1.15 - 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.

Reducing forces in collisions and vehicle safety

• In a collision, an object's momentum changes very quickly, creating large forces that can cause serious injury.
• Vehicle safety features reduce these forces by increasing the time taken for the momentum to change.

Safety features that increase stopping time

• Crumple zones - Areas at the front and back of a car that crumple on impact, increasing the time taken to stop and reducing the force.
• Seat belts - Stretch slightly during a crash, increasing the time taken for the wearer to stop and reducing the force on the chest.
• Air bags - Compress as a person hits them, slowing them down more gradually than the hard dashboard and reducing the force.

Other safety equipment, such as bike helmets and crash mats, uses soft, compressible materials to increase stopping time and reduce the impact force.