IGCSE Physics / Momentum
Force and the rate of change of momentum revision notes
Edexcel International GCSE Physics (4PH1), chapter 4: Momentum, specification point 1.28P. Free lesson.
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A resultant force is the rate at which an object's momentum changes. Use the change in momentum and the time taken to calculate the force, taking care with units and direction.
What force and rate of change of momentum mean
Momentum changes when a force acts. The resultant force equals the change in momentum divided by the time taken. This equation is on the equation list. The top line is final momentum minus initial momentum, so the order matters. F is resultant force, measured in newtons (N). m is mass, measured in kilograms (kg). u is initial velocity and v is final velocity, both in metres per second (m/s). t is the time the force acts for, measured in seconds (s). Because (v − u)/t = a, the momentum equation is another form of F = ma.
How to calculate a force from a change in momentum
Put the values into the equation, with time in seconds. If the object starts at rest, its initial velocity is zero. For example, the football gains momentum when it is kicked, so its average force depends on how quickly that change happens. A millisecond is one thousandth of a second, so convert milliseconds to seconds before calculating.
How to find a braking force
When a car is brought to rest, its final momentum is zero. The momentum change is therefore the final momentum minus the initial momentum. The braking force acts against the car's motion. In the car example, the change in momentum has magnitude 20 000 kg m/s. Dividing this by 4 s gives an average force of 5000 N, against the motion.
How to handle a bounce
Choose one direction as positive and keep the signs for velocity throughout the calculation. If the ball bounces straight back, its final velocity is negative when its initial direction was positive. This means the ball reverses direction, rather than simply slowing down. For a ball travelling towards a wall at +8 m/s and bouncing back at −6 m/s, the velocity change is −6 − 8 = −14 m/s. The negative force means the force acts away from the wall. Its magnitude is 35 N.