Two blocks of masses m1 = 1.85 kg and m2 = 3.70 kg are each released from rest a

Question

Two blocks of masses m1 = 1.85 kg and m2 = 3.70 kg are each released from rest at a height of h = 5.50 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.) mi m2 (a) Determine the velocity of each block just before the collision. m/s m/s (b) Determine the velocity of each block immediately after the collision. m/s m/s (c) Determine the maximum heights to which m1 and m2 rise after the collision

Explanation / Answer

Given,

Masses, m1= 1.85 kg, m2 = 3.70 kg

height, h = 5.5 m

a) m g h = 0.5 m v^2

v = ?(2gh)

v1i = ?(2*9.8*5.5) = 10.38 m/s

v2i = ?(2*9.8*5.5) = 10.38 m/s

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

v1f = (1.85 - 3.70)/(1.85 + 3.7) * (10.38) + (2*3.7)/(1.85 + 3.7) * (-10.38)

v1f = -17.3 m/s

v2f = (2m1)/(m1+m2) v1i + (m2-m1)/(m1+m2) v2i

v2f = (2*1.85)/(1.85+3.7) * (10.38) + (3.7-1.85)/(1.85+3.7) * (-10.38)

v2f = 3.46 m/s

c) m g h = 0.5 m v^2

h = 0.5 v^2 / g

y1f = 0.5*17.3^2/9.8 = 15.27 m

y2f = 0.5*3.46^2/9.8 = 0.611 m

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