Work, Energy & Power
Learn how forces cause work, how energy is stored and transferred, and how power measures the rate of doing work. Use interactive simulators to explore motion, height, mass, and time to understand real-world energy transformations.
- Work β force Γ displacement
- Energy β ability to do work
- Kinetic Energy β energy of motion
- Potential Energy β energy due to position
- Conservation of Energy β energy transforms, not lost
- Power β rate of doing work
Key formulas
Real-world applications
Lifting objects & cranes
Cranes do work by applying an upward force over a vertical distance. The work done equals the force times the displacement in the direction of the force.
Key insight: Work = Force Γ displacement (W = FΒ·s). Lifting the same mass higher requires more work.
Roller coasters
As the car climbs, kinetic energy converts to potential energy; as it drops, PE converts back to KE. Friction converts some mechanical energy to thermal.
Key insight: KE β PE conversion; total mechanical energy is conserved when friction is small.
Hydroelectric dams
Water at height has gravitational PE; as it falls it gains KE, which turns turbines to generate electricity. Energy is conserved and transformed.
Key insight: Conservation of energy: PE (water high) β KE (flow) β electrical energy.
Electric appliances
Power ratings (e.g. 100 W) tell you how much work (energy per second) the appliance uses. Same work in less time means higher power.
Key insight: Power = work done per second (P = W/t). Compare fast vs slow lift in the Power simulator.
Common misconceptions & tips
Work depends on both force and displacement in the direction of the force: W = FΒ·s (or F s cos ΞΈ). A small force over a long distance can do the same work as a large force over a short distance. No work is done when the force is perpendicular to the displacement.
π Distance alone does not define work; the force component along the displacement matters.
π’ W = FΒ·s or W = F s cos ΞΈ
π§ͺ In the simulator, change force and displacement to see how work updates.
Energy is conserved: it is transferred or transformed, not destroyed. When work is done, energy moves from one form or object to another (e.g. kinetic to potential, or mechanical to thermal due to friction). The total energy of an isolated system stays constant.
π Energy changes form; it does not disappear. Thermal energy is still energy.
π’ Conservation of energy: ΞKE + ΞPE + ΞE_other = 0
π§ͺ Toggle friction in the Conservation Lab and watch total energy.
KE = Β½mvΒ² depends on both mass and speed. At the same speed, a heavier object does have more KE. But at different speeds, a lighter object can have more KE if it is much faster. Doubling speed quadruples KE; doubling mass only doubles KE.
π KE depends on mass and on the square of speedβso speed has a larger effect.
π’ KE = Β½mvΒ²
π§ͺ Compare different masses and speeds in the Speed vs KE simulator.
Gravitational potential energy is PE = mgh: it depends on mass m, gravitational field strength g, and height h. Doubling the mass doubles the PE for the same height. Doubling the height also doubles the PE for the same mass.
π PE is proportional to both mass and height.
π’ PE = mgh
π§ͺ Lift different masses to the same height in the Height & PE simulator.
Tip: Use the simulators above to explore work (W = FΒ·s), KE and PE, conservation of energy, and power (P = W/t).
Chapter Guide
How to Study This Chapter
- Start with Work (W = FΒ·s)
- Build: Energy β KE and PE
- Conservation of energy
- Power as rate of work
What You'll Learn
- Calculate work and when it is zero
- Relate KE and PE to motion and height
- Apply conservation of energy
- Compare power for same work, different time
Subtopics β Work, Energy & Power
Each subtopic has a dedicated page with clear explanations and an interactive simulator.
Work
Work is done when a force causes a displacement. W = FΒ·sΒ·cos ΞΈ. Unit: joule (J). Zero work when force is perpendicular to displacement.
Read more βEnergy
Energy is the ability to do work. It can be kinetic (motion), potential (position), or other forms. Energy is transferred when work is done.
Read more βKinetic Energy
Kinetic energy is the energy of motion: KE = Β½mvΒ². Doubling speed quadruples KE.
Read more βPotential Energy
Gravitational potential energy PE = mgh. It increases with height and mass; it depends on the planet (g).
Read more βLaw of Conservation of Energy
Energy cannot be created or destroyed; it can only be transformed or transferred. In a closed system, total energy is constant.
Read more βPower
Power is the rate of doing work: P = W/t. Same work in less time means higher power. Unit: watt (W).
Read more β