Question

Cart 1 with inertia (mass) 1 kg and initial velocity 1 m/s collides on a frictionless track with cart 2, with initial velocity 1/3 m/s. If the final velocity of cart 1 is, 1/3 m/s and the final velocity of cart 2 is 2/3 m/s:

a. Is this a perfectly elastic collision?

b. What is the mass of cart 2?

please provide explanation

Answer 1

a)

e is usually a positive, real number between 0 and 1:

e = 0: This is a perfectly inelastic collision. This means kinetic energy along the common normal is 0. Kinetic energy is converted to heat or work done in deforming the objects.

0 < e < 1: This is a real-world inelastic collision, in which some kinetic energy is dissipated.

e = 1: This is a perfectly elastic collision, in which no kinetic energy is dissipated, and the objects rebound from one another with the same relative speed with which they approached.

BUT as given the values of the relative velocities we find that the value of co-efficient of restitution , e= 1/2 .

So, it is not a perfectly elastic collision.

b) The conservation of the total momentum before and after the collision is expressed by:

as given in the question : m₁ = 1kg, let m₂= m , u₁ = 1m/s , u₂ = 1/3 m/s , v₁ = 1/3 m/s , v₂ = 2/3 m/s

putting all the values in the equation we get ,

m= 2 .