Part I Multiple Choice (4 points. ea.)

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1 ach xam usually consists of 10 ultiple choice questions which are conceptual in nature. They are often based upon the assigned thought questions from the homework. There are also 4 problems in each exam, based upon the assigned homework problems. Partial credit may be awarded for the problems. Physical constants and equation sheets are provided for the exam. Part I ultiple Choice (4 points. ea.). Which of the following diagrams most closely represents the gravitational forces that the earth and the moon exert on each other? (A) (C) () (B) (D). If two planets have the same average density and one has twice the mass of the other, then the more massive planet has (A) twice the radius and twice the surface gravity of the lighter. (B) 2 1/3 times the radius and 2 1/3 times the surface gravity of the lighter. (C) twice the radius and half the surface gravity of the lighter. (D) 2 1/3 times the radius and twice the surface gravity of the lighter. () 8 times the radius and 1/32 times the surface gravity of the lighter.. If two planets have the same average density and one has a greater radius than the other, then compared to the smaller planet the larger planet has (B) the same surface gravity. (C) less surface e gravity. (D) more information on the details of the planets are needed to answer this question.. If two planets have the same radius and one has a greater density (and hence a greater mass) than the other, then compared to the first planet the more massive planet will have (B) the same surface gravity. (C) less surface gravity. (D) more information on the details of the planets are needed to answer this question. If two planets have the same mass and one has a greater radius than the other, then compared to the smaller planet the larger planet will have (B) the same surface gravity. (C) less surface gravity. (D) more information on the details of the planets are needed to answer this que 1

2 . If two planets have the same radius and one has a greater mass than the other, then compared to the first planet the planet with the larger mass will have (B) a greater escape velocity. (C) a larger density. (D) all of the above () none of the above. Pluto is in an elliptical orbit around the sun. After exactly one complete orbit, the net work done by the sun s gravity on the Pluto is (A) positive. (B) negative. (C) zero. (D) any of the above depending upon the eccentricity of the orbit.. A satellite is in a circular orbit around the earth. After one complete orbit, the net work done by earth s gravity on the satellite is (A) positive. (B) negative. (C) zero. (D) any of the above depending upon the actual radius of the orbit.. A satellite is in a circular orbit around the earth. After one complete orbit, the net work done by earth s gravity on the satellite is (A) positive. (B) negative. (C) zero. (D) any of the above depending upon the actual radius of the orbit.. A planet which is farther from the Sun than the arth (A) will take less than a year to orbit the Sun. (B) will take more than a year to orbit the Sun. (C) will also take a year to orbit the Sun (D) will eventually begin orbiting the arth.. The gravitational force exerted on the earth by the moon (A) is greater than the gravitational force exerted on the moon by the earth. (B) is less than the gravitational force exerted on the moon by the earth. (C) is the same as the gravitational force exerted on the moon by the earth. (D) is zero.. The total energy (K +P) of a simple harmonic oscillator is (A) a maximum when the mass is at the equilibrium position. (B) a maximum when the mass is at its maximum displacement from equilibrium. (D) constant. (D) always zero 2

3 . The kinetic energy of a simple harmonic oscillator is (A) a maximum when the mass is at the equilibrium position. (B) a maximum when the mass is at its maximum displacement from equilibrium. (D) constant. (D) always zero. The potential energy of a simple harmonic oscillator is (A) a maximum when the mass is at the equilibrium position. (B) a maximum when the mass is at its maximum displacement from equilibrium. (C) constant. (D) always zero. The amplitude of a simple harmonic oscillator does not affect its (A) frequency. (B) maximum speed. (C) maximum acceleration. (D) maximum K.. The amplitude of the motion of an object undergoing Simple Harmonic otion is (A) the total range of motion. (B) its maximum displacement on either side of the equilibrium position. (C) its minimum displacement on either side of the equilibrium position. (D) the number of cycles per second it undergoes. The amplitude of a simple harmonic oscillator does not affect its (A) frequency. (B) maximum speed. (C) maximum acceleration. (D) maximum K. The frequency of oscillations of a mass on a spring do not depend upon (A) the mass. (B) the spring constant. (C) the amplitude of oscillations. () none of the above.. A mass on a spring oscillates at a particular frequency. If the mass is replaced with a larger mass, then (A) the spring constant will be larger. (B) the frequency of oscillations will be smaller. (C) the period of oscillations will be smaller.. A mass on a spring oscillates at a particular frequency. If the spring is replaced with a stiffer spring, then (A) the spring constant of the new spring is larger. (B) the frequency of oscillations will be larger. (C) the period of oscillations will be smaller. 3

