Question

A bullet of mass $20$g travelling horizontally with a speed of $500$ m/s passes through a wooden block of mass $10.0$kg initially at rest to 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 in the figure.$(g=10m/s^2)$

Answer 1

Mass of bullet , m = 0.02 kg

Initial velocity of bullet , v₁ = 500 m/s

Mass of block , M = 10 kg

Initial velocity of block , v₂ = 0

Final velocity of bullet , v₁' = 100 m/s

Let the final velocity of block when bullet comes out , if block = v'

mv₁ + Mv₂ = mv₁' + Mv'

0.02 x 500 = 0.02 x 100 + 10 x v'

v' = 0.8 m/s

After moving a distance 0.2 m it stops .

Change in Kinetic Energy = Work done

0 - 0.5 x 10 x (0.8)² = -μ x 10 x 10 x 0.2

μ = 0.16