Physic Labs

Problem 1

A simple pendulum of length ℓ\ell carries a small mass mm. It is displaced to angle θ0\theta_0 and released from rest. Neglect resistance. Find its speed and string tension at the lowest point. Assume the string, pulley, electrical source, or optical apparatus is ideal as stated, and neglect any effect not specified. State a clear sign convention, identify the physical Keep one model and sign convention throughout. Reuse each intermediate result with the same convention, then check that the answer has the required physical dimensions. (a) Set up the physical relation. (b) Find an intermediate quantity. (c) Obtain the answer and check its conditions and units.
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Δh=ℓ(1−cos⁡θ0)\Delta h=\ell(1-\cos\theta_0)
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The bob drops by ℓ(1−cos⁡θ0)\ell(1-\cos\theta_0) between release and the lowest point. This is consistent with the stated model and the chosen sign convention.