exam02_sol_practice - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 Fall Term 2008 Practice Problems for Exam 2 Solutions Part I Concept Questions: Circle your answer. 1) A spring-loaded toy dart gun is used to shoot a dart straight up in the air, and the dart reaches a maximum height h m . The same dart is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. How far up does the dart go this time, neglecting friction and assuming an ideal spring? a) h m b) h m /2 c) h m /4 d) 2 h m e) 4 h m f) escapes to infinity Answer: (c). The energy of the spring-dart-earth system is constant so for the first case if x is the distance compressed then 1` 2 kx 2 = mgh m . For the second case, 2 k ( x /2) 2 = mgh . So 1 4 1 2 kx 2 = mgh or 1 4 ( mgh m ) = mgh . Thus h = 1 4 h m .
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2 2) Two wheels, suspended with frictionless bearings in the hubs, start from rest, with forces 1 F r and 2 F r applied as shown. The larger wheel has twice the radius and mass as the smaller wheel. Assume the mass of the hubs and spokes are very small compared to the mass of the rims, so that the moment of inertia about the axle is I = mR 2 . In order to impart identical angular accelerations, the magnitude of the force 2 F r applied to the larger wheel must be a) one fourth b) one half c) equal to d) twice e) four times the magnitude of the force 1 F r applied to the smaller wheel. Answer: (e). (Larger wheel has times greater moment of inertia, so it requires 4 times greater torque. As radius is 2 times greater, torque requires is 4 times greater force.)
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3 3) To make a projectile escape from the Earth, we must give it an initial speed larger than the magnitude of the escape velocity. This escape velocity, at the surface of the Earth, depends on a) the radius of the Earth. b) the mass of the Earth. c) the mass of the projectile. d) a) and b). e) a) and c). f) b) and c). g) all of the above Answer: (d). The magnitude of the escape velocity satisfies 1 2 mv esc 2 = Gmm e R e 2 , so v esc = 2 Gm e R e 2 .
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4 4) A dumbbell consists of two identical objects of mass m attached at each end of a rod of length l . A force F r in the x -direction is applied to the dumbbell for a time interval Δ t . It is first applied at the center of the dumbbell, as shown in (a), and the same force is then applied directly to one of the two objects, as shown in (b). Assume that the time Δ t is so short that the dumbbell does dot move significantly during Δ t . The dumbbell in case ( b ) has a) larger center of mass speed and larger kinetic energy b) equal center of mass speed and larger kinetic energy c) smaller center of mass speed and larger kinetic energy d) larger center of mass speed and equal kinetic energy e) equal center of mass speed and equal kinetic energy f) smaller center of mass speed and equal kinetic energy g) larger center of mass speed and smaller kinetic energy h) equal center of mass speed and smaller kinetic energy i) smaller center of mass speed and smaller kinetic energy than the dumbbell in case (a) Answer: (b). (Just after the impulse F
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exam02_sol_practice - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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