Question

Two cars slide on the air track in Regener Hall. The blue car is on the left, has a mass m₁ = 5.00 kg, and is moving to the right with a velocity v₁i = 3.00m/s. The green car is on the right, has a mass m₂ = 2.50 kg, and is also moving to the right with an initial velocity v₂i = 2.00 m/s. The two cars collide. (a) If [the coefficient of restitution] B= 1, what are the final velocities of the two cars after the collision? How much energy is dissipated in the collision? (b) Repeat part (a) for the case that B= 0.5

Answer 1

a] Let final velocity be v1f and v2f. By momentum conservation,

m1v1f + m2v2f = m1v1i + m2v2i

5v1f + 2.5v2f = 5*3 + 2.5*2 = 20

or 2v1f + v2f = 8

also by coefficient of restitution, velocity of approach = velocity of separation/1

v2f - v1f = 1*(3-2) = 1

putting this, 3v1f + 1 = 8,

v1f = 2.33 m/s, v2f = 3.33 m/s

b) coefficient of restitution, velocity of approach = velocity of separation/0.5

3-2 = [v2f - v1f]/0.5

  v2f - v1f = 0.5 or v2f = v1f + 0.5

putting this in momentum equation, we get, 3v1f + 0.5 = 8

v1f = 2.5 m/s

v2f = 3 m/s