Physic Labs

Problem 1

A simple pendulum consists of a small bob of mass m=0.50m=0.50 kg on a light inextensible string of length L=1.25L=1.25 m attached to a fixed support. The string is displaced to one side until it makes 60∘60^\circ with the vertical and is released from rest. Neglect resistance and take g=10g=10 m/s2^2. (a) Find the bob's height above the lowest point just before release. (b) Find its speed through the lowest point. (c) Find the string tension there. (d) Find the angle to the vertical where kinetic energy equals potential energy above the lowest point.
problems.proof.stepOf
problems.proof.prevStepproblems.proof.nextStep
mgL(1−cos⁡60∘)=12mv02⇒v02=gL=12.5⇒v0=12.5=3.54 m/smgL(1-\cos60^\circ)=\frac12mv_0^2\Rightarrow v_0^2=gL=12.5\Rightarrow v_0=\sqrt{12.5}=3.54\ \mathrm{m/s}
problems.proof.analysis

Take potential energy zero at the bottom. Since release is from rest and tension is perpendicular to the displacement, it does no work; all lost potential energy becomes kinetic energy.