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Home›Physics

Energy

Work, kinetic energy, potential energy, the conservation of energy and power, with the numbers worked out. The energy lab runs a roller coaster with energy bars and a friction slider, and lets you push or lift a load to see the work and power.

Progress

About this course

Writing an exam or holding a heavy bag feels like hard work, but in physics neither counts. Work has a strict meaning: a force does work on an object only when the object moves, and only by the part of the force that points along the motion. When work is done, energy is transferred, and that link is the reason the idea matters.

The six units are what energy is, work as force times distance, kinetic energy, potential energy, conservation of energy and the roller coaster, and power. A gardener pushes a lawn mower with 75.0 N along a handle 35° below the horizontal for 25.0 m, and the work is 75.0 × 25.0 × cos 35° = 1,536 J, which is 0.37 kcal of food energy. Kinetic energy has a square in it, so going from 60 km/h to 90 km/h is 1.5 times the speed but 2.25 times the braking distance. Running the formula backwards, a tennis ball at 100 km/h with about 22 J gives a mass of 57 g, which is the mass of a real tennis ball. The energy lab runs a roller coaster with energy bars and a friction slider, and lets you push or lift a load to see the work and power.

On the coaster, potential energy turns into kinetic energy down a hill and back again going up the next. Real tracks and air do negative work, so KE + PE slowly shrinks, but the energy is not destroyed: KE + PE + heat stays the same. The power unit gives 1 hp = 746 W and notes that a 60 W incandescent bulb gives only about 5 W of light.

Before you start

Work is force times distance, so it pays to know what a newton is from Forces, and speed from Motion. The formulas include a square for kinetic energy and a cosine for one lawn mower problem, and most answers need a calculator.

When you finish

You can calculate work from a force and a distance, the kinetic energy of a car, and the potential energy stored by lifting a box or squeezing a spring. You can explain why doubling speed quadruples kinetic energy, predict a roller coaster's speed at the bottom of a hill, find the power of someone running upstairs and turn a computer's daily use into kWh.

  1. 1What energy isOne joule lifts a 100 g apple about 1 m; a 1,000 kg car at 90 km/h carries about 310,000 of them.
  2. 2Work: force times distancePushing a lawn mower 25 m with 75 N at 35° below the horizontal does 1,540 J of work, about a third of a food Calorie.
  3. 3Kinetic energyA car at 100 km/h carries four times the kinetic energy it has at 50 km/h.
  4. 4Potential energyRaising a 0.500 kg cuckoo clock weight by 1 m stores 4.90 J, which the clock spends as the weight sinks.
  5. 5Conservation of energy and the roller coasterA roller coaster starting from rest at the top of a 20.0 m hill reaches 19.8 m/s at the bottom if friction is negligible, whatever its mass.
  6. 6Power: how fast work is doneA 60.0 kg woman running up 3.00 m of stairs in 3.50 s puts out 538 W, a little under one horsepower.

Related courses

  • Motion
    Position, speed, velocity and acceleration, then falling and flying objects. The motion lab launches a ball on Earth, the Moon or Mars and works out the time, height and range as you watch.
  • Forces
    Pushes, pulls, friction and gravity, and the three laws Newton used to connect force with motion. The motion lab swings a pendulum on Earth, the Moon or Mars and times it against the formula.
  • Waves and sound
    What a wave is, how wavelength, frequency and speed fit together, how sound travels, how waves add up, why strings and pipes ring at set notes, and the electromagnetic spectrum. The wave lab draws ropes, springs, sound in a tube, ripple tanks and standing waves from the same formulas used in the lessons.
  • Light
    Shadows and straight-line light, mirrors, refraction and total internal reflection, lenses and the eye, colour and prisms, and the long effort to measure how fast light goes. The wave lab traces rays through glass, water and lenses with Snell’s law and the thin lens equation.
Sources for this course (8)
  • OpenStax College Physics 2e (openstax.org/books/college-physics-2e): 7.1 Work: the scientific definition (W = F d cos θ, briefcase cases, 1 J = 1 N·m, 1 J lifts a 100 g apple about 1 m, lawn mower 75.0 N at 35° for 25.0 m = 1.54 × 10³ J, 1 kcal = 4186 J, under 10% of food energy goes into work)
  • 7.2 Kinetic energy and the work-energy theorem (KE = ½ m v², 30.0 kg package at 0.500 m/s = 3.75 J, 120 N push with 5.00 N friction over 0.800 m = 92.0 J net, final speed 2.53 m/s, a car at 100 km/h has four times the KE it has at 50 km/h)
  • 7.3 Gravitational potential energy (ΔPE = m g h, reference level, path independence, 0.500 kg cuckoo clock weight raised 1.00 m = 4.90 J, 60.0 kg person landing stiffly from 3.00 m, roller coaster 20.0 m hill: 19.8 m/s, and 20.4 m/s with a 5.00 m/s start, mass cancels)
  • 7.4 Conservative forces and potential energy (spring PE = ½ k x², 0.100 kg toy car, k = 250 N/m, 4.00 cm, 0.180 m rise)
  • 7.5 Nonconservative forces (friction turns mechanical energy into thermal energy)
  • 7.6 Conservation of energy (statement of the law, forms of energy, Table 7.1: 1000 kg car at 90 km/h 3.1 × 10⁵ J, tennis ball at 100 km/h 22 J, mosquito 1.3 × 10⁻⁶ J, daily food intake 1.2 × 10⁷ J, 1 gallon gasoline 1.2 × 10⁸ J, 1 g fat 3.9 × 10⁴ J; efficiency, Table 7.2: cycling and climbing 20%, swimming at the surface 2%, gasoline engine 30%, diesel 35%, coal power plant 42%, electric motor 98%, solar cell 10%)
  • 7.7 Power (P = W ÷ t, 1 W = 1 J/s, 1 hp = 746 W, 60.0 kg woman up 3.00 m stairs in 3.50 s reaching 2.00 m/s = 538 W, Table 7.3: Sun 4 × 10²⁶ W, car 8 × 10⁴ W, person at rest 100 W, heart at rest 8 W, clothes dryer 4 × 10³ W, a 60 W incandescent bulb gives 5 W of light, power plants turn 35 to 40% of fuel energy into electricity, E = P t, 0.200 kW computer 6.00 h a day for 30.0 days = 36.0 kWh, $4.32 at $0.120 per kWh)
  • g = 9.8 m/s² as in OpenStax examples (NIST standard gravity 9.80665 m/s², physics.nist.gov/cgi-bin/cuu/Value?gn).

Checked: 2026-10-17