Elastic Collision why I am wrong?

[cks]

From the pictures(my solutions) I submitted, I know that I can straightly find the magnitude of the velocity of the puck B by using conservation of energy in the lab frame.

However, my gut feelings tell me that answering the question using conservation of energy in the moving frame (puck A) will do.

But I find something awkward when I write down all the equations. Equation (3) which is the conservation of energy in the moving frame give equation that contradicts equation (2) (which is the conservation of momentum in the y-direction) .

Why is this so? I have checked everything and couldn't see anything that are against the law of physics.

Thank you.


An elastic collision of two pucks on a frictionless air-hockey table. Puck A has mass mA=0.500 kg and puck B has mass mB=0.300 kg. Puck A has an initial velocity of 4.00 m/2 in the positive x-direction and a final velocity of 2.00 m/2 in an unknown direction. Puck B is initially at rest. Find the final speed of VB2 of puck B and the angles Alpha and Beta in the figure.

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[Office_Shredder]

I'll be honest, I didn't read your pages of equations which require scrolling to see.

To find B's final momentum, it's simple conservation of energy. You know the total momentum in the y-direction is zero. So your equations should be something like:

m is mass of A
M is mass of B
v is velocity of A
V is velocity of B

1/2mv_initial² = 1/2(mv² + MV²

mv_initial = mvcos(alpha) + MVcos(beta)

MVsin(beta) = mvsin(alpha)

Now, your unknowns are alpha, beta, and V, and you have three equations. So you should be able to solve for them.. first get V from conservation of energy, then work on the angles (it's possibly easier if you use some trigonometric relationships first, such as sin²x + cos²x = 1). I would recommend squaring both sides of equation 3, then solving for cos of alpha and beta

 

[kyle8921]

I appreciate your curiosity and desire to understand the concepts of elastic collisions. It is commendable that you are questioning your approach and trying to understand why there may be a contradiction in your equations.

Firstly, let me clarify that there is no single "correct" way to solve a problem. Different approaches may lead to different equations and solutions, but as long as they are based on sound scientific principles and laws, they are all valid.

In this case, it seems that your approach using conservation of energy in the lab frame is yielding the correct solution for the final velocity of puck B. However, when using conservation of energy in the moving frame, you are finding a contradiction with conservation of momentum in the y-direction.

This is likely due to a mistake in your calculations or assumptions. It is important to carefully check your equations and ensure that all of your variables and values are correct. Additionally, it may be helpful to draw free-body diagrams for each puck and analyze the forces acting on them.

In elastic collisions, both conservation of energy and conservation of momentum must be satisfied. If there is a contradiction between the two, it is likely that there is an error in your calculations. I would suggest going through your equations step by step and double-checking your work to identify any mistakes.

Overall, your approach using conservation of energy in the lab frame is correct and valid. However, if you are still interested in solving the problem using conservation of energy in the moving frame, I recommend reviewing your calculations and identifying any errors. Keep up the good work in questioning and understanding the concepts of physics!