A 60kg painter on a 15 kg platform. A rope attached to the platform and passing over an overhead pulley allows the painter to raise himself along with the platform.

To get started, he pulls the rope down with aforce of 400N. Find the acceleration of the platform as well as that of the painter.

Explanation

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`
or `a=(2T-(M+m)g)/(M+m)`
Here `M=60Kg,m15Kg,T=400N`
`g=10m//s^(2)`
`a=(2(400)-(60+15)(10))/(60+15)=0.67m//s^(2)`