Three carts of masses m1 = 4.50 kg, m2 = 12.00 kg, and m3 = 3.00 kg move on a fr

Question

Three carts of masses m1 = 4.50 kg, m2 = 12.00 kg, and m3 = 3.00 kg move on a frictionless, horizontal track with speeds of v1 = 4.50 m/s to the right, v2 = 3.00 m/s to the right, and v3 = 6.00 m/s to the left, as shown below. Velcro couplers make the carts stick together after colliding. (a) Find the final velocity of the train of three carts. magnitude Your response differs from the correct answer by more than 100%. m/s direction (b) Does your answer require that all the carts collide and stick together at the same moment? Yes No What if they collide in a different order?

Explanation / Answer

apply the conservation of momentum

consider the left as positive direction

initial momentum = 4.5 x 4.5 + 12 x 3 - 3 x 6

= 38.25 kg m/s

let us assume that finally all the carts stick together and move with a velocity v towards left

so final momentum = 19.5 x v

initial momentum = final momentum

19.5 x v = 38.25

v = 1.962 m/s towards left

it doesnt matter in what order the collisions take place as the momentum remains conserved through out the motion

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