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Astrophysics: Friction, Potential Energy, and Kinetic Energy

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1. A spring with k = 40.0 N/m is at the base of a frictionless 30.0° inclined plane. A 0.50-kg object is pressed against the spring, compressing it 0.20m from its equilibrium position. The object is then released. If the object is not attached to the spring, how far up the incline does it travel before coming to rest and then sliding back down? Please see the attached document for an illustration.

2. Calculate the change in potential energy of 1 kg of water as it passes over Niagara Falls ( a vertical descent of 50m) b) At what rate is gravitational potential energy lost by the water of the Niagara River? The rate of flow is 5.5 x 10 kg/s. c) If 10% of this energy can be converted into electrical energy, how many households would the electricity supply? (An average household uses an average electrical power of about 1kW.

3. A 0.010-kg bullet traveling horizontally at 400.0 m/s strikes a 4.0-kg stuffed bunny sitting at the edge of a table. The bullet is lodged into the stuffed bunny. If the table height is 1.2m, how far from the table does the block hit the floor?

4. A pole-vaulter converts the kinetic energy of running to elastic potential energy in the pole, which is then converted to gravitational potential energy. If a pole-vaulter's center of gravity is 1.0m above the ground while he sprints at 10.0 m/s, what is the maximum height of his center of gravity during the vault? For an extended object, the gravitational potential energy is U=mgh, where h is the height of the center of gravity.
( In 1988, Sergei Bubka was the first pole-vaulter ever to clear 6m).

5. A 75-kg man is at rest on ice skates. A 0.20-kg ball is thrown to him. The ball is moving horizontally at 25 m/s just before the man catches it. How fast is the man moving just after he catches the ball?

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This solution provides guidelines on calculating distance on problems surrounding friction, potential energy, kinetic energy, and acceleration.

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