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2001BAP - 163 2001 A ball of mass M is attached to a string...

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A ball of mass M is attached to a string of length R and negligible mass. The ball moves clockwise in a vertical circle, as shown above. When the ball is at point P, the string is horizontal. Point Q is at the bottom of the circle and point Z is at the top of the circle. Air resistance is negligible. Express all algebraic answers in terms of the given quantities and fundamental constants. a. On the figures below, draw and label all the forces exerted on the ball when it is at points P and Q, respectively. b. Derive an expression for v min the minimum speed the ball can have at point Z without leaving the circular path. c. The maximum tension the string can have without breaking is T max Derive an expression for v max , the maximum speed the ball can have at point Q without breaking the string. d. Suppose that the string breaks at the instant the ball is at point P. Describe the motion of the ball immediately after the string breaks. 163 2001

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An incident ball A of mass 0.10 kg is sliding at 1.4 m/s on the horizontal tabletop of negligible friction shown above. It makes a head-on collision with a target ball B of mass 0.50 kg at rest at the edge of the table. As a result of the collision, the incident ball rebounds, sliding backwards at 0.70 m/s immediately after the collision. a. Calculate the speed of the 0.50 kg target ball immediately after the collision. The tabletop is 1.20 m above a level, horizontal floor. The target ball is projected horizontally and initially strikes the floor at a horizontal displacement d from the point of collision. b. Calculate the horizontal displacement d. In another experiment on the same table, the target ball B is replaced by target ball C of mass 0.10 kg. The incident ball A again slides at 1.4 m/s, as shown above left, but this time makes a glancing collision with the target ball C that is at rest at the edge of the table. The target ball C strikes the floor at point P, which is at a horizontal displacement of
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2001BAP - 163 2001 A ball of mass M is attached to a string...

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