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Potential energy and conservation of energy and linear momentum

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1.) The two masses in the Atwood's machine shown in the figure below are initially at rest at the same height. After they are released, the large mass, m2, falls through a height h and hits the floor, and the small mass, m1, rises through a height h.

a.) Find the speed of the masses just before m2 lands. Assume the ropes and pulley have negligible mass and that friction can be ignored. (Use m1 for m1, m2 for m2, and h and g as necessary.)
2.) A 93 kg astronaut and a 1100 kg satellite are at rest relative to the space shuttle. The astronaut pushes on the satellite, giving it a speed of 0.19 m/s directly away from the shuttle. Seven-and-a-half seconds later the astronaut comes into contact with the shuttle. What was the initial distance from the shuttle to the astronaut?
3.) A 1300 kg car drives up a hill that is 17.2 m high. During the drive, two nonconservative forces do work on the car: (i) the force of friction, and (ii) the force generated by the car's engine. The work done by friction is -2.95x105 J; the work done by the engine is +6.48x105 J. Find the change in the car's kinetic energy from the bottom of the hill to the top of the hill.

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Potential energy and conservation of energy and linear momentum is examined.

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SHM With Conservation of Momentum, energy: Vertical spring

For lunch you and your friends decide to stop at the nearest deli and have a sandwich made fresh for you with 0.300 of Italian ham. The slices of ham are weighed on a plate of mass 0.400 placed atop a vertical spring of negligible mass and force constant of 200 . The slices of ham are dropped on the plate all at the same time from a height of 0.250 . They make a totally inelastic collision with the plate and set the scale into vertical simple harmonic motion (SHM). You may assume that the collision time is extremely small.

What is the amplitude of oscillation of the scale after the slices of ham land on the plate? Express your answer numerically in meters and take free-fall acceleration to be = 9.80 .

What is the period of oscillation of the scale? Express your answer numerically in seconds.

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