Chapter 7, Problem 106P

(a)

To determine

To show: That the tangential component of Newton’s second law gives $dv/dt=-g\sin \theta$ .

(b)

To determine

To show: That the $v$ can be written as $v=Ld\theta /dt$

(c)

To determine

The expression $\frac{dv}{dt}=\frac{dv}{d\theta }\frac{v}{L}$ using resultsin part (b).

(d)

To determine

Combine the results of parts (a) and (c) to obtain $vdv=-gL\sin \theta d\theta$ .

(e)

To determine

To show: the result of part (d) is equivalent to $v=\sqrt{2gh}$ .