A block moving horizontally on a smooth surface with a speed of 20 m/s bursts into two equal parts continuing in the same direction. If one of the parts moves at 30 m/s, with what speed does the second part move and what is the fractional change in the kinetic energy?

Explanation

Applying momentum conservation ,
`m xx 20=(m)/(2)V+(m)/(2)xx30`
`rArr 20=(V)/(2)+15`
So, `V=10m//s`
initial kinetic energy `=(1)/(2)m xx (20)^(2)=200 m`
final kinetic energy `=(1)/(2).(m)/(2). (10)^(2)+(1)/(2)xx(m)/(2)(30)^(2)`
`=25m +225 m =250m`
fractional change in kinetic energy `=(("final K.E")-("initial K.E"))/("initial K.E")=(250m-200m)/(200m)=(1)/(4)`