Question

A $250g$ block slides on a rough horizontal table. Find the work done by the frictional force in bringing the block to rest if it is initially moving at a speed of $40cm/s$. If the friction coefficient between the table and the block is $0.1$, how far does the block move before coming to rest?

Answer 1

Given, Initial velocity$=40cm/s=0.4m/s$, Mass $m=250g=0.25kg$, $\mu =0.1$

Using Work-Energy theorem, Total work done= change in kinetic energy

$\therefore$ Work done by friction $\left(W_f\right)=\Delta KE$

$\Rightarrow W_f=0-\frac{1}{2}m{v}^2=-0.02J$

Let it travels distance $s$ before coming to rest. retardation $a=\mu g=0.1\times 10=1m/s^2$,

Using $v^2=u^2+2as$

$\Rightarrow 0={.4}^2-2\times 1\times s$ $\Rightarrow s=0.08m=8cm$