Bermuda Motorcross Racing (Photo: Takara Dill)
6.3 - Inelastic and Elastic Collisions
- To be able to calculate the KE before and after an event such as a collision or explosion.
- To know that KE is conserved during elastic collisions but not during inelastic collisions.
- To be able to use the conservation of momentum and conservation of energy in situations such as the ballistic pendulum or collsions involving springs.
Momentum is always conserved during collisions - this is due to Newton's First Law of Motion. However, the same is not true for the kinetic energy. Usually some of the KE going into a collision is transferred to heat. The work done on the moving objects is equal to this change in KE.
Mathematically it can be seen that if the product of \(mass \times velocity\) is kept constant despite a change in mass, then it is impossible for the product of the mass x velocity squared to remain constant. If KE is lost during a collision, we call it an INELASTIC COLLISION. A perfectly inelastic collision results in the objects sticking to each other.
Rarely, the KE is conserved and this situation is known as ELASTIC COLLISION. This only really happens with things like atoms but can be approximated with steel balls.
So - for all collisions: momentum IS conserved.
KE is only conserved during elastic collisions between two very hard objects or if they do not actually touch (think electrostatics).
The most common example of a complex system is the ballistic pendulum. An object (e.g. bullet) is fired at another object suspended by a rope. The two objects collide and there is a recoil. This requires the use of the conservation of momentum. The recoil is constrained by the rope and the object(s) rise upwards. As there is a change in vertical height we can apply the principle of conservation of energy as the KE of the objects is transferred to GPE. Put another way, the kinetic energy from the impact is converted to work in raising the object upwards against gravity.
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Physics Aviary - Ballistic Pendulum.
Determine the original speed of the incoming ball by the maximum height achieved by the pendulum after the collision using the conservation of momentum and the conservation of energy. (Produced by Frank McCulley) |
Other Resources
PhET SImulation: Collision Lab