A cart of mass m traveling in the X-direction at a speed v collides head-on with

Question

A cart of mass m traveling in the X-direction at a speed v collides head-on with a cart that has triple the mass and is moving in the positive x-direction at 80% of the speed of the first cart. The carts stick together after the collision. At what speed did they move? Assume vf is the final speed. A cart of mass m traveling in the X-direction at a speed v collides head-on with a cart that has triple the mass and is moving in the positive x-direction at 80% of the speed of the first cart. The carts stick together after the collision. At what speed did they move? Assume vf is the final speed.

Explanation / Answer

mass of the 1st cart = m

speed = v

momnetum   = mv   ( +ve x-direction)

mass of the second cart = 3m   ( 3 times the first cart)

speed of the sceond cart = 0.8v   (80 % o of the first cart)

momnetum of the scond cart = 3m*0.8v = 2.4mv

It is a non-elastic collision as the carts stick together after collision.

Only momnetum is conserved

Total momneutm before collision = mv + 2.4mv = 3.4 mv

if vf is the final speed of the carts together thenmomnetum after collision

                          = (m+3m) vf   = 4mvf

conserving the momentum

4mvf = 3.4mv

vf = 3.4 v/4 = 0.85 v

The cart together move at 85% of the speed of the first cart before collision.

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