a particle of mass m1 moving with a velocity u makes a head-on elastic collision with a particle of...

Question

a particle of mass m1 moving with a velocity u makes a head-on elastic collision with a particle of mass 2m initially at rest.Show that the particle of mass m1 loses (8/9)th of initial kinetic energy in the collision.

Robert · Accepted Answer

TTs250812_pau35854_1.dvi
Suppose the velocity of m1 after the collision is v
′, since now it is with the second artile, we know from the
theorem of momentum:
mv + 0 ∗ 2m = (m+ 2m)v′ ⇒ v′ =
1
3
v
As a result, the energy of m1 has changed from e = 0.5mv
2 to 0.5m ∗ (v/3)2 = 1
9
e.

a particle of mass m1 moving with a velocity u makes a head-on elastic collision with a particle of mass 2m initially at rest.Show that the particle of mass m1 loses (8/9)th of initial kinetic energy...

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