Answer to Question #269497 in Physics for samantha

Question

A 3.56 kg block resting on a smooth horizontal surface is attached to a string that passes over a frictionless pulley as shown in the figure. The pulley has a radius of 0.28 m. A force of 7.5 N pulls the other end of the string. As a result, the block moves a distance of 0.2 m starting from rest. Find the (a) acceleration of the block, (b) angular acceleration of the pulley, and (c) moment of inertia of the pulley. 

Answer 1

Assume that the moving time is 1.5 s.

(a) $s=at^2/2\to a=2s/t^2=2\cdot0.2/1.5^2=0.18\ (m/s^2)$

(b) $\epsilon=a/r=0.18/0.28=0.64\ (rad/s^2)$

(c) $T=ma$

$Fr-Tr=Ia/r$

$Fr-mar=Ia/r\to I=\frac{r(Fr-mar)}{a}=$

$=\frac{0.28\cdot(7.5\cdot 0.28-3.56\cdot 0.18\cdot 0.28)}{0.18}=3\ (kg\cdot m^2)$