A `4.00g` bullet travelling horizontally with a velocity of magnitude `500m//s` is fired into a wooden block with a mass of `1.00kg`, initially at rest on a level surface. The bullet passes through the block and emerges with speed `100m//s`. The block slides a distance of `0.30m` along the surface from its initial position.
(a) What is the coefficient of kinetic friction between block and surface?
(b) What is the decrease in kinetic energy of the bullet?
(c) What is the kinetic energy of the block at the instant after the bullet has passed through it? Neglect friction during collision of bullet with the block.

Answer

A, B, C, D

Explanation

(a) `p_i=p_f`
`:. mv_0=mv_1+mv_2`
`:. v_2=(mv_0-mv_1)/(M)`
`=((0.004)(500-100))/(1.0)`
`=1.6m//s`
Retardation due to friction,
`a=(mumg)/(m)=mug=(10mu)`
`s=(v_2^2)/(2a)=(v_2^2)/(20mu)`
`:. mu=(v_2^2)/(20s)`
`=((1.6)^2)/(20xx0.3)=0.43`
(b) Decrease in kinetic energy of bullet
`=1/2m(v_0^2-v_1^2)`
`=1/2xx0.004[(500)^2-(100)^2]`
`=480J`
(c) Kinetic energy of block,
`=1/2Mv_2^2`
`=1/2xx1.0xx(1.6)^2`
`=1.28J`