSWER: Correct Part G The work done by force is ANSWER: Correct In the next series of questions, you will use the formula to calculate the work done by various forces on an object that moves 160 meters to the right. F  6 positive negative zero F  7 positive negative zero W =  = cos  F  s  F   s  Part H Find the work done by the 18-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Part I Find the work done by the 30-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Part J Find the work done by the 12-newton force. Use two significant figures in your answer. Express your answer in joules. W W = 2900 J W W = 4200 J W ANSWER: Correct Part K Find the work done by the 15-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Introduction to Potential Energy Learning Goal: Understand that conservative forces can be removed from the work integral by incorporating them into a new form of energy called potential energy that must be added to the kinetic energy to get the total mechanical energy. The first part of this problem contains short-answer questions that review the work-energy theorem. In the second part we introduce the concept of potential energy. But for now, please answer in terms of the work-energy theorem. Work-Energy Theorem The work-energy theorem states , where is the work done by all forces that act on the object, and and are the initial and final kinetic energies, respectively. Part A The work-energy theorem states that a force acting on a particle as it moves over a ______ changes the ______ energy of the particle if the force has a component parallel to the motion. W = -1900 J W W = -1800 J Kf = Ki + Wall Wall Ki Kf Choose the best answer to fill in the blanks above: ANSWER: Correct It is important that the force have a component acting in the direction of motion. For example, if a ball is attached to a string and whirled in uniform circular motion, the string does apply a force to the ball, but since the string's force is always perpendicular to the motion it does no work and cannot change the kinetic energy of the ball. Part B To calculate the change in energy, you must know the force as a function of _______. The work done by the force causes the energy change. Choose the best answer to fill in the blank above: ANSWER: Correct Part C To illustrate the work-energy concept, consider the case of a stone falling from to under the influence of gravity. Using the work-energy concept, we say that work is done by the gravitational _____, resulting in an increase of the ______ energy of the stone. Choose the best answer to fill in the blanks above: distance / potential distance / kinetic vertical displacement / potential none of the above acceleration work distance potential energy xi xf ANSWER: Correct Potential Energy You should read about potential energy in your text before answering the following questions. Potential energy is a concept that builds on the work-energy theorem, enlarging the concept of energy in the most physically useful way. The key aspect that allows for potential energy is the existence of conservative forces, forces for which the work done on an object does not depend on the path of the object, only the initial and final positions of the object. The gravitational force is conservative; the frictional force is not. The change in potential energy is the negative of the work done by conservative forces. Hence considering the initial and final potential energies is equivalent to calculating the work done by the conservative forces. When potential energy is used, it replaces the work done by the associated conservative force. Then only the work due to nonconservative forces needs to be calculated. In summary, when using the concept of potential energy, only nonconservative forces contribute to the work, which now changes the total energy: , where and are the final and initial potential energies, and is the work due only to nonconservative forces. Now, we will revisit the falling stone example using the concept of potential energy. Part D Rather than ascribing the increased kinetic energy of the stone to the work of gravity, we now (when using potential energy rather than work-energy) say that the increased kinetic energy comes from the ______ of the _______ energy. Choose the best answer to fill in the blanks above: ANSWER: force / kinetic potential energy / potential force / potential potential energy / kinetic Kf + Uf = Ef = Wnc + Ei = Wnc + Ki + Ui Uf Ui Wnc Correct Part E This process happens in such a way that total mechanical energy, equal to the ______ of the kinetic and potential energies, is _______. Choose the