Two blocks of masses m 1 = 2.10 kg and m 2 = 4.20 kg are each released from rest

Question

Two blocks of masses m1 = 2.10 kg and m2 = 4.20 kgare each released from rest at a height of h = 4.90 m on a frictionless track, as shown in the figure below, and undergo an elastic head-on collision. (Let the positive direction point to the right. Indicate the direction with the sign of your answer.)

(a) Determine the velocity of each block just before the collision.

(b) Determine the velocity of each block immediately after the collision.

(c) Determine the maximum heights to which m1and m2 rise after the collision.

y1f =

y2f =

v1i =

v2i =

Explanation / Answer

part a )

v1i = sqrt(2gh) = 9.8 m/s

v2i = sqrt(2gh) = -9.8 m/s

part b )

y using ellastic collision formuaa

v1f = [(m1-m2)v1i / (m1+m2) ] + [2m2 v2i / (m1+m2) ]

v1f = -16.33 m/s

v2f = 2m1v1i / (m1+m2) + (m2- m1) v2i / (m1+m2)

v2f = 3.267 m/s

part c )

using energy conservation

mgh = 1/2 * mv^2

h = v^2/2g

y1f = v1f^2/2g

y1f = 13.61 m

y2f = v2f^2/2g

y2f = 0.545 m

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