# Chapter 6: Momentum

Momentum

The momentum is given by the following equation:

Momentum = mass × velocity

p= mv

Since it depends on the velocity and not the speed, momentum is a vector quantity.  Momentum is measured in kilogram per second, kg m/s or kgms-1.

Conservation of momentum In an isolated system i.e. if no external force is acting on it, the linear momentum is conserved.

Total momentum before = total momentum after

In the given situation in the diagram, car 1 and 2 travel to the right with the initial velocities u1 and u2 respectively. Car 1 catches up to car 2 and they collide. After the collision the cars continue to move to the right but car 1 now travels at velocity v1 and car 2 with v2.

Since momentum is conserved,

Total momentum before= total momentum after

M1u1 + m2u2 = m1v1 + m2v2    (this is in perfectly elastic collision)

In perfectly elastic collision kinetic energy is conserved and in inelastic collision the kinetic energy is not conserved.

Explosions

It is similar to collision, the total momentum before is equal to the total momentum after. In the explosions the total momentum before is zero.

The momentum is given by;

M1u1 + m2u2 = m1v1 + m2v2

Since the momentum before is zero, equation becomes,

0 = m1v1 + m2v2

But since v1 is negative due to explosion,

0 = -m1v1 + m2v2

M1v1 = m2v2