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Work-Energy Theorem

Part of the Mechanics section of Coddy's Physics journey. Lesson 52 of 97.

The work-energy theorem: the net work done on an object equals the change in its kinetic energy.

Wnet=12mv2−12mv02W_{\text{net}} = \tfrac{1}{2} m v^2 - \tfrac{1}{2} m v_0^2

Positive net work speeds the object up; negative net work, like braking, slows it down.

A 2 kilogram cart starts at rest on the left; a net force F pushes it over a distance d, and it ends on the right moving with speed v

The net work F d becomes the cart's kinetic energy.

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Challenge

A 1200 kg1200\ \mathrm{kg} car moving to the right at 15 m/s15\ \mathrm{m/s} brakes on a level road and stops in 30 m30\ \mathrm{m}. Draw the forces on the car while it brakes (the picture shows it at the start and where it stops: draw them on the first one), then find the size of the braking force FF.

Try it yourself

Physics diagram: cart, vec; arrows v 0 = 15 m/s

Solve for FF

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This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Mechanics

1Introduction

What is Physics?Your First EquationTurning a Rule Around

4Inclined Planes

Forces on an InclineGravity ComponentsFrictionless InclineIncline with FrictionWill It Slide?Recap - Ramp Challenge

7Projectile Motion

Independent AxesHorizontal LaunchLaunch at an AngleRange and Max HeightRecap - Hit the Target

10Work and Energy

WorkKinetic EnergyWork-Energy TheoremGravitational PEConservation of EnergyPowerRecap - Roller Coaster

13Impulse and Momentum

MomentumImpulseConservation of MomentumElastic CollisionsInelastic CollisionsRecap - Air Track

16Simple Harmonic Motion

What is SHM?Mass on a SpringThe PendulumSHM GraphsEnergy in SHMRecap - Oscillator

2Vectors and Newton's Laws

Right TrianglesWhat is a Vector?Adding VectorsAxes and DirectionsVector ComponentsForces Around UsFriction and TensionNewton's First LawNewton's Second LawNewton's Third LawRecap - Net Force

5Kinematics in 1D

Position and DisplacementVelocityAccelerationMotion GraphsEquations of MotionRecap - Braking Car

8Kinematics and Newton

From Forces to MotionFrom Motion to ForcesTwo-Stage MotionRecap - Elevator

11Springs

Hooke's LawSprings in SeriesSprings in ParallelRecap - Spring Scale

14Momentum in 2D

Momentum as a Vector2D CollisionsExplosionsRecap - Billiards

17Gravitation

Law of GravitationGravity and AltitudeSatellitesKepler's LawsGravitational EnergyEscape VelocitySatellite EnergyRecap - Mission to Orbit

3Friction

What is Friction?Static FrictionKinetic FrictionFriction and Newton's LawsRecap - Sliding Crate

6Vertical Motion

Free FallThrowing UpwardTime in the AirRecap - Dropped Ball

9Project: Delivery Drone

Mission BriefingTakeoff ThrustClimb to AltitudeCruise and BrakePackage Drop

12Elastic Energy

Elastic Potential EnergySpring LaunchersEnergy with SpringsRecap - Spring Launcher

15Circular Motion

Uniform Circular MotionCentripetal AccelerationHorizontal CirclesVertical CirclesLoop the LoopRecap - Car on a Curve

18Final Challenges

Recap - Stunt RampRecap - Crash TestRecap - Space Probe