xposure Evaluation – Single substance, different exposure time, different concentrations: 3- A person is working in a factory producing. This person is exposure to different concentrations of Toluene with different exposures time. The results of a personal sampling in an 8-hour shift is shown here: Exposure Time Concentration 3 hr. 35 min 790 mg/m^3 43 min 27 ppm 3.70 hr. 800 mg/m^3 What is this worker’s time weighted average of exposure in mg/m^3? Is the company in compliance with the OSHA requirement? 6- Phenyl ether can be used in soap factories as fragrance. A worker is exposed to this material during 9-hour shift and the exposure information is given in the following table: Exposure Time Concentration 1 hr. 45 min 4×〖10〗^(-6 ) mg/〖cm〗^3 2 hr. 5 min 7×〖10〗^(-6 ) mg/〖cm〗^3 65 min 3×〖10〗^(-3 ) mg/L Remaining Time 7.5 mg/m^3 What is this worker’s time weighted average of exposure in mg/m^3? Is the company in compliance with the OSHA requirement? 7- One of the major ingredients of insect repellents is Naphthalene. Consider a situation in which a worker is exposed to this material. The exposure time and concentration is given in a table below: Exposure Time Concentration 275 min 12 ppm 40 min 5 ppm 165 min 10 ppm What is this worker’s time weighted average of exposure? Is the condition hazardous? Exposure Evaluation – Multiple substance, equal exposure time, constant concentrations: 1- A person is exposed to the vapors of Benzene and Ethyl alcohol. Tests show that the concentration of Benzene is 1 ppm and Ethyl alcohol is 450 ppm. What is the threshold limit value of the mix? Is this person at risk? 6- Several workers at a rubber and leather manufacturing company are exposed to vapors of Vinyl chloride, Toluene and Xylene with concentration of 0.2 ppm, 135 ppm 200 mg/m^3 respectively. What is the threshold limit value of the mix? Are the employees at risk? 7- Several workers exposed to vapors of Ammonia, Arsine, Chloroform and Acetone with concentration of 12 ppm, 0.04 mg/m^3, 15 ppm, and 570 mg/m^3 respectively. What is the threshold limit value of the mix? Are the employees at risk?

xposure Evaluation – Single substance, different exposure time, different concentrations: 3- A person is working in a factory producing. This person is exposure to different concentrations of Toluene with different exposures time. The results of a personal sampling in an 8-hour shift is shown here: Exposure Time Concentration 3 hr. 35 min 790 mg/m^3 43 min 27 ppm 3.70 hr. 800 mg/m^3 What is this worker’s time weighted average of exposure in mg/m^3? Is the company in compliance with the OSHA requirement? 6- Phenyl ether can be used in soap factories as fragrance. A worker is exposed to this material during 9-hour shift and the exposure information is given in the following table: Exposure Time Concentration 1 hr. 45 min 4×〖10〗^(-6 ) mg/〖cm〗^3 2 hr. 5 min 7×〖10〗^(-6 ) mg/〖cm〗^3 65 min 3×〖10〗^(-3 ) mg/L Remaining Time 7.5 mg/m^3 What is this worker’s time weighted average of exposure in mg/m^3? Is the company in compliance with the OSHA requirement? 7- One of the major ingredients of insect repellents is Naphthalene. Consider a situation in which a worker is exposed to this material. The exposure time and concentration is given in a table below: Exposure Time Concentration 275 min 12 ppm 40 min 5 ppm 165 min 10 ppm What is this worker’s time weighted average of exposure? Is the condition hazardous? Exposure Evaluation – Multiple substance, equal exposure time, constant concentrations: 1- A person is exposed to the vapors of Benzene and Ethyl alcohol. Tests show that the concentration of Benzene is 1 ppm and Ethyl alcohol is 450 ppm. What is the threshold limit value of the mix? Is this person at risk? 6- Several workers at a rubber and leather manufacturing company are exposed to vapors of Vinyl chloride, Toluene and Xylene with concentration of 0.2 ppm, 135 ppm 200 mg/m^3 respectively. What is the threshold limit value of the mix? Are the employees at risk? 7- Several workers exposed to vapors of Ammonia, Arsine, Chloroform and Acetone with concentration of 12 ppm, 0.04 mg/m^3, 15 ppm, and 570 mg/m^3 respectively. What is the threshold limit value of the mix? Are the employees at risk?

