Force and momentum - Higher

When a force acts on an object that is moving, or able to move, there is a change in momentum:

  • in equations, change in momentum is shown as m \Delta v
  • \Delta v is the change in velocity (∆ is the Greek letter delta, representing 'change in')

Calculating rate of change of momentum

The two equations can be combined to show how to calculate the force involved when a change in momentum happens:

force = mass × acceleration

F = m \times a

acceleration = \frac{change~in~velocity}{time~taken}

a = \frac{\Delta v}{\Delta t}

Acceleration (a) appears in both equations, giving:

force = \frac{change~in~momentum}{time~taken}

F = \frac{m \Delta v}{\Delta t}

This is when:

  • force (F) is measured in newtons (N)
  • change in momentum (m∆v) is measured in kilogram metres per second (kg m/s)
  • time taken (∆t) is measured in seconds (s)

The equation shows that the force involved is equal to the rate of change of momentum.

Example calculation

A 1,500 kg car accelerates from rest to a velocity of 30 m/s. This takes 20 seconds. Calculate the force acting on the car.

F = \frac{m \Delta v}{\Delta t}

\Delta v = 30 - 0 = 30~m/s

F = \frac{1,500 \times 30}{20}

F = 2,250~N