Problem 1

A simple pendulum consists of a small bob of mass

m=0.50

kg on a light inextensible string of length

L=1.25

m attached to a fixed support. The string is displaced to one side until it makes

60^\circ

with the vertical and is released from rest. Neglect resistance and take

g=10

m/s

^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.prevStep problems.proof.nextStep

K=U\Rightarrow \frac12mv^2=mgy,\quad mgh_0=\frac12mv^2+mgy\Rightarrow y=h_0/2

problems.proof.analysis

The total mechanical energy is $mgh_0$ . If $K=U$ , each form carries half of it, so the required height is $h_0/2$ above the lowest point.