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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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1. Develop a thought experiment that attempts to uncover hidden assumptions about human freedom. 2. Find a paragraph from a book, magazine, ect. First, tell whether there are claims in the paragraph. If there are, identify the types of claims (descriptive, normative, a priori, a posteriori) in the paragraph

1. Develop a thought experiment that attempts to uncover hidden assumptions about human freedom. 2. Find a paragraph from a book, magazine, ect. First, tell whether there are claims in the paragraph. If there are, identify the types of claims (descriptive, normative, a priori, a posteriori) in the paragraph

Let us think of a thought experiment that wants to … Read More...
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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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: Incorrect; Try Again 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 = s t = 0 s cm cm/s Typesetting math: 100% Incorrect; Try Again Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). 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: 0 = g cm s Typesetting math: 100% 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 Part B The period. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part C 3.00 Nm x(t) = (2.0 cm)cos(10t − /4) t 2.00 cm 0.628 s Typesetting math: 100% The spring constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Part D The phase constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Incorrect; Try Again Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). Part G Typesetting math: 100% This question will be shown after you complete previous question(s). Part H This question will be shown after you complete previous question(s). Part I This question will be shown after you complete previous question(s). 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? 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? N/m cm s Typesetting math: 100% 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 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 m = 110 g vmax = 49 cms m L T Typesetting math: 10T0% L , 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. ANSWER: T = 2 Lg −−  g T/2 T &2T 2T g/6 T/6 T/&6 &6T 6T Typesetting math: 100% 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. 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. 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. g ( s Typesetting math: 100% 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. 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: L = 19 cm m lmoon = 0.35 m m g 1.0 MHz N amax = 6.6 μm Typesetting math: 100% 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 81.4%. You received 117.25 out of a possible total of 144 points. 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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 Typesetting math: 100% 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: Incorrect; Try Again 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 = s t = 0 s cm cm/s Typesetting math: 100% Incorrect; Try Again Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). 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: 0 = g cm s Typesetting math: 100% 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 Part B The period. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part C 3.00 Nm x(t) = (2.0 cm)cos(10t − /4) t 2.00 cm 0.628 s Typesetting math: 100% The spring constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Part D The phase constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Incorrect; Try Again Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). Part G Typesetting math: 100% This question will be shown after you complete previous question(s). Part H This question will be shown after you complete previous question(s). Part I This question will be shown after you complete previous question(s). 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? 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? N/m cm s Typesetting math: 100% 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 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 m = 110 g vmax = 49 cms m L T Typesetting math: 10T0% L , 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. ANSWER: T = 2 Lg −−  g T/2 T &2T 2T g/6 T/6 T/&6 &6T 6T Typesetting math: 100% 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. 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. 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. g ( s Typesetting math: 100% 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. 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: L = 19 cm m lmoon = 0.35 m m g 1.0 MHz N amax = 6.6 μm Typesetting math: 100% 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 81.4%. You received 117.25 out of a possible total of 144 points. vmax = 41 ms

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Book review The Shareholder Value Myth: How Putting Shareholders First Harms Investors, Corporations, and the Public by Lynn Stout Provide 1) a 900 word review of this book (word range 900-1,200) and 2) a 350 word reflection where you force yourself to relate the message of the book . As per the format of the review, I like the ones done by the folks of the WSJ. This is an example: http://forums.delphiforums.com/diversecity/messages?msg=17531.1264 or http://www.wsj.com/articles/book-review-how-adam-smith-can-change-your-life-by-russ-roberts-1413846808?KEYWORDS=book+reviews

Book review The Shareholder Value Myth: How Putting Shareholders First Harms Investors, Corporations, and the Public by Lynn Stout Provide 1) a 900 word review of this book (word range 900-1,200) and 2) a 350 word reflection where you force yourself to relate the message of the book . As per the format of the review, I like the ones done by the folks of the WSJ. This is an example: http://forums.delphiforums.com/diversecity/messages?msg=17531.1264 or http://www.wsj.com/articles/book-review-how-adam-smith-can-change-your-life-by-russ-roberts-1413846808?KEYWORDS=book+reviews

