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Genearal mechanics question

1. A motorcyclist is coasting with the engine off at a steady speed 17 m/s but enters a sandy stretch where the coefficient of friction is .80. Will the cyclist emerge from the sandy stretch without having to start the engine if the sand lasts for 15 m. If so, what will be the speed upon emerging?

2. One car has twice the mass of a second car, but only half as much kinetic energy. When both cars increased their speed by 5.0 m/s, they have the same kinetic energy. What were the original speeds of the two cars?

3. A ball is attached to a horizontal cord of length L whose other end is fixed. If the ball is released, what will be its speed at the lowest point of its path? A peg is located a distance h directly below the point of attachment of the cord. If h=0.8L, what will be the velocity of the ball when it reaches the top of its circular path about the peg?

4. A ring, a disk, and a sphere of equal masses and radius start rolling down the hill. Which of these three objects will reach the bottom of the hill first?

5. A block slides a distance d down a frictionless plane and then comes to a stop after sliding a distance s across a rough horizontal plane. What fraction of the distance s does the block slide before its speed is reduced to one - third of the maximum speed it had at the bottom of the ramp?

6. A uniform rod of mass m and length L can pivot freely (without friction) about a hinge attached to a wall. The rod is held horizontally and then released. Determine the linear velocity of the tip of the rod when it touches the wall.

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