Week 10 Homework Assignment PDF

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Week 10 Homework Assignment

Due Tuesday Recitation, Week 11

1. A 2.00-kg stone is sliding to the right on a frictionless horizontal surface at 5 m/s when it is suddenly struck by an object that exerts a large horizontal force on it for a short period of time. The graph shows the magnitude of this force as a function of time. (a) What impulse does this force exert on the stone? (b) Just after the force stops acting, find the magnitude and direction of the stone’s velocity if the force acts (i) to the right (ii) to the left.

2. An atomic nucleus suddenly bursts apart (fissions) into two pieces. Piece A (mass mA) travels off to the left with speed vA. Piece B (mass mB) travels off to the right with speed vB. (a) Use conservation of momentum to solve for vB in terms of mA, mB and vA (b) Use the results of part (a) to show that KA/KB = mB/mA where KA and KB are the kinetic energies of the two pieces.

3. A diver comes off a board with arms straight up and legs straight down, giving her a moment of inertia about her rotation axis of 18 kgm2. She then tucks into a small ball, decreasing this moment of inertia to 3.6 kgm2. While tucked, she makes two complete revolutions in 1.0 s. If she hadn’t tucked at all, how many revolutions would she have made in the 1.5 s from board to water? 4. You are a volunteer at the Museum of Natural History. Because of your interest in the environment and your physics experience, you have been asked to assist in the production of an animated film about the survival of hawks in the wilderness. In the script, a hawk (mass mH) is hovering in the air so it is stationary with respect to the ground when it sees a goose flying below it. The hawk dives straight down. When it strikes the goose and digs its claws into the goose's body, it has a speed vH. The goose, which has a mass mG, was flying north at vG just before it was struck by the hawk and killed instantly. The animators want to know the velocity (magnitude and direction) of the hawk and dead goose just after the strike.

5. Answer ONE of the following questions. 5_alt1. Consider the situation depicted in the comic below.

http://xkcd.com/162/ How much could you reasonably extend the night by spinning in place? How does this time depend on your latitude? Clarify any assumptions you make, about the shape of the person spinning for instance.

5_alt2. In Superman, The Movie (1978), Superman flies around the Earth in order to reverse time and save Lois Lane: https://www.youtube.com/watch?v=TjgsnWtBQm0 Assuming for a moment that getting the Earth to spin backwards would reverse time (!), and viewing the Earth + Superman as an isolated system, how fast would Superman have to fly to save Lois? Is this reasonable? Is he even going the right direction?...