Two blocks of masses m1 = 2.15 kg and m2 = 4.30 kg are each released from rest a

Question

Two blocks of masses m1 = 2.15 kg and m2 = 4.30 kg are 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 m1 and m2 rise after the collision.

y1f =

y2f =

v1i =

v2i =

Explanation / Answer

Since there is no friction, velocity is independent of the mass of the object.
Both has a velocity v = 2gh = (19.6*4.9 = 9.8 m/s
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Since there is no friction, the collision is elastic.
Choosing a reference frame riding with the right side mass,
Velocity of approach = 9.8+9.8 = 19.6
v1’ = (m1-m2) u1/ (m1+m2) = (2.15 - 4.3)* 19.6/ (6.45) = -6.53 m/s
v2’ = 19.6 – 6.53 =13.07 m/s
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In the ground reference frame,
The final velocity of 2.15 kg is -6.53 - 9.8 = -16.33 m/s
The final velocity of 4.3 kg is 13.07 – 9.8 = 3.27 m/s
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Height is found using
h =v^2/ 2g
The height of 2.15 kg is 16.33^2/(19.6) = 13.6 m
The height of 4.3 kg is 3.27^2/(19.6) = 0.546 m

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