Question

define one dimensional elastic collision, prove that in elastic collision velocity of approach equal to velocity of separation? ​

Answer 1

Explanation:

Work, Energy and Power. Show that in one dimension elastic collision, velocity of separation is equal to the velocity of approach. i.e. relative velocity of approach is equal to relative velocity of separation.

Here, for collision to happen, V

1

>V

2

velocity of approach =U

1

−U

2

[velocity w.r.t]

velocity of separation =V

2

−V

2

[vel.w.r.t]

As we know,

Coefficient of restitution (e) =

vel.ofapproach

vel.ofseperation

∴e=

U

1

−U

2

V

2

−V

1

........(1)

and, e=1 for elastic collision.

1=

U

1

−U

2

V

2

−V

1

U

1

−U

2

=V

2

−V

1

.

So,

velocity of approach=velocity of separation