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PRACTICE COLLECTION / 23 PROBLEMS

Energy & momentum

Choose a system and follow what is conserved. Each problem includes progressive hints, guided reasoning and a question to test the idea again. Problems marked “Free sample” are complete for everyone; membership opens the rest.

LEARN BEFORE YOU PRACTISE

Build the reasoning first.

Work, stored energy and power

Choose a system, account for each transfer and read possible motion from an energy balance.

11 worked examples · 9 checks →

Impulse, momentum and collisions

Choose the system and interval, then connect momentum exchange to centre-of-mass motion and impact outcomes.

10 worked examples · 10 checks →

CONCEPTS IN THIS COLLECTION

Work-energy theorem ↗Elastic potential energy ↗Power ↗Potential-energy diagrams ↗Mechanical energy conservation ↗

PRACTISE AT YOUR PACE

Problems in this collection

23 problems · Showing 12

Beginner01

Energy & momentum

A conservative force closes its work ledger

What work does that same force do from C to A along any return route?

Apply a principle
Conservative forces
Start problem
IntermediateFree sample02

Energy & momentum

Read force from the energy curve

Use the slope of potential energy, including its sign.

Read graphs & measurements
Potential-energy diagrams
Start problem
Intermediate03

Energy & momentum

Combine two momentum directions

Find the speed of the combined body immediately afterward.

Connect concepts
Two-dimensional collisionsLinear momentum
Start problem
Intermediate04

Energy & momentum

Follow the system, not either cart

What is their center-of-mass velocity throughout this interaction?

Apply a principle
Motion of the center of massLinear momentum
Start problem
IntermediateFree sample05

Energy & momentum

Does a longer smooth track mean a slower finish?

Gravity remembers the change in height, not the length of the path.

Apply a principle
Mechanical energy conservationGravitational potential energy
Start problem
Intermediate06

Energy & momentum

How much does a triangular force pulse change velocity?

What is the cart’s velocity immediately after the pulse?

Read graphs & measurements
ImpulseForce-time graphs
Start problem
Intermediate07

Energy & momentum

Where does the cart’s kinetic energy go?

What is the maximum compression of the spring?

Connect concepts
Elastic potential energyMechanical energy conservation
Start problem
Intermediate08

Energy & momentum

How do you add up a changing force?

How much work does this force do?

Read graphs & measurements
Force-displacement graphsWork by a variable force
Start problem
IntermediateFree sample09

Energy & momentum

Power needed to raise the load

At constant speed the useful work is the increase in gravitational potential energy.

Apply a principle
PowerGravitational potential energy
Start problem
Intermediate10

Energy & momentum

The electricity bill includes losses

Find its input power.

Find a missing quantity
Power
Start problem
Intermediate11

Energy & momentum

A fast cart needs less drive force

Find the instantaneous driving force.

Find a missing quantity
Power
Start problem
Intermediate12

Energy & momentum

An area becomes kinetic energy

Find its final speed.

Connect concepts
Work by a variable forceWork-energy theorem
Start problem

12 of 23 shown

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