Question

The $9kg$ cradle is supported as shown by two uniform disks that roll without sliding at all surfaces of contact. The mass of each disk is $m=6kg$ and the radius of each disk is $r=80mm$. Knowing that the system is initially at rest, determine the velocity of the cradle after it has moved $250mm.$

Answer 1

In rolling without sliding on a stationary ground,work done by friction is zero. Hence work done by the applied force
$=$ change in kinetic energy
$\therefore \left(30\right)\left(0.25\right)=\frac{1}{2}\times 9\times v_2$
$+2[\frac{1}{2}\times 6\times v^2+\frac{1}{2}\times \frac{1}{2}\times 6\times r^2\times \frac{v^2}{r^2}]$
or $7.5=13.5v^2$ $\therefore v=0.745m/s$