Elastic Collision of two marbles

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SUMMARY

The discussion centers on the elastic collision of two identical marbles, specifically a 45g marble colliding with a stationary marble. The incident marble continues at an angle of 55 degrees to its original direction, leading to the conclusion that the angle between the direction of the target marble and the original direction of the incident marble is 35 degrees. This conclusion is based on the principles of conservation of momentum and energy, which dictate that the final velocities of the two marbles will be perpendicular under specific conditions: equal mass, one stationary mass, and a non-head-on collision.

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Homework Statement


A 45g marble collides with an identical stationary marble, and continues at 55 degrees to it's original direction. The collision is perfectly elastic. What is the angle between the direction taken by the target ball and the original direction of the incident ball?


Homework Equations





The Attempt at a Solution


Since elastic collisions in 2 dimensions result in 2 perpendicular velocities after the collision, I'm getting the feeling that the answer is simply 90-55=35 degrees. Is this right?
 
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Yes. The final velocities will be perpendicular if all of the following conditions are met

(1) the collision is elastic
(2) the two masses are equal
(3) one of the masses is initially at rest
(4) the collision is not a direct, head-on collision
(5) the objects do not pick up spin in the collision

Are any other conditions required? (Don't know if I'm overlooking something. At first I intended to list only the first three; the other two came to me while typing.)
 
Elastic collision and identical mass with one at rest.
Conservation of energy

(vo)2=(v1)2+(v2)2
This is a right angle triangle.

β=90-θ

Head on collision.
Conservation of momentum.
1.Ball#1 stop and ball#2 moves.
2.Ball#2 stays and Ball#1 continue moving. Ball#1 like ghost, passing through. Unphysical.
Maybe in billions years as I've seen on Discovery Channel, Quantum World.
 
Last edited:

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