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

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 m_2 = 7 m_1, m_1 = 0.046 kg, and h = 0.64 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 Web Assign.)

Explanation / Answer

here

m1 = 0.046 kg

m2 = 7 * m1 = 0.322 kg

h = 0.64 m

speed of ball 1 before the collison , u1 = sqrt(2 * g * h)

u1 = 3.54 m/s

speed of ball 2 before the collison , u2 = - sqrt(2 * g * h/2)

u2 = - 2.5 m/s

let the final speeds be v1 and v2

using conservation of momentum

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

3.54 - 7 * 2.5 = v1 + 7 * v2 ....(1)

using conservation of kinetic energy

0.5 * m1*u1^2 + 0.5 * m2*u2^2 = 0.5 * m1*v1^2 + 0.5 8 m2 * v2^2

3.54^2 + 7 * 2.5^2 = v1^2 + 7 * v2^2 ....(2)

from (1 ) and (2)

v1 = - 7.03 m/s and v2 = -0.99 m/s

or

v1 = 3.54 m/s and v2 = - 2.5 m/s

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