Question

Arrive at an expression for elastic collision in one dimension and discuss various cases. ​

Answer 1

Explanation:

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Class 11

>>Physics

>>Work, Energy and Power

>>Collisions in One Dimension

>>Show that in case of one - dimensional e

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Show that in case of one-dimensional elastic collision of two bodies, the relative velocity of separation after the collision is equal to the relative velocity of approach before the collision.

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Solution

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Refer image.

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

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