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 and b. and the corresponding tensions in the string are T and Tb. It and I have magnitudes T and T. Find 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 and up should not appear in your final answer. View Available Hint(s) Tb-Tt= IVE ΑΣΦ ?

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Chapter1: Units, Trigonometry. And Vectors
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The image depicts a swinging pendulum in circular motion. The diagram shows a mass \( m \) attached to the end of a string with length \( L \). The mass is shown moving along a circular path, indicated by a dashed circle. An arrow suggests the direction of motion, showing the path of the mass as it moves clockwise in a circular trajectory. The pivot point from which the pendulum swings is marked at the center of the circle.
Transcribed Image Text:The image depicts a swinging pendulum in circular motion. The diagram shows a mass \( m \) attached to the end of a string with length \( L \). The mass is shown moving along a circular path, indicated by a dashed circle. An arrow suggests the direction of motion, showing the path of the mass as it moves clockwise in a circular trajectory. The pivot point from which the pendulum swings is marked at the center of the circle.
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 \( v_t \) and \( v_b \), and the corresponding tensions in the string are \( \vec{T}_t \) and \( \vec{T}_b \). \( \vec{T}_t \) and \( \vec{T}_b \) have magnitudes \( T_t \) and \( T_b \).

Find \( T_b - T_t \), 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 \( v_t \) and \( v_b \) should not appear in your final answer.

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Transcribed Image Text: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 \( v_t \) and \( v_b \), and the corresponding tensions in the string are \( \vec{T}_t \) and \( \vec{T}_b \). \( \vec{T}_t \) and \( \vec{T}_b \) have magnitudes \( T_t \) and \( T_b \). Find \( T_b - T_t \), 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 \( v_t \) and \( v_b \) should not appear in your final answer. [View Available Hint(s)] There is an input box for entering the solution, with formatting options for mathematical expressions, as well as a "Submit" button.
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