best answer to fill in the blanks above: ANSWER: Correct Problem 11.7 Part A How much work is done by the force 2.2 6.6 on a particle that moves through displacement 3.9 Express your answer to two significant figures and include the appropriate units. ANSWER: work / potential force / kinetic change / potential sum / conserved sum / zero sum / not conserved difference / conserved F  = (− + i ^ ) N j ^ ! = r m i ^ Correct Part B How much work is done by the force 2.2 6.6 on a particle that moves through displacement 3.9 Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.10 A 1.8 book is lying on a 0.80- -high table. You pick it up and place it on a bookshelf 2.27 above the floor. Part A How much work does gravity do on the book? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B W = -8.6 J F  = (− + i ^ ) N j ^ ! = r m? j ^ W = 26 J kg m m Wg = -26 J How much work does your hand do on the book? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.12 The three ropes shown in the bird's-eye view of the figure are used to drag a crate 3.3 across the floor. Part A How much work is done by each of the three forces? Express your answers using two significant figures. Enter your answers numerically separated by commas. ANSWER: WH = 26 J m W1 , W2 , W3 = 1.9,1.2,-2.1 kJ Correct Enhanced EOC: Problem 11.16 A 1.2 particle moving along the x-axis experiences the force shown in the figure. The particle's velocity is 4.6 at . You may want to review ( pages 286 - 287) . For help with math skills, you may want to review: The Definite Integral Part A What is its velocity at ? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the work–kinetic energy theorem? What is the kinetic energy at ? How is the work done in going from to related to force shown in the graph? Using the work–kinetic energy theorem, what is the kinetic energy at ? What is the velocity at ? ANSWER: kg m/s x = 0m x = 2m x = 0 m x = 0 m x = 2 m x = 2 m x = 2 m Correct Part B What is its velocity at ? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the work–kinetic energy theorem? What is the kinetic energy at ? How is the work done in going from to related to force shown in the graph? Can the work be negative? Using the work–kinetic energy theorem, what is the kinetic energy at ? What is the velocity at ? ANSWER: Correct Work on a Sliding Block A block of weight sits on a frictionless inclined plane, which makes an angle with respect to the horizontal, as shown. A force of magnitude , applied parallel to the incline, pulls the block up the plane at constant speed. v = 6.2 ms x = 4m x = 0 m x = 0 m x = 4 m x = 4 m x = 4 m v = 4.6 ms w  F Part A The block moves a distance up the incline. The block does not stop after moving this distance but continues to move with constant speed. What is the total work done on the block by all forces? (Include only the work done after the block has started moving, not the work needed to start the block moving from rest.) Express your answer in terms of given quantities. Hint 1. What physical principle to use To find the total work done on the block, use the work-energy theorem: . Hint 2. Find the change in kinetic energy What is the change in the kinetic energy of the block, from the moment it starts moving until it has been pulled a distance ? Remember that the block is pulled at constant speed. Hint 1. Consider kinetic energy If the block's speed does not change, its kinetic energy cannot change. ANSWER: ANSWER: L Wtot Wtot = Kf − Ki L Kf − Ki = 0 Wtot = 0 Correct Part B What is , the work done on the block by the force of gravity as the block moves a distance up the incline? Express the work done by gravity in terms of the weight and any other quantities given in the problem introduction. Hint 1. Force diagram Hint 2. Force of gravity component What is the component of the force of gravity in the direction of the block's displacement (along the inclined plane)? Express your answer in terms of and . Hint 1. Relative direction of the force and the motion Remember that the force of gravity acts down the plane, whereas the block's displacement is directed up the plane. ANSWER: Wg L w w  ANSWER: Correct Part C What is , the work done on the block by the applied force as the block moves a distance up the incline? Express your answer in terms of and other given quantities. Hint 1. How to find the work done by a constant force Remember that the work done on an object by a particular force is the integral of the dot product of the force and the instantaneous displacement of the object, over the path followed by the object. In this case, since the force is