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3.2Work, Energy, and Power

Work — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 9 parts Lesson 5 of 14 1 quiz

📚 AP PHYSICS 1 Hub / Topical Revision
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Lesson summary

3.2 Work — AP PHYSICS 1 notes: Describe the work done on an object or system by a force or collection of forces.Work = energy transferred into or out of a system when a force acts through a displacement.Unit — joule, 1 J = 1 N·m = 1 kg·m2/s2.Scalar — work has magnitude only but c…

  • W = Fd cosθ
  • What the symbols mean
  • Perpendicular forces
  • Kinetic friction
  • Variable force
  • Below the axis

Part 1 of 7Defining work

Work
Work energy transferred into or out of a system when a force acts through a displacement.
Unit
  • Unit joule, 1 J = 1 N·m = 1 kg·m2/s2.
Scalar
  • Scalar work has magnitude only but can be positive, negative or zero.
W
Fd cosθ
  • θ is the angle between the force and the displacement,
  • so W = F∥d.
    What the symbols mean: W = work done = energy transferred (J) · F = force (N) · d, s or x = distance moved in the direction of the force (m)
  • Only the parallel component does work.
  • If a force is applied but there is no displacement, no work is done.

Part 2 of 7Sign of work

AngleWorkEnergy and speed
0° ≤ θ < 90°PositiveEnergy transferred into the object; speed increases
θ = 90°ZeroNo energy transfer
90° < θ ≤ 180°NegativeEnergy transferred out; speed decreases
Perpendicular forces
  • Perpendicular forces the normal force on a sliding block and tension in uniform circular motion do zero work.
Kinetic friction
  • Kinetic friction opposes displacement, so Wf = −μkFNd and heats the surfaces.

Part 3 of 7Work from a force–position graph

Variable force
  • Variable force work equals the area under the F∥ against x graph.
Below the axis
  • Below the axis area counts as negative work.
Spring
  • F = −kx, so stretching from 0 to x gives the triangle ½kx2.

Part 4 of 7Conservative forces

Conservative force
  • Conservative force conserves mechanical energy within a system.
    • (gravity, spring force, electrostatic force)
Path independence
  • Path independence its work depends only on initial and final configurations.
Returning to start
  • Returning to start its work, and the change in potential energy, is zero if the system returns to its initial configuration.
Potential energy
  • Potential energy is associated only with conservative forces.

Part 5 of 7Nonconservative forces

Nonconservative force
  • Nonconservative force does not conserve mechanical energy;
    • examples are friction, air resistance, and applied pushes or pulls such as tension.
Path dependence
  • Path dependence a longer path dissipates more energy through friction.
Dissipated energy
  • Dissipated energy typically equals the friction force times the length of the path.

Part 6 of 7Work–energy theorem

Work–energy theorem
Wnet = ΔK
  • Wnet = ΔK net work equals ½mvf2 − ½mvi2.
System as an object
  • System as an object if the centre of mass and the point of application move the same distance, only the system's kinetic energy can change.
External versus internal
  • External versus internal external work changes total energy; internal forces transfer energy between forms.
1
Choose the object as the system and draw a free-body diagram.
2
Find the angle between each force and the displacement.
3
Calculate each work with W = Fd cosθ or the area under F against x.
4
Add the works with their signs to find Wnet.
5
Set Wnet = ½mvf2 − ½mvi2 and solve.

Part 7 of 7More from the specification

Constant
  • Not changing.
Gravitational potential
  • Work done per unit mass in bringing a test mass from infinity to the point.

Key terms

TermMeaning
WorkEnergy transferred by a force through a displacement.
JouleUnit of work and energy, 1 N·m.
Conservative forceForce whose work is path-independent.
Nonconservative forceForce whose work depends on the path, dissipating energy.
Work–energy theoremWnet = ΔK.

Avoid these mistakes

1
Using the full force instead of its parallel component.
2
Thinking a force perpendicular to the displacement does work.
3
Calling the work done by friction on a sliding object positive.
4
Treating work as a vector.
5
Believing that holding an object still does work.

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