### GCSE Physics

Energy
Forces
Forces and Motion
Waves in Matter
Electricity
Magnetism and Electromagnetism
Particle Model of Matter
Atomic Structure
Space Physics

# Force and Momentum

When a resultant force (that is not zero) acts on a stationary or moving object, the object changes velocity. When the velocity changes, so does the momentum.

To calculate the force acting on an object, we multiply the mass of the object by its acceleration. This is represented by the equation:

Force = Mass × Acceleration

• F = m × a

To calculate the acceleration, we divide the change in velocity by the time taken (change in time):

Acceleration = Change in velocity / Time taken

• $a=\dfrac{\Delta v}{t}$

We can combine the two equations to form:

Force = (Mass × Change in velocity) / Time taken

• $F=\dfrac{m\Delta v}{\Delta t}$

The mass multiplied by the change in velocity is another way of saying the change in momentum. So:

Force = Change in momentum / Time taken

You can also say that Force = the rate of change in momentum

## Example

A man and a woman are in a car travelling at 25 m/s.

• The man has a mass of 83 kg
• The woman has a mass of 72 kg

If the car comes to a stop in one second:

a) Calculate the forces acting on the man

b) Calculate the forces acting on the woman

• Mass of man = 83 kg
• Mass of woman = 72 kg
• Initial velocity = 25 m/s
• Final velocity = 0 m/s
• Time taken = 1 s

a) Force (N) = $\frac{Mass\:(kg) \times Change\:in\:velocity\:(m/s)}{Time\:taken\:(s)}$

Force (N) = $\frac{83\:kg \times 25\:(m/s)}{1\:s}$

Force on man = 2075 N

b) Force (N) = $\frac{72\:kg \times 25\:(m/s)}{1\:s}$

Force on woman = 1800 N

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