Momentum

Momentum

Momentum of a body is equal to the mass of it times its velocity. It is a vector and is measured in kgm/s.

Momentum = mass * velocity

Principle of conservation of momentum

When bodies in a system interact, the total momentum remains constant, provided that no external force acts on the system.

m_Au_A + m_Bu_B = m_Av_A + m_Bv_B

where m_A, m_B are the mass of the objects, u_A, u_B are the initial velocity and v_A, v_B are the velocity after interation.

In fact, this principle is not just limited to 2 objects only, but all objects involved in interation. More important, there should be no external force acting on the system in using this principle.

Animation showing the principle of conservation of momentum

Why need momentum?

Momentum provides us methods in studying collision of 2 or more objects. From the principle of conservation of momentum, we find out the relationship between the objects before collision and after collision. Thus, we can use this to calculate what's will happened after interaction of objects.

Three types of collision

1. Perfectly Elastic Collision

If a ball is dropped to the ground and it bounces back to the same height, the collision is said to be perfectly elastic. In perfectly elastic collision, the overall kinetic energy is conserved.

2. Partly Elastic Collision with energy loss

After the collision, the particles involved move apart with an overall kinetic energy. Most daily events belong to this type of collision. Although kinetic energy is not conserved, momentum is always conserved.

3. Perfectly Inelastic Collision

If a lump of plastic is dropped and it sticks to the ground, the collision is said to be perfectly inelastic. That means two bodies stick together after collision. The kinetic energy loss is the greatest, compared to other cases.

Changing momentum

Changing momentum is the measurement of the external force F acts on an object of mass m changing its velocity from u to v in time t.

From Newton's second law, F = ma = m(v - u) / t = (mv - mu) / t

Thus, Unbalanced Force = rate of change of momentum

Don't underestimate the force of impact. Since time of impact can be very small, F can be very large.

Impulse

Impulse is the product of the force and the time for which the object acts. It is equal to the change in momentum of the object. It is measured in Ns or kgm/s

Impulse = Ft = mv - mu

This equation is very important in calculation as we can find out the force of impact (happens in very short time which is difficult to measure directly) by getting the velocity before and after the collision. We can only find out this using momentum principle.