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AP Physics C Chapter 11, 14 Test 1/17/2012 1. Of the satellites shown revolving around the planet in the accompanying diagram, the one with the greatest speed is a) b) c) d) e) 2. Two planets, which we label A and B, orbit a star of mass M. Planets A and B have masses mA and mB respectively, and travel in circular orbits of radii rA and rB, respectively, about the star, with orbital speeds vA and vB, (again) respectively. Planet B is twice as far from the star as planet B (rB=2rA). From Newton’s Law of Universal Gravitation and the expression for centripetal force, we can show that a) b) c) d) e) 3. 1.9 1.9 3.6 3.6 3.6 x x x x x 10-57 10-54 10-53 10-47 10-41 N N N N N A woman whose weight on earth is 500 N is lifted to a height of two earth radii above the surface of the earth. Her weight a) b) c) d) e) 5. vA = vB vA = (1/2) vB. vA = 2 vB vA = 2½ vB We need to know the mass of the star before we can figure this one out. What is the force of gravity between the proton and electron in a hydrogen atom, given that G = 6.67 x 10-11 N-m2/kg2, mass of a proton = 1.67 x 10-27 kg, mass of an electron = 9.1 x 10-31 kg, and average radius of the electron’s orbit in the hydrogen atom = 0.0529 nm? (1 nm = 10-9 m) a) b) c) d) e) 4. 1 2 3 4 5 decreases decreases decreases decreases decreases to to to to to one-half of the original amount. one-quarter of the original amount. one-fifth of the original amount. one-third of the original amount. one-ninth of the original amount. Two planets have masses M and m, and the ratio M/m = 25. The distance between the planets is R. The point P is between the planets as shown, and the distance between M and P is x. At P the gravitational forces on an object due to M and m are equal in magnitude. The value of x is a) b) c) d) e) 5R/6 25R/36 R/25 6R/5 None of these is correct. -1- AP Physics C Chapter 11, 14 Test 6. Five homogeneous planets have relative masses and sizes as shown in the figure (the radii of the larger ones are twice the radii of the smaller). A body of mass m would weigh the least on which planet? a) b) c) d) e) 7. 1 2 3 4 5 The mass of the earth is M, and its radius is R. If a projectile of mass m is launched from the surface of the earth with escape speed, its total energy (K + U) is a) b) c) d) e) 8. 1/17/2012 GMm/R GMm/2R zero (1/2)mv2 2GMm/R Again, let the mass of the earth be M and the radius of the earth be R. Suppose a rocket is fired vertically from the surface of the earth with one-half the escape speed. How far from the center of the earth will the rocket get before it falls back to the earth? a) b) c) d) e) 3R/2 4R/3 2R 3R 4R 9. The escape speed for a rocket at Earth's surface is ve . What would be the rocket's escape speed from the surface of a planet with twice Earth's mass and the same radius as Earth? a) 2 ve b) 2ve c) ve d) ve 2 e) ve/2 10. A satellite is orbiting the earth (mass M) in a circular orbit of radius r from the center of the planet. The total energy (kinetic + potential) of the satellite is a) b) c) d) e) zero GMm/r - GMm/r - GMm/2r None of these is correct -2- AP Physics C Chapter 11, 14 Test 1/17/2012 11. Test masses are used to measure the gravitational field at various positions in and near a solid sphere of uniform density. The gravitational field will have its greatest value at point(s) a) b) c) d) e) 1 2 3 4 5 12. A tunnel passes all the way through a planet of uniform density, along a diameter of the planet. Position r is measured from the center of the planet (r = 0) to an infinite distance from the planet. The radius of the surface of the planet is R. There are two points, one inside the planet and one outside the planet, where the magnitude of the gravitational field is one-half the value that it has on the surface of the planet. What is the value of r for these two points? a) b) c) d) e) r = 0, 2R r = R/2, R r = R/2, 2½ R r = R/4, 2½ R None of these is correct. 13. Any body moving with simple harmonic motion is being acted on by a force that is a) b) c) d) e) Constant. Proportional to a sine or cosine function of the displacement. Proportional to the inverse square of the displacement. Directly proportional to the displacement. Proportional to the square of the displacement. 14. A particle moving with a simple harmonic motion has its maximum displacement of +18 cm at time t = 0s. The frequency of the motion is 10 s-1 (10 Hz). At time t = 0.65 s, the position of the particle is a) b) c) d) e) +18 cm Zero – 13 cm – 18 cm + 7.3 cm -3- AP Physics C Chapter 11, 14 Test 1/17/2012 15. You want a mass that, when hung on the end of a spring, oscillates with a period of 1 s. If the spring has a constant of 10 N/m, the mass should be a) 10 kg b) 10 kg c) 4π2(10) kg d) 10/(4π2) kg e) None of these is correct; the period depends on the length of the spring. 