The momentum of an object is defined as the product of its mass and velocity.
p = m × v (kg m s‾¹)
1. Within a closed system the total momentum in any direction is constant. Therefore for a closed system in any direction ⇒ total momentum of objects before collision = total momentum of objects after collision
♦ In a perfectly elastic collision, the relative speed of approach equals the relative speed of separation. The kinetic energy is completely conserved.
momentum before collision = m × v
momentum after collision = m × (-v)
change in momentum = 2mv
2. In an inelastic collision between two objects, with masses m, and velocities v and -v respectively:
total kinetic energy of the system = ½m v² × 2 = m v²
Momentum and Newton’s laws of motion
Newton’s first law
An object tends to stay at rest if it is at rest, or keep travelling at a constant velocity, unless a net external force acts on the object.
Newton’s second law
The net force acting on an object is directly proportional to its mass, and its rate of change of linear momentum. This can be further derived to give: Force = Mass x Acceleration.
Newton’s third law
When two bodies interact, the forces they exert on each other are equal in magnitude but opposite in direction.
Newton’s Cradle is a perfect example of conservation of momentum.