Question

A load W is suspended from a self-propelled crane by a cable of length $d$. The crane and load are moving at constant speed $v_0$. The crane is stopped by the bumper and load on the cable swings. Given that the angle of swing is ${60}^o$ and $d=5m$. lf the initial velocity of the crane is $v_0$ m/s, find $v_0$.

Answer 1

The energy of load is conserved
$\Rightarrow \frac{1}{2}\left(\frac{W}{g}\right)v_0^2+0=0+W(d-d\cos \theta )$

$\Rightarrow v_0^2=2gd(1-\cos \theta )$

$=4gd{\sin }^2\frac{\theta }{2}$

$\Rightarrow v_0=2\sqrt{gd}\sin \frac{\theta }{2}$

Given:$d=5m,\theta ={60}^0$

$\Rightarrow v_0=2\sqrt{\left(9.8\right)\left(5\right)}\sin {30}^0$

$=7m/s$