Question

A 1.10-kg ball, moving to the right at a velocity of +1.34 m/s on a frictionless table, collides head-on with a stationary 6.90-kg ball. Find the final velocities of (a) the 1.10-kg ball and of (b) the 6.90-kg ball if the collision is elastic. (c) Find the magnitude and direction of the final velocity of the two balls if the collision is completely inelastic.

Answer 1

Case 1 if collision is elastic

Using momentum conservation:

m1u1 + m2u2 = m1v1 + m2v2

m1 = 1.1 kg

m2 = 6.9 kg

u1 = + 1.34 m/sec

u2 = 0 m/sec

1.1*1.34 + 6.9*0 = 1.1*v1 + 6.9*v2

1.1*v1 + 6.9*v2 = 1.474

Now for elastic collision

v2 - v1 = u1 - u2

v2 = v1 + 1.34 - 0

1.1*v1 + 6.9*(v1 + 1.34) = 1.474

8*v1 = 1.474 - 6.9*1.34

v1 = (1.474 - 6.9*1.34)/8

(a) v1 = -0.972 m/sec

(b) v2 = -0.972 + 1.34 = +0.368 m/sec

When collision is inelastic

m1u1 + m2u2 = (m1 + m2)*V

(c)

V = (1.1*1.34 + 6.9*0)/8 = 0.184 m/sec