Initially, ball 1 rests on an incline of height h, and ball 2 rests on an incline of height h/2 as shown in Figure P11.40. They are released from rest simultaneously and collide elastically in the trough of the track. If m2 = 4 m1, m1 = 0.045 kg, and h = 0.65 m, what is the velocity of each ball after the collision?
The velocity of each ball after collision.
Answer to Problem 41PQ
The velocity of ball 1 after collision is
Explanation of Solution
Apply conservation of energy for a ball falling from incline of height
Here,
Rearrange above equation to get
For ball 1 height
Substitute
Here,
From figure P11.40, it’s clear that ball 1 is moving along
Write the expression for the velocity of ball 1 before collision.
Here,
Substitute
Here,
From figure P11.40, it’s clear that ball 2 is moving along
Write the expression for the velocity of ball 2 before collision.
Here,
Put equation (II) in the above equation.
It is given that the collision is elastic so that both kinetic as well as potential energy are conserved during the collision.
Write the expression for the velocity of the ball 1 after collision.
Here,
Write the expression for the velocity of the ball 2 after collision.
It is given that
Put equation (III) in equation (IV) and replace
Put equation (II) in the above equation to get final expression for
Put equation (III) in equation (V) and replace
Put equation (II) in the above equation to get final expression for
Conclusion:
It is given that the value of
Substitute
Substitute
Therefore, the velocity of ball 1 after collision is
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Chapter 11 Solutions
Physics for Scientist and Engineers (Foundations And Connection; Volume I and II) LLF edition
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