Conservation of momentum in a collision involving three objects

In summary, the conversation discusses the calculation of velocities for three spheres involved in a simultaneous collision, with known masses and coefficient of restitution. The equation for momentum conservation is corrected to remove the coefficient of restitution, and the use of a coefficient of restitution in a three-object collision is questioned.
  • #1
jeanius
11
0
Say two stationary spheres are struck by a third moving sphere (each different masses), such that they are both hit at the same time and at the same magnitude angle, and coefficient of restitution e is known. If I want to calculate the velocity of each sphere, would the conservation of momentum and energy equations be:

e*m1*v1i = m1*v1f+m2*v2f+m3*v3f (in vector form)

and

((1/2)*m1*v1f^2 + (1/2)*m2*v2f^2 + (1/2)*m3*v3f)/((1/2)*m1*v1i^2) = e^2

?

I'm not sure if I'm extending this from a two-object model to a three-object model correctly. Can someone provide a little insight into this?
 
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  • #2
Your momentum conservation equation is incorrect. There should be no coefficient of restitution ##e## on the left hand side.

The second equation is the ratio of the final KE to the initial KE. The CoE is defined for collisions between two objects. I am not sure whether it makes sense to have a meaningfully useful coefficient of restitution in a simultaneous collision involving three objects.
 

FAQ: Conservation of momentum in a collision involving three objects

What is conservation of momentum in a collision involving three objects?

Conservation of momentum in a collision involving three objects is a fundamental law of physics that states that the total momentum of a closed system remains constant before and after a collision. This means that the total momentum of the three objects involved in the collision will be the same before and after the collision occurs.

How is momentum calculated in a collision involving three objects?

Momentum is calculated by multiplying an object's mass by its velocity. In a collision involving three objects, the total momentum can be calculated by adding together the individual momentums of each object. The equation for momentum is: p = m * v, where p is momentum, m is mass, and v is velocity.

What factors affect the conservation of momentum in a collision involving three objects?

The conservation of momentum in a collision involving three objects is affected by several factors, including the mass and velocity of the objects, the angle and direction of their collision, and any external forces acting on the objects during the collision. In a closed system, the total momentum will remain constant regardless of these factors.

Can the law of conservation of momentum be violated in a collision involving three objects?

No, the law of conservation of momentum cannot be violated in a collision involving three objects. This is because momentum is a conserved quantity, meaning it cannot be created or destroyed. If the total momentum of the three objects before and after the collision is not the same, then there must be an external force acting on the system.

How does the law of conservation of momentum apply to real-life situations involving three-object collisions?

The law of conservation of momentum applies to real-life situations involving three-object collisions in the same way it applies to any other collision. For example, in a car accident involving three cars, the total momentum of the cars before the collision will be the same as the total momentum after the collision. This law helps scientists and engineers understand and predict the outcome of collisions in various scenarios.

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