In elastic collisions, total kinetic energy and momentum are both conserved. On a frictionless track, cart 1 is moving with a constant, rightward (+) velocity of 1.0m/s. Cart 2 is also moving rightward with constant velocity of 5.0m/s. After a while, cart 2 collides cart 1 from behind. (It is an elactic collision.) If the final velocity of cart 2 becomes 3.0m/s, what is the final velocity of cart 1? (SHOW ALL YOUR WORK.)

Question

Physics

Daniel

27 September, 10:12

In elastic collisions, total kinetic energy and momentum are both conserved. On a frictionless track, cart 1 is moving with a constant, rightward (+) velocity of 1.0m/s. Cart 2 is also moving rightward with constant velocity of 5.0m/s. After a while, cart 2 collides cart 1 from behind. (It is an elactic collision.) If the final velocity of cart 2 becomes 3.0m/s, what is the final velocity of cart 1? (SHOW ALL YOUR WORK.)

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Vegas · Answer 1

mass of cart 1, m1 = m

mass of cart 2, m2 = m

initial velocity of cart 1, u1 = 1 m/s

initial velocity of cart 2, u2 = 5 m/s

final velocity of cart 2, v2 = 3 m/s

Let the final velocity of cart 1 is v1.

Use the conservation of momentum

m1 x u1 + m2 x u2 = m1 x v1 + m2 x v2

m x 1 + m x 5 = m x v1 + m x 3

6 = v1 + 3

v1 = 3 m/s