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Published byJustina Carson Modified over 2 years ago

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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.

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(a) On the figures below, draw and label all the forces exerted on the ball when it is at points P and Q, respectively. T T mg mg 4 points - One point for each correctly drawn and labeled force

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T mg 1 point - Summing forces 1 point - Identifying that the only force is that due to gravity 1 point - Expression for centripetal acceleration 1 point - Correct answer (b) Derive an expression for vmin, the minimum speed the ball can have at point Z without leaving the circular path R

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(c) The maximum tension the string can have without breaking is Tmax, Derive an expression for vmax, the maximum speed the ball can have at point Q without breaking the string R 1 point - Summing forces 1 point - Indicating that Tmax is larger that mg 1 point - Subtracting forces 1 point - Correct answer 1 point - Expression for centripetal acceleration Tmax mg

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(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. 1 point - Velocity is upward 1 point - Ball would be slowing down The ball has an initial upward velocity and a downward acceleration.

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