The Shareholder Value Myth: How Putting Shareholders First Harms Investors, … Read More...
Name Tutorials in Introductory Physics ©Pearson Custom Publishing McDermott, Shaffer, & P.E.G., U. Wash. Updated Preliminary Second Edition, 2011 Mech HW–39 1. A block initially at rest is given a quick push by a hand. The block slides across the floor, gradually slows down, and comes to rest. a. In the spaces provided, draw and label separate free-body diagrams for the block at each of the three instants shown. A quick push by a hand… 1. (Initially at rest) the sliding block slows… 2. v and is finally at rest. 3. b. Rank the magnitudes of all the horizontal forces in the diagram for instant 1. Explain. c. Are any of the forces that you drew for instant 1 missing from your diagram for instant 2? If so, for each force that is missing, explain how you knew to include the force on the first diagram but not on the second. d. Are any of the forces that you drew for instant 1 missing from your diagram for instant 3? If so, for each force that is missing, explain how you knew to include the force on the first diagram but not on the third. NEWTON’S SECOND AND THIRD LAWS Newton’s second and third laws Tutorials in Introductory Physics ©Pearson Custom Publishing McDermott, Shaffer, & P.E.G., U. Wash. Updated Preliminary Second Edition, 2011 Mech HW–40 2. Two crates, A and B, are in an elevator as shown. The mass of crate A is greater than the mass of crate B. a. The elevator moves downward at constant speed. i. How does the acceleration of crate A compare to that of crate B? Explain. ii. In the spaces provided below, draw and label separate free-body diagrams for the crates. Free-body diagram for crate A Free-body diagram for crate B iii. Rank the forces on the crates according to magnitude, from largest to smallest. Explain your reasoning, including how you used Newton’s second and third laws. iv. In the spaces provided at right, draw arrows to indicate the direction of the net force on each crate. If the net force on either crate is zero, state so explicitly. Explain. Is the magnitude of the net force on crate A greater than, less than, or equal to that on crate B? Explain. Elevator (moving down at constant speed) A B Cable Crate A Crate B Direction of net force Newton’s second and third laws Name Tutorials in Introductory Physics ©Pearson Custom Publishing McDermott, Shaffer, & P.E.G., U. Wash. Updated Preliminary Second Edition, 2011 Mech HW–41 b. As the elevator approaches its destination, its speed decreases. (It continues to move downward.) i. How does the acceleration of crate A compare to that of crate B? Explain. ii. In the spaces provided below, draw and label separate free-body diagrams for the crates in this case. Free-body diagram for crate A Free-body diagram for crate B iii. Rank the forces on the crates according to magnitude, from largest to smallest. Explain your reasoning, including how you used Newton’s second and third laws. iv. In the spaces provided at right, draw arrows to indicate the direction of the net force on each crate. If the net force on either crate is zero, state so explicitly. Explain. Is the magnitude of the net force on crate A greater than, less than, or equal to that on crate B? Explain. Crate A Crate B Direction of net force Newton’s second and third laws Tutorials in Introductory Physics ©Pearson Custom Publishing McDermott, Shaffer, & P.E.G., U. Wash. Updated Preliminary Second Edition, 2011 Mech HW–42 3. A hand pushes three identical bricks as shown. The bricks are moving to the left and speeding up. System A consists of two bricks stacked together. System B consists of a single brick. System C consists of all three bricks. There is friction between the bricks and the table. a. In the spaces provided at right, draw and label separate free-body diagrams for systems A and B. b. The vector representing the acceleration of system A is shown at right. Draw the acceleration vectors for systems B and C using the same scale. Explain. c. The vector representing the net force on system A is shown at right. Draw the net force vectors for systems B and C using the same scale. Explain. d. The vector representing the frictional force on system A is shown below. Draw the remaining force vectors using the same scale. NBH NAB NBA fAT fBT Explain how you knew to draw the force vectors as you did. A B Free-body diagram for system A Free-body diagram for system B Acceleration of A Acceleration of B Acceleration of C Net force on A Net force on B Net force on C

