6.21 - Momentum & Force

Force as the rate of change of momentum

• A resultant force causes an object's momentum to change.
• The resultant force equals the rate of change of momentum.

Formula for force and change of momentum

Where:

• $F$ = Resultant force, in newtons (N)
• $\mathrm{\Delta }(mv)$ = Change in momentum, in kilogram metres per second (kg m/s)
• $\mathrm{\Delta }t$ = Time taken for the change, in seconds (s)

For a given change in momentum, the longer the time taken, the smaller the force.

Worked example - Resultant force from a change in momentum

A car of mass 1,200 kg slows from 15 m/s to 10 m/s in 10 s. Calculate the resultant force on the car.

Vehicle safety features via work done over distance

• When a vehicle stops, work is done to transfer its kinetic energy to other stores.
• Since work done = force × distance, increasing the stopping distance reduces the force needed to stop the vehicle.
• Safety features increase the distance over which work is done to stop passengers, reducing the force on them and lowering the risk of injury.

Safety features that increase stopping distance

• Crumple zones - Areas at the front and back of the car that crumple easily, increasing the distance over which the car slows down and reducing the force.
• Seat belts - Stretch slightly when a large force acts on them, slowing passengers over a longer distance and reducing the force.
• Air bags - Compress as passengers hit them, increasing the distance over which they slow down and reducing the force.