constant and the path is a straight segment of length up the inclined plane, the dot product becomes simple multiplication. ANSWER: Correct Part D What is , the work done on the block by the normal force as the block moves a distance up the inclined plane? Express your answer in terms of given quantities. Hint 1. First step in computing the work Fg|| = −wsin() Wg = −wLsin() WF F L F L WF = FL Wnormal L The work done by the normal force is equal to the dot product of the force vector and the block's displacement vector. The normal force and the block's displacement vector are perpendicular. Therefore, what is their dot product? ANSWER: ANSWER: Correct Problem 11.20 A particle moving along the -axis has the potential energy , where is in . Part A What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. N  L = 0 Wnormal = 0 y U = 3.2y3 J y m y y = 0 m Fy = 0 N y y = 1 m ANSWER: Correct Part C What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.28 A cable with 25.0 of tension pulls straight up on a 1.08 block that is initially at rest. Part A What is the block's speed after being lifted 2.40 ? Solve this problem using work and energy. Express your answer with the appropriate units. ANSWER: Correct Fy = -9.6 N y y = 2 m Fy = -38 N N kg m vf = 8.00 ms Problem 11.29 Part A How much work does an elevator motor do to lift a 1500 elevator a height of 110 ? Express your answer with the appropriate units. ANSWER: Correct Part B How much power must the motor supply to do this in 50 at constant speed? Express your answer with the appropriate units. ANSWER: Correct Problem 11.32 How many energy is consumed by a 1.20 hair dryer used for 10.0 and a 11.0 night light left on for 16.0 ? Part A Hair dryer: Express your answer with the appropriate units. kg m Wext = 1.62×106 J s = 3.23×104 P W kW min W hr ANSWER: Correct Part B Night light: Express your answer with the appropriate units. ANSWER: Correct Problem 11.42 A 2500 elevator accelerates upward at 1.20 for 10.0 , starting from rest. Part A How much work does gravity do on the elevator? Express your answer with the appropriate units. ANSWER: Correct W = 7.20×105 J = 6.34×105 W J kg m/s2 m −2.45×105 J Part B How much work does the tension in the elevator cable do on the elevator? Express your answer with the appropriate units. ANSWER: Correct Part C Use the work-kinetic energy theorem to find the kinetic energy of the elevator as it reaches 10.0 . Express your answer with the appropriate units. ANSWER: Correct Part D What is the speed of the elevator as it reaches 10.0 ? Express your answer with the appropriate units. ANSWER: Correct 2.75×105 J m 3.00×104 J m 4.90 ms Problem 11.47 A horizontal spring with spring constant 130 is compressed 17 and used to launch a 2.4 box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface is 0.15. Part A Use work and energy to find how far the box slides across the rough surface before stopping. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.49 Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward slope and a large coefficient of rolling friction as the truck tires sink into the gravel brings the truck safely to a halt. Suppose a gravel ramp slopes upward at 6.0 and the coefficient of rolling friction is 0.45. Part A Use work and energy to find the length of a ramp that will stop a 15,000 truck that enters the ramp at 30 . Express your answer to two significant figures and include the appropriate units. ANSWER: Correct N/m cm kg l = 53 cm kg m/s l = 83 m Problem 11.51 Use work and energy to find an expression for the speed of the block in the following figure just before it hits the floor. Part A Find an expression for the speed of the block if the coefficient of kinetic friction for the block on the table is . Express your answer in terms of the variables , , , , and free fall acceleration . ANSWER: Part B Find an expression for the speed of the block if the table is frictionless. Express your answer in terms of the variables , , , and free fall acceleration . ANSWER: μk M m h μk g v = M m h g Problem 11.57 The spring shown in the figure is compressed 60 and used to launch a 100 physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the incline is 0.12 . Part A What is the student's speed just after losing contact with the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How far up the incline does the student go? Express your answer to two significant figures and include the appropriate units. ANSWER: v = cm kg 30 v = 17 ms Correct Score Summary: Your score on this assignment is 93.6%. You received 112.37 out of a possible total of 120 points. !s = 41 m