Name Tutorials in Introductory Physics ©Pearson Custom Publishing McDermott, Shaffer, & P.E.G., U. Wash. Updated Preliminary Second Edition, 2011 Mech HW–39 1. A block initially at rest is given a quick push by a hand. The block slides across the floor, gradually slows down, and comes to rest. a. In the spaces provided, draw and label separate free-body diagrams for the block at each of the three instants shown. A quick push by a hand… 1. (Initially at rest) the sliding block slows… 2. v and is finally at rest. 3. b. Rank the magnitudes of all the horizontal forces in the diagram for instant 1. Explain. c. Are any of the forces that you drew for instant 1 missing from your diagram for instant 2? If so, for each force that is missing, explain how you knew to include the force on the first diagram but not on the second. d. Are any of the forces that you drew for instant 1 missing from your diagram for instant 3? If so, for each force that is missing, explain how you knew to include the force on the first diagram but not on the third. NEWTON’S SECOND AND THIRD LAWS Newton’s second and third laws Tutorials in Introductory Physics ©Pearson Custom Publishing McDermott, Shaffer, & P.E.G., U. Wash. Updated Preliminary Second Edition, 2011 Mech HW–40 2. Two crates, A and B, are in an elevator as shown. The mass of crate A is greater than the mass of crate B. a. The elevator moves downward at constant speed. i. How does the acceleration of crate A compare to that of crate B? Explain. ii. In the spaces provided below, draw and label separate free-body diagrams for the crates. Free-body diagram for crate A Free-body diagram for crate B iii. Rank the forces on the crates according to magnitude, from largest to smallest. Explain your reasoning, including how you used Newton’s second and third laws. iv. In the spaces provided at right, draw arrows to indicate the direction of the net force on each crate. If the net force on either crate is zero, state so explicitly. Explain. Is the magnitude of the net force on crate A greater than, less than, or equal to that on crate B? Explain. Elevator (moving down at constant speed) A B Cable Crate A Crate B Direction of net force Newton’s second and third laws Name Tutorials in Introductory Physics ©Pearson Custom Publishing McDermott, Shaffer, & P.E.G., U. Wash. Updated Preliminary Second Edition, 2011 Mech HW–41 b. As the elevator approaches its destination, its speed decreases. (It continues to move downward.) i. How does the acceleration of crate A compare to that of crate B? Explain. ii. In the spaces provided below, draw and label separate free-body diagrams for the crates in this case. Free-body diagram for crate A Free-body diagram for crate B iii. Rank the forces on the crates according to magnitude, from largest to smallest. Explain your reasoning, including how you used Newton’s second and third laws. iv. In the spaces provided at right, draw arrows to indicate the direction of the net force on each crate. If the net force on either crate is zero, state so explicitly. Explain. Is the magnitude of the net force on crate A greater than, less than, or equal to that on crate B? Explain. Crate A Crate B Direction of net force Newton’s second and third laws Tutorials in Introductory Physics ©Pearson Custom Publishing McDermott, Shaffer, & P.E.G., U. Wash. Updated Preliminary Second Edition, 2011 Mech HW–42 3. A hand pushes three identical bricks as shown. The bricks are moving to the left and speeding up. System A consists of two bricks stacked together. System B consists of a single brick. System C consists of all three bricks. There is friction between the bricks and the table. a. In the spaces provided at right, draw and label separate free-body diagrams for systems A and B. b. The vector representing the acceleration of system A is shown at right. Draw the acceleration vectors for systems B and C using the same scale. Explain. c. The vector representing the net force on system A is shown at right. Draw the net force vectors for systems B and C using the same scale. Explain. d. The vector representing the frictional force on system A is shown below. Draw the remaining force vectors using the same scale. NBH NAB NBA fAT fBT Explain how you knew to draw the force vectors as you did. A B Free-body diagram for system A Free-body diagram for system B Acceleration of A Acceleration of B Acceleration of C Net force on A Net force on B Net force on C

Develop a 4 page-500 word précis on Chapter 7 “How to Monitor & Control a TPM Project” of the Wysocki 7th Ed. text.”

Develop a 4 page-500 word précis on Chapter 7 “How to Monitor & Control a TPM Project” of the Wysocki 7th Ed. text.”

