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Physics problems section 1 (6-4-02) |
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1. A hard rubber ball of radius a is thrown onto the floor (assume that the ball's collisions with the floor are perfectly elastic and that the there is sufficient friction for there to be no slipping at the point of contact between the floor and the ball. How should the ball be thrown if it is to bounce back and forth as shown in the figure? |
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2. There is a spaceship with mass M and cross-sectional area A coasting with an initial velocity of vo. At t=0, it encounters a stationary dust cloud of uniform density
r. As the ship is traveling through the dust cloud, the dust sticks to its surface. Assuming that A is constant, solve for the motion of the spaceship. |
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3. A "skyhook" satellite is described by sci-fi author Robert A. Heinlein as a long rope placed in orbit above the equator so as to appear as if it were suspended. Assuming that the rope has a uniform linear mass density, what is its length? The "hanging" end lies just above the surface of the Earth (radius R). |
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4. Three identical objects of mass m are coupled together with identical springs (with spring constant k). At t=0, the objects are at rest. Object A is then driven by a force, F(t) = A cos(f t), where A is the max amplitude of the force and f is the angular frequency (both are constants). Solve for the motion of object C. |
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