Problem 1
A simple pendulum of length carries a small mass . It is displaced to angle 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.
problems.proof.stepOf
problems.proof.analysis
Solving the energy relation gives the speed; mass cancels because gravity and inertia scale together. This is consistent with the stated model and the chosen sign convention.
problems.proof.pitfall. At the lowest point centripetal acceleration points upward, so .