Three carts of masses m 1 = 5.00 kg, m 2 = 10.50 kg, and m 3 = 3.00 kg move on a

Question

Three carts of masses m1 = 5.00 kg, m2 = 10.50 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 = 5.50 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.

(b) Does your answer require that all the carts collide and stick together at the same moment?

What if they collide in a different order?

Explanation / Answer

(a) Take velocity towards the right to be positive, and the left to be negative:

m1v1 + m2v2 - m3v3 = (m1 + m2 + m3) vfinal

vfinal = (m1v1 + m2v2 - m3v3) / (m1 + m2 + m3)

= (5.00 kg x 4.50 m/s + 10.50 kg x 3.00 m/s - 3.00 kg x 5.50 m/s) / (5.00 kg + 10.50 kg + 3.00 kg)

= (22.5 kgm/s + 31.5 kgm/s - 16.5 kgm/s) / (18.50 kg) = 37.5 kgm/s / 18.50 kgm/s = + 2.027 m/s

The three carts move toward the right in the velocity of 2.027 m/s.

(b) No. The final momentum, and thus the final velocity, is only dictated by the respective masses and velocities of the carts.

(c) No. Same reason as above.

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