The blocks shown in figure have equal masses. The surface of A is smooth but that of B has a friction coefficient of 0.10 with the floor. Block A is moving at a speed of 10 m/s towards B which is kept at rest. Find the distance travelled by B if a. the collision is perfectly elastic and b. the collision is perfectly inelastic. Take `g=10 m/s^2`.

Explanation

`V_1=10 m/s`
`V_2=0`
`v_1, v_2rarr` velcity of A and B after collision a. if the collision is perfectly elastic
`mV_1+mV_2=Mv_1+mv_2`
`rarr 10+0=v_1+v_2`
`v_1+v_2=10`…..i
Again `v_1+v_2=-(u_1-v_2)`
`=-(10.0)=-10`…ii
Substracting ii frm ii
`2v_2=20`
`rarr v_2=10 m/s`
the deceleration of B
`putting work energy principle
`:.(1/2)xxmxx(0)^2-91/2)xxmxxv^2`
`=-mxxaxxh`
`rarr -(1/2)xx (10)^2=-mugxxh
`rarr h=100/(2xx1xx10)=50m`
b. if the collision is perfectly in elastic
`mxxu_1+mxxu_2=(m+m)xxv`
`rarr mxx10+mxx0=2mxxv`
`rarr v=(10/2)=5m/s`
The two blocks will move together sticking to each other
`:. Putting work energy principle
`(1/2)xx2mxx(0)^2xx2mxx(v)^2`
`=2mxxmugxxs`
`rarr ((5)^2)/(0.1xx10xx2)=S`
`=S=12.5m`