Three carts of masses 4.00kg, 10.00kg, and 3.00kg move on a frictionless, horizo

Question

Three carts of masses 4.00kg, 10.00kg, and 3.00kg move on a frictionless, horizontal track with speeds of 5.00 m/s, 3.00 m/s, and 4.00 m/s. Velcro couplers make the carts stick together after colliding. Find hte final velocity of the train of three carts. (image attached)

A ballistic pendulum is an apparatus used to measure the speed of a fast-moving projectile such as a bullet. A bullet of mass m1 is fired into a large block of wood of mass of m2 suspended from some light wires. The bullet embeds in the block, and the entire system swing through a height h. Determine the speed (unknown) of the bullet from the height h. Three carts of masses 4.00 kg. 10.0 kg, and 3.00 kg move on a frictionless, horizontal track with speeds of 5.00 m/s. 3.00 m/s, and 4.00 m/s as shown in figure. Velcro couplers make the carts stick together after colliding. Find the final velocity of the train of three carts.

Explanation / Answer

initial momentum= 4*5 +10*3 - 3*4= +38 kg-m/s

by conservation of momentum

final momentum = initial momentum

==> (m1+m2)m3)*v= 38 kg-m/s

==>17 *v =38 kg-m/s

==> v = +2.235 m/s (to the right)

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