Conceptual Collision Question -- What

[golf20]

1. Question: Ball A of mass m_a is traveling along the x-axis with velocity v_ao when it strikes Ball B of mass m_b, which is at rest. After the collision, Ball A travels at an angle θ above the x-axis and Ball B travels at an angle φ below the x-axis. The final velocities of Balls A and B are v_af and v_bf, respectively. Write an expression that gives the velocity of Ball A, v_af, after the collision.

2. Relevant Info: Law of Conservation of Linear Momentum

3. Solution: The expression I get for v_af is v_ao / (cosθ + sinθcotφ). I find this expression strange because it shows that v_af is independent of the masses of Balls A and B. However, the expression for v_bf does include mass. I do not understand how this makes sense conceptually -- Could someone provide an explanation?

 

[haruspex]

1. Question: Ball A of mass m_a is traveling along the x-axis with velocity v_ao when it strikes Ball B of mass m_b, which is at rest. After the collision, Ball A travels at an angle θ above the x-axis and Ball B travels at an angle φ below the x-axis. The final velocities of Balls A and B are v_af and v_bf, respectively. Write an expression that gives the velocity of Ball A, v_af, after the collision.

2. Relevant Info: Law of Conservation of Linear Momentum

3. Solution: The expression I get for v_af is v_ao / (cosθ + sinθcotφ). I find this expression strange because it shows that v_af is independent of the masses of Balls A and B. However, the expression for v_bf does include mass. I do not understand how this makes sense conceptually -- Could someone provide an explanation?

Try letting B have an initial velocity v_boalong the x axis. That should restore the symmetry. I think you will see then that when one initial velocity goes to zero the masses disappear from the after velocity of the other ball.
This does mot mean that the mass of the resting ball is immaterial. If you were to run the same experiment, just changing that mass, the departure angles would change.

 

[Suraj M]

My understanding is that the angle at which these bodies move after collision is actually taking into consideration, their mass. I'm not sure about this though.