A ball of mass m is attached to a string of length L. It is being swung in a vertical circle with enough speed so that the string remains taut throughout the ball's motion. (Figure 1)Assume that the ball travels freely in this vertical circle with negligible loss of total mechanical energy. At the top and bottom of the vertical circle, the ball's speeds are vt and vb, and the corresponding tensions in the string are T⃗ t and T⃗ b. T⃗ t and T⃗ b have magnitudes Tt and Tb. Find Tb−Tt, the difference between the magnitude of the tension in the string at the bottom relative to that at the top of the circle. Express the difference in tension in terms of m and g. The quantities vt and vb should not appear in your final answer.
A ball of mass m is attached to a string of length L. It is being swung in a vertical circle with enough speed so that the string remains taut throughout the ball's motion. (Figure 1)Assume that the ball travels freely in this vertical circle with negligible loss of total mechanical energy. At the top and bottom of the vertical circle, the ball's speeds are vt and vb, and the corresponding tensions in the string are T⃗ t and T⃗ b. T⃗ t and T⃗ b have magnitudes Tt and Tb. Find Tb−Tt, the difference between the magnitude of the tension in the string at the bottom relative to that at the top of the circle. Express the difference in tension in terms of m and g. The quantities vt and vb should not appear in your final answer.
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter11: Angular Momentum
Section: Chapter Questions
Problem 11.53AP
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A ball of mass m is attached to a string of length L. It is being swung in a vertical circle with enough speed so that the string remains taut throughout the ball's motion. (Figure 1)Assume that the ball travels freely in this vertical circle with negligible loss of total mechanical energy. At the top and bottom of the vertical circle, the ball's speeds are vt and vb, and the corresponding tensions in the string are T⃗ t and T⃗ b. T⃗ t and T⃗ b have magnitudes Tt and Tb.
Find Tb−Tt, the difference between the magnitude of the tension in the string at the bottom relative to that at the top of the circle.
Express the difference in tension in terms of m and g. The quantities vt and vb should not appear in your final answer.
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