Two spheres collide and assume that the collision is perfectly elastic

In summary, the conversation discusses the relationship between the velocities of two objects in a perfectly elastic collision. This is represented by the equation (va' - vb') dot N = -(va - vb) dot N, where N is the normal vector at the point of collision and va and vb are the initial velocities of object A and B, respectively. The conversation also mentions using the center of mass frame to solve the equation and the importance of considering kinetic energy in elastic collisions.
  • #1
nullspace7
2
0
Two spheres collide and assume that the collision is perfectly elastic. Also --only linear momentum.

I have the relationship:

(va' - vb') dot N = -(va - vb) dot N

Where N is the normal vector at the point of collision. va and vb are initial velocities of object A and B, respectively. And va' and vb' are the final velocities of object A and B respectively.

I want to know how this relationship is derived.

This is what I try:

Relative to object B, object A has velocity v_ab. Relative to object B,
object B has velocity 0.

m_a*v_a + m_b*v_b = m_a*v_a' + m_b*v_b'

Relative to B:

m_a*v_ab + 0= m_a*v_ab' + 0

v_ab = v_ab'

That would give me this: (va' - vb') dot N = (va - vb) dot N

But I am missing the negative sign, because they should be opposite. Please
advise. Thanks in advance.
 
Physics news on Phys.org
  • #2
As I'm sure you're aware, in an elastic collision, both kinetic energy and momentum are conserved. If you write both sets of equations and solve them simultaneously, you'll get (va' - vb') = - (va - vb)
 
  • #3
Yeah (needed KE), I've solved it now. I solved it in the center of mass frame, which seemed easier.
 

What is a perfectly elastic collision?

A perfectly elastic collision is a type of collision between two objects where there is no loss of kinetic energy. In other words, the total kinetic energy before and after the collision remains the same.

What happens to the momentum in a perfectly elastic collision?

In a perfectly elastic collision, the total momentum of the two objects is conserved. This means that the total momentum before the collision is equal to the total momentum after the collision.

How is the direction of the objects' velocities affected in a perfectly elastic collision?

In a perfectly elastic collision, the direction of the objects' velocities may change, but their magnitudes will remain the same. This means that the objects may bounce off each other and move in different directions after the collision.

What is an example of a perfectly elastic collision in real life?

One example of a perfectly elastic collision is when two billiard balls collide on a pool table. Assuming there is no friction, the two balls will bounce off each other with the same speed and direction as before the collision.

What factors can affect the elasticity of a collision?

The elasticity of a collision can be affected by factors such as the materials of the objects involved, the temperature, and the amount of force applied during the collision. In general, objects made of more elastic materials will have a higher chance of experiencing a perfectly elastic collision.

Similar threads

  • Mechanics
Replies
6
Views
1K
Replies
5
Views
787
Replies
5
Views
3K
Replies
1
Views
965
Replies
3
Views
909
  • Introductory Physics Homework Help
Replies
3
Views
735
  • Atomic and Condensed Matter
Replies
4
Views
1K
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
2K
Replies
3
Views
1K
Back
Top