4 The maximum speed of a mass on a spring undergoing simple harmonic oscillations will depend upon (A) the mass. (B) the spring constant. (C) the amplitude of oscillations. () none of the above.. Suppose a uniform spring is cut in half. The force constant for each half of the spring would be (A) half the spring constant for the original spring. (B) the same as the spring constant for the original spring. (C) twice the spring constant for the original spring. (D) 2 times the spring constant for the original spring. () 1 2 times the spring constant for the original spring.. A mass on a spring oscillates at a particular frequency. If the spring is replaced with a stiffer spring, then (A) the spring constant of the new spring is larger. (B) the frequency of oscillations will be larger. (C) the period of oscillations will be smaller.. A pendulum clock, which keeps correct time on earth, is taken to the surface of the moon. The clock will (A) run fast (i.e. clock s seconds are shorter than real seconds). (B) run slow (i.e. clock s seconds are longer than real seconds). (C) still run correctly. (D) will not run at all because there is no gravity on the moon.. A pendulum clock, which keeps correct time on earth, is taken to the surface a planet with a much stronger surface gravity than earth. The clock will (A) run fast (i.e. clock s seconds are shorter than real seconds). (B) run slow (i.e. clock s seconds are longer than real seconds). (C) still run correctly. (D) will not run at all because there is no gravity on the moon.. A pendulum clock that is placed in an elevator that is accelerating at a constant rate upwards will (A) run fast (i.e. clock s seconds are shorter than real seconds). (B) run slow (i.e. clock s seconds are longer than real seconds). (C) still run correctly. (D) will not run at all because there is no gravity on the moon.. In order to double the period of a simple pendulum, the length of the string must be (A) shortened to ½ of its original length. (B) shortened to ¼ times its original length. (C) lengthened to 2 times its original length. (D) lengthened to 4 times its original length. 4

5 . Adding dampening (friction) to a simple harmonic oscillator will cause the total energy to (A) increase. (B) remain constant. (C) decrease. (D) oscillate.. Of the following procedures, which will lower the pitch (fundamental frequency of vibration) in a guitar string? (A) decrease the tension. (B) lengthen the string. (C) use a heavier string.. The speed of a wave on a stretched string depends upon (A) the tension in the string. (B) the wavelength of the wave. (C) the amplitude of the wave.. The speed of a wave on a stretched string does not depend upon (A) the amplitude of the wave. (B) the density (or heaviness) of the string. (C) the tension in the string.. The lower the frequency of a wave, (A) the lower its speed. (B) the longer its wavelength. (C) the greater its amplitude. (D) the shorter its period.. Wave motion in a medium transfers (A) neither mass nor energy. (B) energy, only. (C) both mass and energy. (D) mass, only. 5

