Three carts of masses m1 = 5.00 kg, m2 = 8.50 kg, and m3 = 3.00 kg move on a fri

Question

Three carts of masses m1 = 5.00 kg, m2 = 8.50 kg, and m3 = 3.00 kg move on a frictionless, horizontal track with speeds of v1 = 4.00 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.(Please provide numerical answer in m/s).

(b) Does your answer require that all the carts collide and stick together at the same moment? (Yes or No)

(c)What if they collide in a different order?

Explanation / Answer

a) m1v1 + m2v2 + m3v3 = (m1+m2+m3)vf
(5)(4) + (8.5)(3) - (3)(6) = (5+8.5+3)(vf)
vf = (5)/(3)
vf = 1.6666 m/s

b)
No, because there is no deceleration due to friction, resulting in no resisting force, hence the formula does not involve time.

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