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?
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?
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…