Section 1 of 5Momentum and Resultant Force
Momentum and Resultant Force
Momentum
- Momentum p = mv is the product of mass and velocity, measured in kg m/s, and it has the same direction as the velocity.
Resultant force
- A resultant force makes an object accelerate, and acceleration is the change of velocity divided by time taken.
Change in momentum
- Δp = mv − mu, where u is the initial velocity and v the final velocity of an object whose mass stays constant.
Newton's second law
- Combining F = ma with a = (v − u)/t gives F = (mv − mu)/t, so force equals the rate of change of momentum.
Section 2 of 5Using the Equation
Follow these steps for any momentum and force question.
1
Choose a positive direction, and give velocities in the opposite direction a negative sign.
2
Calculate the initial momentum mu and the final momentum mv, keeping their signs.
3
Subtract to find the change in momentum, Δp = mv − mu, measured in kg m/s.
4
Divide by the time over which the change happens to find the resultant force in newtons.
5
Check the sign of the answer to see which way the force acts.
Section 3 of 5Time of Contact
Same change, different time
- For a given change in momentum, force and time are inversely proportional, so doubling the time halves the force.
Short impact
- A rigid collision stops the object quickly, so the time is tiny and the force acting is very large.
Long impact
- A cushioned collision spreads the same momentum change over more time, so the force is much smaller.
Rebounds
- If an object bounces back, its velocity reverses, so the momentum change is bigger than if it simply stopped.
| Quantity | Symbol | Unit |
|---|---|---|
| Force | F | newton (N) |
| Mass | m | kilogram (kg) |
| Velocity | u, v | metre per second (m/s) |
| Time | t | second (s) |
| Change in momentum | Δp | kilogram metre per second (kg m/s) |
Section 4 of 5Worked Example
Question
- A car of mass 1000 kg accelerates uniformly from rest to 20 m/s in 8.0 s.
- Calculate the resultant force acting on it.
- Initial momentum = 1000 × 0 = 0 kg m/s.
- Final momentum = 1000 × 20 = 20 000 kg m/s.
- Change in momentum = 20 000 − 0 = 20 000 kg m/s.
- F = Δp ÷ t = 20 000 ÷ 8.0 = 2500 N.
Answer 2500 N in the direction of motion.
Section 5 of 5Exam Checklist & Tips
1.3.2 – Key Points for the Exam
- Momentum The product of an object's mass and velocity, a vector measured in kg m/s.
- Resultant force The single force that has the same effect as all the forces acting on an object.
- Change in momentum The final momentum minus the initial momentum, Δp = mv − mu.
- Rate of change of momentum The change in momentum divided by the time taken, equal to the resultant force.
- Inversely proportional Describes two quantities where one halves when the other doubles.
Common Mistakes
- Forgetting the sign of velocity when an object rebounds, so the momentum change is too small.
- Writing the unit of momentum as N m or kg m; it is kg m/s (equivalent to N s).
- Using the final velocity only, instead of the difference between final and initial momentum.
- Mixing up mass and weight; mass in kilograms is used, not weight in newtons.