How do you solve for impulse in a system where both carts are moving in the same direction and they collide?

Question

Hi So my question is as follows: there is a 34kg mass and a 81kg mass on a track. they collide, where both are moving in the same direction, and have a final velocity of 0.9m/s. the 34kg block's velocity is unknown (it is at the back), and the 81kg block's initial velocity is 0.5m/s. The surface is frictionless. I need help finding the magnitude of the impulse for the 34kg block due to collision.

Answer 1

If I understood the problem in a right way, after the collision two carts moved with the same speed

v = 0.9 m/s. It means this is inelastic collision and then we can write the law of conservation of linear momentum as

m₁v₁ + m₂v₂ =( m₁ + m₂)v ,

here

m₁v₁ - linear momentum of the first body before the collision,

m₂v₂ - linear momentum of the second body before the collision

( m₁ + m₂)v - linear momentum of the 2 bodies after the collision

From this equation the momentum of the first body

p₁ = ( m₁ + m₂)v - m₂v₂



Just put in this equation all known values and you are done!