6 Part II Problems Show all work. No work = no credit! (15 points each) Planets can be used to determine the mass of the star they orbit. Venus has a nearly circular orbit about the sun with an orbit radius of m and an orbital period 225 days. It also has a mass of kg. Determine (A) Venus s orbital speed, (B) Centripetal acceleration, (C) the necessary centripetal force required to keep Venus in orbit, and (D) the necessary mass of the sun so that the sun s gravitational attraction can create the centripetal force required to keep Venus in orbit. () Could (D) have been determined solely from the orbit radius and orbital period if the mass of Venus were unknown? (Yes or No) Planet Hollywood has decided to place a hotel/space-station in circular orbit about Jupiter (mass = kg) so that the Jupiter's Great Red Spot will always be in view. As a result, the time for one orbit must match the rotation rate of Jupiter (which is 9.90 hours for one rotation). Use your knowledge of Centripetal Acceleration, Newton's Laws and Universal Gravitation to determine the radius of the desired circular orbit. It will be helpful to relate the speed of the station along its orbit to the circumference of the orbit and the time for one orbit. A pendulum clock designed for use on the arth is transported to ercury (mass kg, radius m, orbital distance m), where it is used without modification or adjustment. The clock s primary timing mechanism is a simple pendulum. The period for the simple pendulum is designed to be 1.00 s on arth. A) What is the length of the pendulum s string? B) What is the acceleration of gravity on the surface of the ercury? C) What is the period of the pendulum on ercury? Does the clock run fast or slow? Three masses each exert a gravitational force on a fourth. 1 is located at (0,4m) and has a mass of 5.00 kg. 2 is located at (0,0) and has a mass of 8.00 kg. 3 is located at (3m, 0) and has a mass of 4.00 kg. a) Calculate the net gravitational force (x and y components) on the mass m (mass of 2.00 kg) located at the point (3m, 4m). b) Calculate the gravitational potential energy of the mass m due to the other three masses. 1 m 2 3 The moon orbits the earth at a distance of 3.848m. ach orbit takes 27.3 days. The mass of the moon has been determined to be kg and the mass of the earth has been determined to be kg. Determine: (A) the speed of the moon as it orbits the earth, (B) the centripetal acceleration of the moon, (C) the force necessary to keep the moon in its circular path, and (D) the gravitational attraction of the earth for the moon using Newton's Law of Universal Gravitation (compare your result for part D to your answer to part C) 6

7 A spring with a spring constant of 500 N/m is attached to a.800 kg mass. The mass undergoes simple harmonic motion with an amplitude of.0500 m. Determine (A) the frequency of oscillations (in Hz), (C) the maximum speed of the mass, (D) the speed of the mass when it is.0200 m from equilibrium, () the acceleration of the mass when it is m from equilibrium. A spring with a spring constant of 400 N/m is attached to a.250 kg mass. The mass undergoes simple harmonic motion with an initial speed of 2.00 m/s at the equilibrium position. Determine (A) the frequency of oscillations (in Hz), (C) the amplitude of the oscillations, (D) the speed of the mass when it is.0125 m from equilibrium, () the acceleration of the mass when it is m from equilibrium.. A spring with an unknown spring constant is attached to a.5 kg mass. The mass undergoes simple harmonic motion with an amplitude of m at a frequency of Hz. Determine (A) the force constant of the spring (C) the maximum speed of the mass, (D) the speed of the mass when it is m from equilibrium, () the acceleration of the mass when it is m from equilibrium. A spring with a spring constant of 400 N/m is attached to an unknown mass. The mass undergoes simple harmonic motion with an amplitude of m at a frequency of Hz. Determine (A) the mass attached to the spring (C) the maximum speed of the mass, (D) the speed of the mass when it is m from equilibrium, () the acceleration of the mass when it is m from equilibrium. A steel wire 2.00 m long and 4.00 g in mass is under a tension of 160 N. (A) What is the velocity of waves on the wire? (B) What is wavelength of the fundamental mode of vibration? (C) What is the frequency of the fundamental mode of vibration? (D) What is the frequency of the first overtone (aka the second harmonic)? () What must the tension be changed to in order to double the fundamental frequency? A steel wire 1.50 m long and 2.00 g in mass is to be tuned to a frequency of 440 Hz. (A) What is wavelength of the fundamental mode of vibration? (B) What is the velocity of waves on the wire? (C) What is the required tension? 7

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