Question

A $60kg$ man stands on a $15kg$ platform. A rope attached to the platform and passing over an overhead pulley allows the man to raise himself along with the platform. To get started, he pulls the rope down with a force of $400N$. Find the acceleration of the platform as well as that of the painter.

• A. $1.3m/s^2$
• B. $0.67m/s^2$
• C. $1m/s^2$
• D. $2.4m/s^2$

Answer 1

The correct option is B $0.67m/s^2$

The free body diagram of the painter and the platform as a system can be drawn as shown in the figure. Note that the tension in the string is equal to the force by which he pulls the rope.
Applying Newton's Second Law
$2T-(M+m)g=(M+m)a$ $ora=\frac{2T-(M+m)g}{M+m}$
Here $M=60kg$; $m=15kg$; $T=400N$
$g=10m/s^2$
$a=\frac{2\left(400\right)-(60+15)\left(10\right)}{60+15}=0.67m/s^2$