Question

A man of mass $50kg$ is pulling on a plank of mass $100kg$ on a smooth floor as shown with force of $100N$. If both & plank move together, find the force of friction acting on man.

• A. $\frac{100}{3}N$ towards left
• B. $\frac{100}{3}N$ towards right
• C. $\frac{250}{3}N$ towards left
• D. $\frac{250}{3}N$ towards right

Answer 1

The correct option is A $\frac{100}{3}N$ towards left

The man is standing on the plank then he is pulling the rope towards himself. He pushes forward with the legs so that pushes the plank "rope backwards

So that friction $f$ acts in forward direction the plank.

The tension $T$ in the rope is $100N$ the fiction force $f$ newtons.

Man's $F_{\text{net}}\Rightarrow T-F=ma$

$F_{\text{net}\left(\mathrm{man}\right)}\Rightarrow T-F=50a$

$Plank$ Fnet $\Rightarrow T+f=ma$

$F_{\text{net}}($ plank$)\Rightarrow T+f=\mathrm{lov}a$

As $T=100N$

$a=\frac{4}{3}m/s^2$

$f=\frac{100}{3}$ newton

(A) $\frac{100}{3}N$ towards left