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Question

Two balls of equal mass undergo head-on collision while each was moving with a speed of 6m/s. If the coefficient of restitution is 1/3, the speed of each ball after impact will be


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Solution

Step 1: Given data

Speed,

u1=6ms

u2=-6ms

Coefficient of restitution is 13.

Step 2: To find

Speed of each ball after impact

Step 3: Calculate the speed of the ball

There is no external force acting, momentum will be conserved.

m1u1+m2u2=m1v1+m2v2m×6-m×6=mv1+mv2v1=-v2 …(1)

Here, u1,u2 are velocity of balls before impact and v1,v2 are velocity of balls after impact. m1,m2 are mass of balls.

e=v2-v1u1-u213=v2-v1u1-u2 …(2)

Here e is a coefficient of restitution.

After solving equations (1) and (2) get the values of speeds are

v1=-2msv2=2ms

Hence, speed of balls are -2ms and 2ms.


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