Question

A bullet of mass 20 g horizontally with a speed of 500 m/s passes through a wooden block of mass 10.0 kg initially at rest on a level surface.The bullet emerges with a speed of 100 m/s and the block slides 20 cm on the surface before coming to rest.Find the friction coefficient between the block and the surface.

Answer 1

Mass of bullet m=0.02 kg

Initial velocity of bullet $V_1=500m/s$

Mass of block, M=10 kg

Initial velocity of block=$U_2=0$

Final velocity of bullet= $100m/s$

= v

Let the final velocity of block when the bullet emerges out,if block=$v^1$

Using conservation of energy, $m{v}_1+M{u}_2=mv+M{v}^1$

$\Rightarrow 0.02\times 500=0.02\times 100+10\times v^1$

$\Rightarrow v^1=0.8m/sec$

After moving a distance 0.02 m it stops.

$\Rightarrow$ Change in K.E.=Work done

$\Rightarrow 0-\left(\frac{1}{2}\right)\times 10\times (0.8{)}^2=M\times 10\times 10\times 0.2$

$\Rightarrow M=0.16$