Question

Two objects with masses represented by m1 and m2 approach each other on a horizontal frictionless table with the same constant speed, v0, as measured by a laboratory observer. The objects undergo a perfectly elastic collision, and it is observed that after the collision, m2 moves off in a direction opposite its original motion with some constant speed v, and m1 is stationary. Determine the following.

(a) the ratio of the two masses, m1/m2

(b) the ratio of their speeds, v/v0

Answer 1

First we will solve part (b) and then part (a) -

(b) For an elastic head-on collision -

Relative velocity of approach = Relative velocity of separation,

Means -

v0 - (-v0) = v - 0

=> 2v0 = v

=> v / v0 = 2 (Answer)

(a) From conservation of momentum -

m1*v0 - m2*v0 = m1*0 + m2*v = m2*2*v0

Divide both sides by v0-

m1 = 2*m2 + m2 = 3*m2

=> m1/m2 = 3 (Answer)