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This is a homework problem, however I am not looking for the solution but trying to know why I got the correct solution and why other methods don't work. Consider the attached diagram. We have two equal spheres of mass m suspended by vertical strings (B and C).A third identical sphere (A) of same mass m simultaneously strikes both the spheres elastically so that their centres at the instant of impact form an equilateral triangle. u is the velocity of (A) just before the collision. Find the velocities just after the impact. I tried to conserve momentum of the system and it doesn't give the correct answer.I do understand that since tension will also produce a large impulse when A hits B and C, momentum is not conserved (Please correct me if I am wrong). Instead of conserving momentum I then tried to apply the Impulse Momentum theorem.See Third image.

J is the impulse due to collision and J' is the impulse due to string [![The question][1]1 Since the collision is elastic, considering any two masses (A and C or A and B) the velocity of separation along the line of impact must be equal to the velocity of approach. Again, this gives the wrong answer.

After applying the Impulse Momentum theorem which I feel, is applicable in all cases, I decide to conserve energy (as the collision is elastic).This gives the correct answer.

I want to know why momentum is not conserved in the situation and why the velocity of approach and velocity of separation of any two masses not same even when the collision is elastic.

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    $\begingroup$ There is no figure that I can see. $\endgroup$
    – mike stone
    Feb 25 at 15:33
  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Feb 25 at 16:38

1 Answer 1

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In this scenario, momentum is not conserved because external forces are acting on the system during the collision. Specifically, the tension in the strings applies an impulse to the spheres during the collision, leading to a change in momentum that cannot be accounted for solely by the momentum of the spheres themselves.

Regarding the velocities of approach and separation, while it's true that in an elastic collision the velocity of separation along the line of impact is equal to the velocity of approach, this principle applies only to the velocities of the colliding objects themselves. In this case, the tension in the strings also plays a crucial role. The tension in the strings causes an impulse during the collision, altering the velocities of the spheres and resulting in velocities after the collision that are not solely determined by the velocities of approach.

Conserving energy, on the other hand, is a valid approach because the collision is elastic, and inelastic losses can be neglected. By conserving kinetic energy, you can accurately determine the velocities of the spheres after the collision.

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