A car (mass 1 kg) on a frictionless track collides with a stationary car (mass 0.5 kg). The velocity of the first car before the collision is 2 m/s. The velocity of the 1st car after the collision is 1 m/s. (a) What is the velocity of the second car? (b) Was the collision elastic? i. Yes ii. No

(a) 2 m/s

(b) Not elastic

Explanation:

m1 = 1 kg, m2 = 0.5 kg

u1 = 2 m/s, u2 = 0

v1 = 1 m/s, v2 = ?

(a) Let the velocity of second car after collision is v2.

By the use of conservation of momentum,

m1 u1 + m2 u2 = m1 v1 + m2 v2

1 x 2 + 0 = 1 x 1 + 0.5 x v2

2 = 1 + 0.5 v2

v2 = 2 m/s

Thus, the velocity of second car after collision is 2 m/s.

(b) The collision is said to be elastic if the kinetic energy is also conserved.

Kinetic energy before collision = 1/2 m1 u1^2 + 1/2 m2 u2^2

= 0.5 x 1 x 4 + 0 = 2 J

Kinetic energy after collision = 1/2 m1 v1^2 + 1/2 m2 v2^2

= 0.5 x 1 x 1 + 0.5 x 0.5 x 4 = 1.5 J

Here, kinetic energy is conserved, so the collision is not elastic.