Energy in 1D Collisions (Edexcel A Level Further Maths): Revision Note

Energy in 1D Collisions

How might energy be involved in collision problems?

• A question may require the change in kinetic energy to be calculated due to a collision, or to an impulse being applied

• Remember that although total energy will be conserved, there may be a change in the kinetic energy of the objects involved in the collision

• The kinetic energy of an object can be calculated using

• If a particle with mass  and velocity  collides with a particle of mass  and velocity , then the loss in kinetic energy would be:

  • 

  • This is essentially the difference between the total kinetic energy before the collision, and the total kinetic energy after the collision

When is kinetic energy conserved in collisions?

• When , which would be a perfectly elastic collision, kinetic energy will be conserved, and no energy is lost due to the impact

• When , some energy will be lost due to the collision

  • In reality, all collisions will have a coefficient of restitution of less than 1, but we may still choose to model some scenarios as perfectly elastic

  • It is also important to understand that energy is not "lost", it is simply transferred to other forms such as heat and sound

• There can also be situations where the kinetic energy of a system increases

  • For example when a cannon is fired, the cannonball and cannon itself start with zero velocity, and hence zero kinetic energy

  • When fired, the cannon ball moves forward, and the cannon recoils backwards, so they now both have velocities, and hence kinetic energy

  • In this scenario, the energy has been converted from chemical energy stored in the gunpowder