Elastic collisions
- When two objects collide, they may spring apart retaining all of the kinetic energy of the system
- This would be a perfect elastic collision
- In an elastic collision, all of the kinetic energy is conserved
- Recall the kinetic energy equation:
- Where:
- Ek = kinetic energy in joules (J)
- m = mass in kilograms (kg)
- v = velocity in metres per second (m s-1)
- Kinetic energy depends on the speed of an object
- In a perfectly elastic collision (such as a head-on collision):
the relative speed of approach = the relative speed of separation
Worked example
Two similar spheres, each of mass m and velocity v are travelling towards each other.
The spheres have a head-on collision. What is the total kinetic energy after the impact?
Answer:
Step 1: Equate the kinetic energy before and after the collision
- In an elastic collision, the kinetic energy of the system is conserved
Step 2: Write an expression for the kinetic energy before the collision
- Therefore, the correct answer is C
Examiner Tip
Despite velocity being a vector, kinetic energy is a scalar quantity and therefore will never include a minus sign.
This is because in the kinetic energy formula, mass is scalar and the v2 will always give a positive value whether its a negative or positive velocity.