Further Mechanics: Momentum and Collisions

Momentum and Collisions

Momentum is a measure of 'unstopability' which originates from a simple thought experiment.

If a body has a large mass but low velocity (Lorry), is it easier to stop than a small mass/high velocity body (Bullet). The truth is that both are difficult to stop suggesting that 'unstopability' is determined by both velocity and mass.

Momentum (kgms-1) = mass (kg) x velocity (ms-1)

P = mv

Momentum is a vector quantity meaning that its direction must be indicated.

Worked Example 1.1

What is the momentum of a body of mass 40kg, traveling at 1.5ms-1 due West?

Solution

P = mv

P = 40 kg x -1.5 ms-1 = -60 kgms-1

Worked Example 1.2

What is the momentum of a raindrop of mass 0.065g falling at 9 ms-1 if a wind blows horizontally at 12 ms-1?

Solution

Horizontal Component of Velocity: 12 ms-1

Vertical Component of Velocity: 9 ms-1

Using Pythagoras, the velocity can be calculated:

v^2 = 9^2 + 12^2

v = 15 ms-1

The direction of the velocity can be calculated:

Angle to vertical = tan-1 (12 / 9) = 53 degrees to the vertical.

Using P = mv, the momentum can be calculated:

P = mv

P = 0.065 EXP -3 x 15

P = 9.8 EXP -4 kgms-1 at 53 degrees to the vertical.

Newton's Second Law of Motion and Momentum Change

Newton's Second Law of Motion states that:

The resultant force F  exerted on a body  is proportional to the rate of change of linear momentum of that body.

The form of the second law applied in unit 1 is F = ma. This can be related to the statement above:

a = dv…