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) acceleration

$s=\frac{at^2}{2}\to a=\frac{2s}{t^2}$

$a=\frac{2×0.2}{1.5^2}=0.18\ (m/s^2)$

(b) angular acceleration

$ϵ=\frac{a}{r}=\frac{0.18}{0.28}=0.64 (rad/s^2)$

(c) moment of inertia

T=ma

$Fr-Tr=\frac{Ia}{r}$

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

$I=\frac{0.28[(7.5×0.28)-(3.56×0.18×0.28)]}{0.18}=3\ (kg/ m^2)$