Skip to content
Dabour HubLEARN · PRACTICE · EXPLORESign inStudent

3.1.2Work, Energy, and Power

Calculating Work Done — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 9 parts Lesson 4 of 14 1 quiz

📚 AP PHYSICS 1 Hub / Topical Revision
🩺
100% Curriculum Specification Match Lesson Doctor Verified
The only platform with 100% curriculum specification match and verified interactive question banks.
0%read
Lesson summary

3.1.2 Calculating Work Done — AP PHYSICS 1 notes: Calculate work done by constant and variable forces, including angled forces, gravity, friction and graphs, and relate net work to change in kinetic energy.Parallel force — W = Fd for a constant force parallel to the displacement;…

  • Angle ranges
  • Perpendicular force
  • Normal force
  • Kinetic friction
  • Spring force
  • Area under F∥ against x

Part 1 of 7Parallel force and angled force

Parallel force
  • W = Fd for a constant force parallel to the displacement; no displacement means no work.
  • A 200 N rope pull raising a bucket 2 m does 400 J.
Angled force
  • W = F∥d = Fd cosθ; only the component along the displacement does work.
  • A suitcase pulled with a handle at 30° does Fd cos30°; F sin30° does no work along the floor.
Angle ranges
  • 0° ≤ θ < 90° gives positive work and more speed;
    • θ = 90° gives zero work;
    • 90° < θ ≤ 180° gives negative work and less speed.
Perpendicular force
  • Perpendicular force can change direction without changing kinetic energy.
    • (circular motion, elastic collisions)

Part 2 of 7Work by common forces

Weight
  • Wg = −mgΔh; positive when descending, negative when rising, independent of path.
Normal force
  • Normal force zero for a stationary surface because it is perpendicular to the displacement.
Kinetic friction
  • W = −fkd, always negative for the sliding object and equal to the thermal energy produced.
Tension
  • W = Td cosθ; zero in circular motion or when perpendicular to the motion.
Spring force
  • Spring force work is the area under the force–extension graph.
Incline
  • Incline the component mg sinθ along the slope does the work; the perpendicular component does none.

Part 3 of 7Variable forces and graphs

Area under F∥ against x
  • Area under F∥ against x equals the work done, for a small force over a large displacement or a large force over a small one.
Splitting shapes
  • Splitting shapes triangle ½ × base × height; trapezoid ½ × width.
    • (sum of parallel sides)
Below the axis
  • Below the axis area counts as negative work.
Units
  • N against m gives joules.
Force–time graph
  • Force–time graph its area is impulse, not work.
Example
  • Example a triangle of ½(80)(250 − 100) = 6000 N·m plus a rectangle of 80 × 100 = 8000 N·m gives 14 000 N·m.

Part 4 of 7Net work and kinetic energy

Wnet
  • Wnet the sum of the works of all forces, or Fnetd cosθ for a constant net force.
Work–energy theorem
  • Wnet = ΔK = ½mvf2 − ½mvi2.
Sign of Wnet
  • Sign of Wnet positive increases speed, negative decreases it, zero leaves it unchanged.
Advantage
  • Advantage finds speeds without needing acceleration or time.

Part 5 of 7Method

1
Identify the object and the displacement.
2
List every force and the angle each makes with the displacement.
3
Compute the work of each force with its sign, or find the net force and its work.
4
If a speed is asked for, apply Wnet = ΔK.
5
Check signs: a force opposing the motion gives negative work.

Part 6 of 7Common situations

1Sliding down an incline of length d
  • Sliding down an incline of length d gravity does +mgd sinθ, friction does −μkmg cosθ × d, the normal force does zero.
2Lifting at constant speed
  • Lifting at constant speed the lifter does +mgΔh and gravity −mgΔh, so net work is zero.
3Braking to a stop
  • Braking to a stop net work −Fd equals minus the initial kinetic energy, so d = ½mv2/F.
4Connected objects
  • Connected objects calculate work on each separately; internal tension can do net zero work on the pair.

Part 7 of 7More from the specification

Potential energy
  • Energy stored by the configuration of a system.
Gravitational potential
  • Work done per unit mass in bringing a test mass from infinity to the point.
Conservative force
  • Force whose work is path-independent.
Nonconservative force
  • Force whose work depends on the path, dissipating energy.
Mechanical energy
  • Sum of kinetic and potential energy.
Distance
  • Total length of path travelled, a scalar.

Key terms

TermMeaning
Work–energy theoremNet work equals the change in kinetic energy.
Net workTotal work by all forces on the object.
Parallel componentComponent of a force in the displacement direction.
Area under a graphProduct of the plotted quantities over the interval.
Thermal energyEnergy of random particle motion, produced by friction.

Avoid these mistakes

1
Using weight times slope length instead of vertical height for gravity's work.
2
Forgetting the sign of friction's work.
3
Adding magnitudes of forces without considering angles.
4
Taking the area of a force–time graph as work.
5
Using the net force with one force's displacement without checking the object moves that way.

Last updated: