1. In the figure provided, the sliding block has a mass of 0.850 kg, the counterweights has a mass of 0.420 kg, and the pulley is a hollow cylinder with a mass of 0.350 kg, an inner radius of 0.020 0 m, and an outer radius of 0.030 0 m. The coefficient of kinetic friction between the block and the horizontal surface is 0.250. The pulley turns without friction on its axle. The light cord does not stretch and does not slip on the pulley. The block has a velocity of 0.820 m/s toward the pulley when it passes through a photo gate.
(a) Use energy methods to predict its speed after it has moved to a second photo gate, 0.700 m away.
(b) Find the angular speed of the pulley at the same moment.
2. A block of mass 0.500 kg is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x as in figure. The force constant of the spring is 450 N/m. When it is released, the block travels along a frictionless, horizontal surface to point B, the bottom of a circular track of R = 1.00 m, and continues to move along the track. The speed of the block at the bottom of the track is v_s = 12.0 m/s, and the block experience an average friction force of 7.00 N while sliding up the track.
(a) What is x?
(b) What speed do you predict for the block at the top of the track?
(c) Does the block actually reach the top of the track, or does it fall off before reaching the top?
3. George of the jungle, with mass m, swings on a light vine hanging from a stationary tree branch. A second vine of equal length hangs from the same point, and a gorilla of larger mass M swings in the opposite direction on it. Both vines are horizontal when the primates start from rest at the same moment. George and the Gorilla meet at the lowest point of their swings. Each is afraid that one vine will break, so they grab each other and hang on. They swing upward together, reaching a point where the vines make an angle of 35.0 with the vertical.
(a) Find the value of the ratio n/M.
(b) What if? Try the following experiment at home. Tie a small magnet and a steel screw to opposite ends of a string. Hold the center of the string fixed to represent the tree branch, and reproduce a model of a motions of George and the Gorilla. What changes in your analysis will make it apply to this situation? What if? Next assume the magnet is strong so that it noticeably attracts the screw over a distance of a few centimeters. Then the screw will be moving faster immediately before it sticks to the magnet. Does this extra magnet strength make a difference?