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PhysicsClassical Physics

Mechanical Energy Sample: Speed and Tension in a Vertical Circle

Use mechanical energy to obtain the top speed, then radial force balance to obtain string tension: about 4.65 m/s at the top, 59.8 N at the bottom, and 1.0 N at the top.

Question

A ball of mass 1.0 kg is attached to a string 2.0 m long and moves in a vertical plane. Its speed at the lowest point is 10 m/s.

(a) Determine its speed at the highest point of the circular path. (b) Determine the string tension at both the lowest and highest points.

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Evidence boundary

This is the ideal-model solution of OpenStax University Physics Volume 1, Chapter 8, Problem 34. A massless inextensible string, fixed pivot, and negligible air resistance are the mechanics assumptions; g = 9.80 m/s² is explicitly chosen because the exercise does not supply g. The positive top tension verifies the taut-string assumption. These are theoretical results, not measured motion or a teacher key.