Force and momentum

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

Calculating the rate of change of momentum

You can combine two equations to show how to calculate the force involved when a change in momentum happens:

force = mass × acceleration

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

  α = \frac {v-u}{t}

Acceleration (α) appears in both equations, giving:

force = mass × \frac{change \ in \ velocity}{time \ taken} = \frac {change \ in \ momentum}{time \ taken}

  F = \frac {mv-mu}{t}

This is when:

  • force (F) is measured in newtons (N)
  • change in momentum (mv - mu) 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

  F = \frac {mv-mu}{t}

 v - u = 30 - 0 = 30~m/s

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

 F = 2,250 \ N

Newton's third law in collisions

When objects collide, they will exert equal and opposite forces on each other all the time they are in contact. This means that the objects will each have the same size force acting for the same amount of time.

  F = \frac {mv-mu}{t}

so

Ft = mv \ - \ mu

The change in momentum is given by the force multiplied by the time it acts for. So in a collision the two objects each gain the same momentum but in opposite directions. These extra bits of momentum add nothing to the whole system. Momentum is a vector and they are in opposite directions so add up to zero.

Car safety features

During a collision there is a change in momentum. The force of the collision is equal to the rate of change of momentum. Car safety features such as seatbelts, airbags and crumple zones all work to change the shape of the car, which increases the time taken for the collision. Crumple zones refer to the areas of a car that are designed to deform or crumple on impact. These different safety features decrease the rate of change of momentum, which decreases the force of the collision on any people within the car.

Side view of a crashed car, showing the crumple zones and activated airbags.
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