# Further Mechanics: Momentum and Collisions

- Created by: Tree
- Created on: 24-12-11 00:22

**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…

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