Question

A sphere of mass m is moving with a velocity 4i - when ithits a smooth wall and rebounds with velocity
i +3j. Find the impulse it receives. Find also the coefficient ofrestitution between the sphere and the wall.​

Answer 1

The final momentum is given as,

m

1

​

v

1

​

=m(i+3j)

The initial momentum is given as,

m

2

​

v

2

​

=m(4i−j)

The change in momentum is given as,

Δmv=m(i+3j)−m(4i−j)

Δmv=m(−3i+4j)

The component of the initial velocity along impulse is given as,

u=

9+16

​

(4i−j)(−3i+4j)

​

=−

5

16

​

The component of the final velocity along impulse is given as,

v=

9+16

​

(i+3j)(−3i+4j)

​

=

5

9

​

The coefficient of restitution between the sphere and the surface is given as,

e=

5

16

​

5

9

​

​

=

16

9

​

Thus, the coefficient of restitution between the sphere and the surface is

16

9

​

hope it helps.

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