- Xmax represents the maximum compressions during collision.
- Before contact, ball two has no kinetic energy (Ek2) .
Ek2 = (1/2)m2V22 = 0 J
- During contact, ball one experiences a force backwards to slow it down, while ball 2 experiences a forward force to speed it up.
- This force also compresses the balls
- During compression, a force is applied through a distance to do work (shaded area on the graph).
- This work results in a build up of elastic potential energy (Ee) in the balls equal to the shaded area on the graph
- Therefore total energy (ET) during contact is given by
ET = Ek1 + Ek2 + Ee
- As the collision proceeds, the kinetic energy of ball one will continually decrease from the moment of first contact, to when the balls are separated (i.e. V1 decreases).
- As the kinetic energy of ball one decreases, the kinetic energy of ball two will be continually increasing while the balls are in contact (i.e. V2 increases).
- Elastic potential energy increases until maximum compressions occurs at Xmax, and then the compression will decrease while the elastic potential energy decreases back to zero once the contact has ended.
- In summary:
- Prior to maximum compression V1 > V2
- At maximum compression V1 = V2
- After maximum compression V1 < V2
- For elastic collisions, the total energy remains constant, but during contact, Total kinetic energy is lost by conversion to elastic potentials energy, which converts back to kinetic energy after maximum compression so that:
Ekbefore contact = Ekafter contact
Elastic and Inelastic Collisions
- The difference between elastic and inelastic collisions is whether the energy stored as potential energy during contact, is retrieved as kinetic energy after contact.
- Retrieval depends upon the mechanisms operating during contact.
- For example, if during conpression, an object is permanently deformed and cannot return to its original shape, then work done to cause the deformation uses up kinetic energy and then:
EkTotal before > EkTotal after
- If work is done to use up kinetic energy in deforming, or other forms of energy appear during contact, that are not transformed back to kinetic energy after, then kinetic energy is lost, and total energy is then given by
ET = Ek1 + Ek2 + Ee + Q + Light + Sound + .......
- This causes the Force - Distance (compression) graph (F - d) to have a different shape depending upon whether compression is occuring (decreasing distance between objects) or expansion is occuring (increasing distance between objects).
- Conditional difference of the Force - Distance graph for elastic and inelastic collisions:
- If the F - d graph has the same shape for decreasing distance as increasing distance, then the collision is elastic