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Assignment 6 Due: 11:59pm on Friday, March 7, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 7.7 A small car is pushing a large truck. They are speeding up. Part A Is the force of the truck on the car larger than, smaller than, or equal to the force of the car on the truck? ANSWER: Correct Conceptual Question 7.12 The figure shows two masses at rest. The string is massless and the pulley is frictionless. The spring scale reads in . Assume that = 4 . The force of the truck on the car is larger than the force of the car on the truck. The force of the truck on the car is equal to the force of the car on the truck. The force of the truck on the car is smaller than the force of the car on the truck. kg m kg

Assignment 6 Due: 11:59pm on Friday, March 7, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 7.7 A small car is pushing a large truck. They are speeding up. Part A Is the force of the truck on the car larger than, smaller than, or equal to the force of the car on the truck? ANSWER: Correct Conceptual Question 7.12 The figure shows two masses at rest. The string is massless and the pulley is frictionless. The spring scale reads in . Assume that = 4 . The force of the truck on the car is larger than the force of the car on the truck. The force of the truck on the car is equal to the force of the car on the truck. The force of the truck on the car is smaller than the force of the car on the truck. kg m kg

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How does the size of China’s economy compare to that of the United States? A. The U.S. economy is almost twice the size of China’s. B. The U.S. economy is almost three times the size of China’s. C. China’s economy is almost twice the size of the United States’. D. China’s economy is almost three times the size of the United States’. E. They are about equal.

How does the size of China’s economy compare to that of the United States? A. The U.S. economy is almost twice the size of China’s. B. The U.S. economy is almost three times the size of China’s. C. China’s economy is almost twice the size of the United States’. D. China’s economy is almost three times the size of the United States’. E. They are about equal.

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Define: 41 Things Philosophy is: 1. Ignorant 2. Selfish 3. Ironic 4. Plain 5. Misunderstood 6. A failure 7. Poor 8. Unscientific 9. Unteachable 10. Foolish 11. Abnormal 12. Divine trickery 13. Egalitarian 14. A divine calling 15. Laborious 16. Countercultural 17. Uncomfortable 18. Virtuous 19. Dangerous 20. Simplistic<br />21. Polemical 22. Therapeutic 23. “conformist” 24. Embarrassi ng 25. Invulnerable 26. Annoying 27. Pneumatic 28. Apolitic al 29. Docile/teachable 30. Messianic 31. Pious 32. Impract ical 33. Happy 34. Necessary 35. Death-defying 36. Fallible 37. Immortal 38. Confident 39. Painful 40. agnostic</br

Define: 41 Things Philosophy is: 1. Ignorant 2. Selfish 3. Ironic 4. Plain 5. Misunderstood 6. A failure 7. Poor 8. Unscientific 9. Unteachable 10. Foolish 11. Abnormal 12. Divine trickery 13. Egalitarian 14. A divine calling 15. Laborious 16. Countercultural 17. Uncomfortable 18. Virtuous 19. Dangerous 20. Simplistic
21. Polemical 22. Therapeutic 23. “conformist” 24. Embarrassi ng 25. Invulnerable 26. Annoying 27. Pneumatic 28. Apolitic al 29. Docile/teachable 30. Messianic 31. Pious 32. Impract ical 33. Happy 34. Necessary 35. Death-defying 36. Fallible 37. Immortal 38. Confident 39. Painful 40. agnostic

Ignorant- A person is said to be ignorant if he … Read More...
Proof  = E exp(-Et/)

Proof  = E exp(-Et/)

Maxwell Model: (Spring and Dashpot in Series)   Maxwell Model … Read More...
5. Which of the following statements is CORRECT? a. If Firms X and Y have the same P/E ratios, then their market-to-book ratios must also be equal. b. If Firms X and Y have the same net income, number of shares outstanding, and price per share, then their P/E ratios must also be the same. c. If Firms X and Y have the same earnings per share and market-to-book ratio, they must have the same price/earnings ratio. d. If Firm X’s P/E ratio exceeds that of Firm Y, then Y is likely to be less risky and/or be expected to grow at a faster rate. e. If Firms X and Y have the same net income, number of shares outstanding, and price per share, then their market-to-book ratios must also be the same.

5. Which of the following statements is CORRECT? a. If Firms X and Y have the same P/E ratios, then their market-to-book ratios must also be equal. b. If Firms X and Y have the same net income, number of shares outstanding, and price per share, then their P/E ratios must also be the same. c. If Firms X and Y have the same earnings per share and market-to-book ratio, they must have the same price/earnings ratio. d. If Firm X’s P/E ratio exceeds that of Firm Y, then Y is likely to be less risky and/or be expected to grow at a faster rate. e. If Firms X and Y have the same net income, number of shares outstanding, and price per share, then their market-to-book ratios must also be the same.

Answer: b No reason for a to be true. b … Read More...