A force varies with position
Find its work from the signed area under the force–position graph.
Watch for this: Force magnitude times distance only works when the relevant component is constant.
2 CHAPTERS / A CONNECTED READING ROUTE
Energy & momentum
Which conservation law fits this stage of the motion?
The big picture
A collision, a rise and a spring compression may belong to one story, but they need not obey the same conservation equation. Divide the event into stages and ask what can cross the boundary of your chosen system in each stage.
Energy is useful when you care about positions and speeds without needing the intervening time. Momentum is useful when external impulse is negligible. Neither law is a shortcut around stating the system and checking its interactions.
What to read, and why
Start at the first stage if the subject is new. Otherwise, use the descriptions to find the missing step in your understanding. All chapter explanations are open; the labels identify chapters whose solutions and answer checks are also free.
STAGE 1
Account for energy
Connect force along a path to work and identify where mechanical energy is stored or transferred.
STAGE 2
Account for impulse
Choose the colliding system and separate momentum conservation from kinetic-energy conservation.
Choose a method before an equation
Use the physical conditions to narrow the choices. A formula becomes useful after you know why its model applies.
Objects stick together
Check external impulse during impact, then use momentum for the combined system.
Watch for this: Kinetic energy generally changes even if momentum is conserved.
An impact is followed by a climb
Finish the impact calculation first; use the resulting speed to start the energy stage.
Watch for this: Do not conserve mechanical energy through a dissipative impact.
Try a complete free problem
These problems include the hints, worked reasoning and answer feedback. Attempt one before opening the solution.
Read force from the energy curve →Intermediate · Read graphs & measurements · Free sampleDoes a longer smooth track mean a slower finish? →Intermediate · Apply a principle · Free sampleFrom a collision to a pendulum rise →Advanced · Connect concepts · Free samplePower needed to raise the load →Intermediate · Apply a principle · Free sample
Browse all energy & momentum problems →Before you move on
Close the worked examples and explain these aloud or on paper. If you need a formula, also state its assumptions.
- Explain how momentum can be conserved while kinetic energy decreases.
- Identify the energy transfers excluded when you write mechanical energy as constant.