A solid 0.7350 kg ball rolls without slipping down a track toward a vertical loop of radius R = 0.8950 m. What minimum translational speed vmin must the ball have when it is a height H = = 1.353 m above the bottom of the loop in order to complete the loop without falling off the track? Assume that the radius of the ball itself is much smaller than the loop radius R. Use g = 9.810 m/s? for the acceleration due to gravity.

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Physics Problem Description**

A solid 0.7350 kg ball rolls without slipping down a track toward a vertical loop of radius \( R = 0.8950 \) m. What minimum translational speed \( v_{\text{min}} \) must the ball have when it is at a height \( H = 1.353 \) m above the bottom of the loop in order to complete the loop without falling off the track?

Assume that the radius of the ball itself is much smaller than the loop radius \( R \). Use \( g = 9.810 \, \text{m/s}^2 \) for the acceleration due to gravity.

\[ v_{\text{min}} = \quad \text{m/s} \]

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**Diagram Explanation**

The diagram accompanying the problem illustrates a track with a ball positioned on it. The track includes an upward slope leading into a loop. The loop is depicted as a circle with radius \( R \). The height \( H \) is marked with a vertical line from the bottom of the loop to the point on the track where the ball is released. There is also a label indicating that the figure is not to scale. The diagram visually represents the situation described in the text, showing the ball's starting position and the configuration of the loop.
Transcribed Image Text:**Physics Problem Description** A solid 0.7350 kg ball rolls without slipping down a track toward a vertical loop of radius \( R = 0.8950 \) m. What minimum translational speed \( v_{\text{min}} \) must the ball have when it is at a height \( H = 1.353 \) m above the bottom of the loop in order to complete the loop without falling off the track? Assume that the radius of the ball itself is much smaller than the loop radius \( R \). Use \( g = 9.810 \, \text{m/s}^2 \) for the acceleration due to gravity. \[ v_{\text{min}} = \quad \text{m/s} \] --- **Diagram Explanation** The diagram accompanying the problem illustrates a track with a ball positioned on it. The track includes an upward slope leading into a loop. The loop is depicted as a circle with radius \( R \). The height \( H \) is marked with a vertical line from the bottom of the loop to the point on the track where the ball is released. There is also a label indicating that the figure is not to scale. The diagram visually represents the situation described in the text, showing the ball's starting position and the configuration of the loop.
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