Initially, ball 1 rests on an incline of height h , and ball 2 rests on an incli

Question

Initially, ball 1 rests on an incline of height h, and ball 2 rests on an incline of height h/2 as shown in the figure below. They are released from rest simultaneously and collide elastically in the trough of the track. If m2 = 8 m1, m1 = 0.042 kg, and h = 0.52 m, what is the velocity of each ball after the collision? (Assume the balls slide but do not roll. Indicate the direction with the sign of your answer. Positive is to the right, and negative is to the left. Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.)

Explanation / Answer

Here ,

for the ball 1 ,

intial speed , u1 = sqrt(2 * g * h)

u1 = sqrt(2 * 9.8 * 0.52)

u1 = 3.19 m/s

for the initial velocity of ball 2

u2 = sqrt(2 * g * h/2)

u2 = sqrt(9.8 * 0.52)

u2 = 2.26 m/s

Now , Using conseravtion of momentum

m1 * 3.19 - 8 * m1 * 2.26 = m1 * v1 + m1 * v2

3.19 - 8 * 2.26 = v1 + 8 v2 -----(1)

for the elastic collision

v2 - v1 = (3.19 - 2.26) ----(2)

solving 1 and 2

v1 = -6.49 m/s

v2 = -1.05 m/s

the final velocity of 1 is 6.49 m/s

final velocity of 2 is 1.05 m/s

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