A ball of mass 2m impinges directly on a ball of mass m, which is at rest .If the velocity with which the larger ball impinges be equal to the velocity of the smaller mass after impact then the coefficient of restitution
Asked by m.nilu
22nd September 2018,
2:26 PM
Answered by Expert
Answer:
Let u1 be the speed of ball whose mass is 2m, before collision. Ball of mass m is at rest.
Let v1 be the speed of ball whose mass is 2m, after collision.
Let v2 be the speed of ball whose mass is m, after collision.
coefficient of restitution e is given by, v1 - v2 = -e×u1 ...............(1)
since it is given that v2 = u1, we write eqn.(1) as v1 - u1 = -e×u1 or v1 = (1-e)×u1 ................(2)
By momentum conservation, 2m×u1 = 2m×v1 + m×v2 = 2m×v1 + m×u1 ..............(3)
from eqn.(3), we get v1 = (1/2) u1 ..............(4)
from eqn.(2) and eqn.(4) we get, e = 1/2
Answered by Expert
23rd September 2018,
10:37 PM
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