Two carts with masses of 4kg and 3kg move toward each other on a frictionless track with speeds of 5.0m/s and 4.0 m/s respectively. The carts stick together after the colliding head on. Find the final speed of the carts.

1.143 m/s

Explanation:

From the law of conservation of momentum,

Total momentum before collision = Total momentum after collision

mu+m'u' = V (m+m') ... Equation 1

Given: m = mass of the first cart, m' = mass of the second cart, u = initial velocity of the first cart, u' = initial velocity of the second cart, V = Final Velocity of the Carts

Making V the subject of the equation,

V = (mu+m'u') / (m+m') ... Equation 2

Given: m = 4 kg, m' = 3 kg, u = 5 m/s, u' = - 4 m/s

Note: Before collision both cart were not moving in the same direction. Assuming the first cart is moving to the left and the second cart is moving to the right.

Substitute into equation 2,

V = [4*5 + 3 * (-4) ] / (4+3)

V = (20-12) / 7

V = 8/7

V = 1.143 m/s.

Hence their final speed after collision = 1.143 m/s