16. A particle is oscillating with simple harmonic motion. The frequency of the motion is 10 Hz and the amplitude of the motion is 5.0 cm. As the particle passes through its central equilibrium position, the acceleration of the particle is a) b) c) d) e) 100 cm/s2 1.6 x 105 cm/s2 4 x 106 cm/s2 zero 3.2 x 106 cm/s2 17. A body of mass 5.0 kg moves in simple harmonic motion according to the equation x 0.040 sin 30t 6 . The units are SI. The period of this motion is a) b) c) d) e) 1/30 s π/15 s π/6 s 15/π s 30 s 18. A body of mass 5.0 kg moves in simple harmonic motion according to the equation x 0.040 sin 30t 6 . The units are SI. The maximum speed of this body is approximately a) b) c) d) e) 0.013 m/s 0.40 m/s 0.60 m/s 1.2 m/s 30 m/s 19. A particle moves in one dimension with simple harmonic motion according to the equation d 2 x / dt 2 4 2 x where the units are SI. Its period is a) b) c) d) e) 4 2 s 2 s 1s 1/(2) s 1/(4 2) s -4- AP Physics C Chapter 11, 14 Test 1/17/2012 20. A 1.0 kg mass oscillates along the x axis with simple harmonic motion. Its position as a function of time is given by x 2 cost / 6 / 3 where the units are SI. When t = 2 s, the kinetic energy of the mass is a) b) c) d) e) 2/24 J 2/72 J 2/9 J 2/9 J 2/4 J 21. A 0.5 kg mass is suspended from a massless spring that has a force constant of 79 N/m. The mass is displaced 0.1 m down from its equilibrium position and released. If the downward direction is negative, the displacement of the mass as a function of time is given by y 0.1cos158t b) y 0.2 cos158t c) y 0.1cos12.6t d) y 0.2 cos12.6t e) y 0.1 cos2t a) 22. To double the period of a pendulum, the length a) b) c) d) e) Must be increased by a factor of 2. Must be decreased by a factor of 2. Must be increased by a factor of 2½. Must be increased by a factor of 4. Need not be affected. 23. A simple pendulum has a period of 2 s for small amplitude oscillations. The length of the pendulum is most nearly a) b) c) d) e) 1/6 m 1/4 m 1/2 m 1m 2m 24. Which of the following equations could represent the angle θ that the pendulum of #22 makes with the vertical as a function of time t ? a) θ = θmax sin b) c) d) e) θ θ θ θ = = = = 2 t θmax sin πt θmax, sin 2πt θmax sin 4πt θmax sin 8πt -5- AP Physics C Chapter 11, 14 Test 1/17/2012 25. A mass M suspended by a spring with force constant k has a period T when set into oscillation on Earth. Its period on Mars, whose mass is about 1/9 and radius 1/2 that of Earth, is most nearly a) b) c) d) e) 1/3 T 2/3 T T 3/2 T 3T 26. A 1.0 kg mass is attached to the end of a vertical ideal spring with a force constant of 400 N/m. The mass is set in simple harmonic motion with an amplitude of 10 cm. The speed of the 1.0 kg mass at the equilibrium position is a) b) c) d) e) 2 m/s 4 m/s 20 m/s 40 m/s 200 m/s 27. When a mass m is hung on a certain ideal spring, the spring stretches a distance d. If the mass is then set oscillating on the spring, the period of oscillation is proportional to a) d g b) g d c) d) e) d mg m2 g d m g 28. A frictionless pendulum of length 3 m swings with an amplitude of 10°. At its maximum displacement, the potential energy of the pendulum is 10 J. What is the kinetic energy of the pendulum when its potential energy is 5 J ? a) b) c) d) e) 3.3 J 5J 6.7 J 10 J 15 J -6- AP Physics C Chapter 11, 14 Test 1/17/2012 29. Which of the following statements concerning the motion of a simple pendulum is incorrect? a) The kinetic energy is a minimum when the displacement is a maximum. b) The acceleration is a maximum when the displacement is a maximum. c) The period is changed if the mass of the bob is doubled and the length of the pendulum is halved. d) The time interval between conditions of maximum potential energy is one period. e) The velocity is a maximum when the acceleration is a minimum. 30. A uniform disk (Icm = ½MR2) of mass M and radius R is suspended from a point on its rim. If it oscillates as a physical pendulum its period is a) 2 3R / 2 g b) 2 3R / g c) 2 g / R d) 2 g / 2 R e) 2 g / 3R 31. The graph shows the square of the period versus the length of a simple pendulum on a certain planet. The acceleration due to gravity on that planet is approximately a) b) c) d) e) 0.100 m/s2 10.0 m/s2 3.95 m/s2 395 m/s2 0.628 m/s2 32. What is the length L of a simple pendulum with the same period as a physical pendulum consisting of a hoop suspended at its rim? 1 R 2 b) L 1 / R c) L 2R d) L R e) L 2 R a) L -7- AP Physics C Chapter 11, 14 Test 1/17/2012 32. In the laboratory, a stick 1 m long is pivoted at various points to illustrate the motion of a physical pendulum. A plot of the period versus the distance of the pivot point from the center of mass is shown. The data presented demonstrate which of the following? a) The motion of the pendulum is circular about the center of mass. b) The center of mass is at 0.4 m. c) The graph is meaningless in this form. d) There is a minimum period in the neighborhood of 1.5 seconds at a pivotal distance of approximately 0.4 m from the center of mass. e) The graph should be drawn as a straight line from A to C; point D is obviously wrong. -8-