# Show that coefficient of restitution for one dimensional elastic collision is equal to one.

2
by vatsalyabaranwal

• Brainly User
2014-10-07T00:53:37+05:30
Let there be two bodies of mass M and m, let the body M be moving with velocity V and the body m be at rest.
Now when the body (M) will collide with the body (m) the KE would be conserved hence the body M will come to rest and body m will move with velocity V.
Putting the value of variables in the equation below;
e=
where V is velocity of separation of body M ,
v is velocity of separation of body m,
U is velocity of approach of body M,
u is velocity of approach of body m.
⇒ e=
since, v=U
⇒ e=1

Hence Proved
2014-10-09T14:16:44+05:30
The coefficient of restitution is a measure of the elasticity in a one-dimensional collision.* Its origin arises from the fact that during a perfectly elastic collision of two bodies, the velocity of approach is always equal to the velocity of separation, so that e = 1 in elastic collisions. In a perfectly inelastic collision the velocity of separation is zero, so that e = 0 in a totally inelastic collisions.
Type
Kinetic Energy
Restitution
Perfectly Elastic
Conserved
= 1
Partially Elastic
Not Conserved
0 < < 1
Perfectly Inelastic
Maximum Possible Loss
= 0
Hyperelastic
Energy Gained
> 1