Question

Two balls of masses `2 kg` and `4 kg` are moved towards each other with velocities `4m//s` and `2m//s`, respectively, on a frictionless surface. After colliding, the `2kg` ball returns back with velocity `2m//s`. then find
a. velocity of the `4 kg` after collision
b. coefficient of restitution e,
c. impulse of deformation `J_(D)`
d. maximum potential energy of deformation,
e. impulse of reformation `J_(R)`

Answer 1

a. By momentum conservation,
`implies2(4)-4(2)=2(-2)+4(v_(2))`
`= v_(2)=1m//s`
b. `e=("velocity of separation")/("velocity of approach")=(-1(-2))/(4-(-2))=3/6=0.5`
c. AT the maximum deformed state, by coservation of momentum, common velocity is v=0.
`J_(D)=m_(2)(v-u_(2))=4[(0-(-2)]=8Ns`
d. Potential energy at the maximum deformed state.
`U=` loss in kinetic energy during deformation
or `U=(1/2m_(1)u_(1)^(2)+1/2m_(2)^(2))-1/2(m_(1)+m_(2))v^(2)`
`=(1/22(4)^(2)+1/24(2)^(2))-1/2(2+4)(0)^(2)=24J`
e. `J_(R)=m_(2)(v_(2)-v)=4(1-0)=4Ns`
also `J_(R)=eJ_(D)=0.5xx8=4Ns`