Force and momentum
When a force acts on an object that is moving, or able to move, there is a change in A quantity relating to a moving object that is calculated by multiplying its mass by its velocity.:
- in equations, change in momentum is shown as m鈭唙
- 鈭唙 is the change in velocity (鈭 is the Greek letter delta, representing 鈥榗hange in鈥)
Calculating 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 脳 acceleration
\(F = m \times a\)
\(acceleration = \frac{change~in~velocity}{time~taken}\)
\(a = \frac{\Delta v}{\Delta t}\)
Acceleration (伪) 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鈭v) is measured in kilogram metres per second (kg m/s)
- time taken (鈭t) is measured in seconds (s)
The equation shows that the force involved is equal to the The amount of change in the size of聽a quantity each second. 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.
\(F = \frac{m \Delta v}{\Delta t}\)
\(\Delta v = 30 - 0 = 30~m/s\)
\(F = \frac{1,500 \times 30}{20}\)
\(F = 2,250~N\)
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.