Question

A ball moving with a speed of `9m//s` strikes an identical ball at rest, such that after the collision, the direction of each ball makes an angle of `30^(@)` with the original line of motion. Find the speeds of the two balls after collision.

Answer 1

Here,`u_(1)=9m//s,u_(2)=0`
Applying principle of conservation of linear momentum, Figure.
(i) along X- axis
`mxx9+mxx0=m upsilon_(1)cos30^(@)+m upsilon_(2)cos30^(@)`
`mxx9=m(sqrt(3))/(2)(upsilon_(1)+upsilon_(2))`
`:. upsilon_(1)+upsilon_(2)=(18)/(sqrt(3))=6sqrt(3)` ..(i)
(ii) along Y-axis
`mxx0+mxx0=m upsilon_(1)sin 30^(@)-m upsilon_(2)sin30^(@)`
`0=m(upsilon_(1)-upsilon_(2))xx(1)/(2), upsilon_(1)upsilon_(2)=0, upsilon_(1)=upsilon_(2)`
From (i) , `upsilon_(1)=upsilon_(2)=3sqrt(3)m//s`
Total KE befroe collision
`=(1)/(2)m(3sqrt(3))^(2)+(1)/(2)m(3sqrt(3))^(2)=27m`
which is less than total KE before collision.
`:.K.E.` is not conserved.