Summary of ‘How to Monitor and Control a TPM Project’ … Read More...
The Geographic Grid The Geographic grid is based on angular measurements from the center of the earth. Latitude measures the angular distance north and south of the plane of the earth’s equator. longitude measures the angular distance east and west of the prime meridian. The angular distance between any two locations on the earth’s surface is simply the latitudinal or longitudinal difference the two locations. Both longitude and latitude are measured in degrees ( o ), minutes ( ‘ ) and seconds ( ” ) of arc. Figure 1 shows the latitude and longitude coordinates of the earth in 10o degree intervals. There are 60′ minutes of arc in 1o . There are 60″ seconds of arc in 1′ minute of arc. One could therefore express the latitude and longitude of a place as 39o 50′ 10″ N, 77o 35′ 15″ W. 1. Using latitude and longitude coordinates, determine the location of the following places. a) Toronto, Ontario ( Canada ) ____________________________________________________________ b) Billings, Montana _____________________________________________________________________ c) Chicago, Illinois ______________________________________________________________________ d) Westminster, England _________________________________________________________________ e) Venice, Italy _________________________________________________________________________ f) Baghdad, Iraq _______________________________________________________________________ g) Tokyo, Japan ________________________________________________________________________ h) Rio de Janeiro, Brazil _________________________________________________________________ 2. Provide the name of the following places located at the given coordinates below. a) 13o 09′ 50.19″ S, 72o 32′ 45.58″ W ______________________________________________________ b) 33o 51′ 35.90″ S, 151o 12′ 40″ E ______________________________________________________ c) 71o 17′ 07.62″ N, 156o 45′ 57.98″ W _____________________________________________________ d) 41o 53′ 29.84″ N, 87o 36′ 01.78″ W ______________________________________________________ The geographic grid uses circles of two different types, great circles and small circles. All great circles pass through the geographic center of the earth. All meridians, the equator, and the circle of illumination are great circles. All parallels other than the equator are small circles. The direction of any grid lines ( meridians and parallels ) can be determined as either an azimuth or a bearing. Azimuths are read in a clockwise direction as degrees ranging from 0o at the North Pole, to 90o at East, to 180o at the South Pole, to 270o at West, and back to 360o at the North Pole. Azimuths only give a direction such as 45o . Bearings are read as quadrants from either the North or South Poles. Hence east is 90o from either North or South. West is also 90o from either North or South. A bearing shows the direction one is traveling as well as the magnitude of the angle from either North or South. Hence a azimuth of 45o is read as a bearing of N 45o E. An azimuth of 150o would as a bearing read S 30o E. Figure 1.2 shows the relationship between azimuths and bearings. 3. Convert the values below. Bearing Azimuth 20o S 500 20′ E 265o 30’ N 20o 20 W Longitudinal and latitudinal distances vary as a result of trying to fit a flat grid onto a spherical surface such as the earth’s curved surface. The grid is constant in a north-south direction, but varies in the east-west direction. The data below shows how the grid values vary ( rounded off to the nearest mile of distance ). 1o of longitude at the equator = 69 miles 1o of longitude at the 30th parallel = 60 miles 1o of longitude at the 60th parallel = 35 miles 1o of longitude at the 90th parallel = 0 miles 1o of latitude along any meridian = 69 miles 4. Determine by calculation the linear ( miles ) and angular ( degree ) distances between the following places. From To Angular Linear Quito, Ecuador Macapa, Brazil 0o S, 78o W 0o N, 51o W Cairo, Egypt Shiraz, Iran 30o N, 31o E 30o N, 52o E Seward, Alaska St Petersburg, Russia 60o N, 149o W 60o N, 30o E Hamhung, North Korea Ankara, Turkey 39o N, 127o E 39o N, 32o E Detroit, Michigan Morristown, Tennessee 42o N, 83o W 36o N, 83o W Sample problem We see that between Quito and Macapa that there is no latitude difference as both places are at 0 degrees latitude. Therefore the angular difference between the two places can only be calculated based upon the longitudinal difference. Seeing that both places are west longitude we simply subtract 78-51 = 27 degrees. Hence the angular distance between Quito and Macapa is 27 degrees. The linear distance is the number of miles ( feet,yards, kilometers, etc.) Quito and Macapa. Bothe places are on the equator so consulting the table above we find that in 1 degree of longitude ate the equator is equal to 69 miles. So multiplying the 69 miles/degree X 27 degrees, the degrees cancel and the remaining units are miles, and the numerical value is 1,863 linear miles.

