Momentum, Work, and Power
Push a heavy cart and a light one at the same speed, and the heavy one is far harder to stop. Lift a box quickly and you feel more strained than lifting it slowly. These everyday experiences are captured by three physics ideas: momentum, work, and power. Each has a simple formula that makes problems straightforward.
This lesson covers momentum, work, and power.
Momentum is mass in motion, found by multiplying mass and velocity. Work is done when a force moves an object, found by multiplying force and distance. Power is the rate of doing work, found by dividing work by time.
What is momentum?
Momentum measures how hard it is to stop a moving object. It depends on both mass and velocity:
[ p = mv ]where (p) is momentum, (m) is mass, and (v) is velocity. A heavy truck moving slowly can have as much momentum as a light car moving fast. Momentum is also conserved in collisions, which is why physics can predict how objects bounce or stick after they hit.
What is work?
In physics, work has a precise meaning: it is done only when a force moves an object through a distance in the direction of the force:
[ W = Fd ]Here (W) is work, (F) is force, and (d) is distance. Holding a heavy bag still does no work in the physics sense, because nothing moves, even though it feels tiring. Push a box (3) meters with (10) newtons of force and you do (W=(10)(3)=30) joules of work.
| Quantity | Formula |
|---|---|
| Momentum | (p=mv) |
| Work | (W=Fd) |
| Power | (P=dfrac{W}{t}) |
What is power?
Power is how fast work is done:
[ P = dfrac{W}{t} ]where (P) is power, (W) is work, and (t) is time. Two people who carry the same load up the same stairs do the same work, but the one who runs up uses more power because they do it in less time. Power is measured in watts, where one watt is one joule per second.
Watch: A Short Video Lesson
Brief Physics walks through this skill clearly in a few minutes. It is a helpful companion to the reading above:
A routine for momentum, work, and power questions
- For momentum, multiply mass by velocity: (p=mv).
- For work, check that the force actually moves the object, then use (W=Fd).
- Remember holding something still does no work.
- For power, divide the work by the time: (P=dfrac{W}{t}).
- Match units: joules for work, watts for power.
Practice questions
- Write the formula for momentum.
- A (2) kg ball moves at (3) m/s. What is its momentum?
- How much work is done pushing a box (5) m with a force of (4) N?
- Why is holding a heavy bag still not “work” in physics?
- Two people lift the same load up the same stairs; one is faster. Who uses more power?
- True or false: power is the rate of doing work.
Answers:
- (p=mv).
- (p=(2)(3)=6) kg·m/s.
- (W=(4)(5)=20) joules.
- Because the object does not move, so no distance is covered.
- The faster person, because they do the same work in less time.
- True.
Where this fits
These ideas build on forces and Newton’s laws and connect to momentum, work, and simple machines and energy and simple machines. Find all topics on the ASVAB General Science Learning Hub.
Recommended Prep Books
These study guides and practice books help you keep building momentum as you prepare:
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