The Geographic Grid The Geographic grid is based on angular measurements from the center of the earth. Latitude measures the angular distance north and south of the plane of the earth’s equator. longitude measures the angular distance east and west of the prime meridian. The angular distance between any two locations on the earth’s surface is simply the latitudinal or longitudinal difference the two locations. Both longitude and latitude are measured in degrees ( o ), minutes ( ‘ ) and seconds ( ” ) of arc. Figure 1 shows the latitude and longitude coordinates of the earth in 10o degree intervals. There are 60′ minutes of arc in 1o . There are 60″ seconds of arc in 1′ minute of arc. One could therefore express the latitude and longitude of a place as 39o 50′ 10″ N, 77o 35′ 15″ W. 1. Using latitude and longitude coordinates, determine the location of the following places. a) Toronto, Ontario ( Canada ) ____________________________________________________________ b) Billings, Montana _____________________________________________________________________ c) Chicago, Illinois ______________________________________________________________________ d) Westminster, England _________________________________________________________________ e) Venice, Italy _________________________________________________________________________ f) Baghdad, Iraq _______________________________________________________________________ g) Tokyo, Japan ________________________________________________________________________ h) Rio de Janeiro, Brazil _________________________________________________________________ 2. Provide the name of the following places located at the given coordinates below. a) 13o 09′ 50.19″ S, 72o 32′ 45.58″ W ______________________________________________________ b) 33o 51′ 35.90″ S, 151o 12′ 40″ E ______________________________________________________ c) 71o 17′ 07.62″ N, 156o 45′ 57.98″ W _____________________________________________________ d) 41o 53′ 29.84″ N, 87o 36′ 01.78″ W ______________________________________________________ The geographic grid uses circles of two different types, great circles and small circles. All great circles pass through the geographic center of the earth. All meridians, the equator, and the circle of illumination are great circles. All parallels other than the equator are small circles. The direction of any grid lines ( meridians and parallels ) can be determined as either an azimuth or a bearing. Azimuths are read in a clockwise direction as degrees ranging from 0o at the North Pole, to 90o at East, to 180o at the South Pole, to 270o at West, and back to 360o at the North Pole. Azimuths only give a direction such as 45o . Bearings are read as quadrants from either the North or South Poles. Hence east is 90o from either North or South. West is also 90o from either North or South. A bearing shows the direction one is traveling as well as the magnitude of the angle from either North or South. Hence a azimuth of 45o is read as a bearing of N 45o E. An azimuth of 150o would as a bearing read S 30o E. Figure 1.2 shows the relationship between azimuths and bearings. 3. Convert the values below. Bearing Azimuth 20o S 500 20′ E 265o 30’ N 20o 20 W Longitudinal and latitudinal distances vary as a result of trying to fit a flat grid onto a spherical surface such as the earth’s curved surface. The grid is constant in a north-south direction, but varies in the east-west direction. The data below shows how the grid values vary ( rounded off to the nearest mile of distance ). 1o of longitude at the equator = 69 miles 1o of longitude at the 30th parallel = 60 miles 1o of longitude at the 60th parallel = 35 miles 1o of longitude at the 90th parallel = 0 miles 1o of latitude along any meridian = 69 miles 4. Determine by calculation the linear ( miles ) and angular ( degree ) distances between the following places. From To Angular Linear Quito, Ecuador Macapa, Brazil 0o S, 78o W 0o N, 51o W Cairo, Egypt Shiraz, Iran 30o N, 31o E 30o N, 52o E Seward, Alaska St Petersburg, Russia 60o N, 149o W 60o N, 30o E Hamhung, North Korea Ankara, Turkey 39o N, 127o E 39o N, 32o E Detroit, Michigan Morristown, Tennessee 42o N, 83o W 36o N, 83o W Sample problem We see that between Quito and Macapa that there is no latitude difference as both places are at 0 degrees latitude. Therefore the angular difference between the two places can only be calculated based upon the longitudinal difference. Seeing that both places are west longitude we simply subtract 78-51 = 27 degrees. Hence the angular distance between Quito and Macapa is 27 degrees. The linear distance is the number of miles ( feet,yards, kilometers, etc.) Quito and Macapa. Bothe places are on the equator so consulting the table above we find that in 1 degree of longitude ate the equator is equal to 69 miles. So multiplying the 69 miles/degree X 27 degrees, the degrees cancel and the remaining units are miles, and the numerical value is 1,863 linear miles.