What is work in science?
In daily life, reading a book feels like work. In science, work is done only when a force moves something. Two things must happen: a force acts, and the object moves in the direction of the force.
Work = force × distance moved in the direction of force, W = F × s.
The unit of work is the joule (J). 1 J is the work done when a force of 1 newton moves an object 1 metre (1 J = 1 N × 1 m).
When is work zero, positive or negative?
- Zero: you push a wall and it does not move (s = 0). Or a coolie holds a load on his head and walks on flat ground: the force is up, the movement is sideways, so gravity and his lifting force do no work.
- Positive: force and movement are in the same direction (you push a cart forward).
- Negative: force is opposite to movement (friction slowing a rolling ball). Then W = −F × s.
Watch step 1 of the 3D: when F = 0 the crate does not move and W = 0 J.
Energy and its forms
Energy is the ability to do work. Its unit is also the joule. An object that has energy can push, lift or move something else. A moving hammer drives a nail: it had energy and it did work.
Forms of energy around you: mechanical (kinetic + potential), heat, light, sound, chemical (food, fuel), electrical and nuclear. A bigger unit is the kilojoule: 1 kJ = 1000 J.
Kinetic energy (energy of motion)
Anything moving has kinetic energy. KE = ½ m v², where m is mass in kg and v is speed in m/s. Double the speed and KE becomes four times, because v is squared.
Potential energy (stored energy)
A body raised above the ground stores energy because of its height. PE = m g h, where g ≈ 9.8 m/s² (we often use 10). A stretched rubber band and a wound spring also store potential energy, because of their changed shape.
PE depends only on the height, not on the path used to lift the object.
Conservation of energy
Law of conservation of energy: energy can neither be created nor destroyed. It can only change from one form to another. The total energy stays the same.
Drop a ball from height h. At the top it has only PE (mgh). As it falls, height goes down and speed goes up, so PE turns into KE. Just before it hits the ground, all the PE has become KE. At every point in between, PE + KE = mgh = constant (if air resistance is ignored).
Step 3 of the 3D shows this with three bars: blue PE shrinks, orange KE grows, green total stays level.
Energy changes you see every day
- Torch: chemical (cell) → electrical → light.
- Hydro power station: PE of stored water → KE → electrical.
- Brakes: KE of a cycle → heat in the brake pads.
Power: how fast work is done
Two people climb the same stairs. Both do the same work, but the one who runs up finishes first. We say the runner has more power.
Power = work done ÷ time taken, P = W ÷ t. Its unit is the watt (W): 1 W = 1 J/s. A bigger unit is the kilowatt: 1 kW = 1000 W.
If the power keeps changing, average power = total work ÷ total time.
Commercial unit of energy
Electricity bills use the kilowatt hour (kWh), called one "unit". 1 kWh is the energy used by a 1000 W appliance in 1 hour. 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J.
Simple machines: levers and pulleys
A simple machine helps us do work more easily: it lets a small force (the effort) move a big weight (the load), or change the direction of the force.
Mechanical advantage (MA) = load ÷ effort. If MA = 4, an effort of 50 N can lift a 200 N load.
Lever
A lever is a rigid bar that turns about a fixed point called the fulcrum. It balances when load × load arm = effort × effort arm. The arm is the distance from the fulcrum. So MA = effort arm ÷ load arm. Keep the fulcrum near the load and the effort arm becomes long, so you need less effort.
- Class I: fulcrum in the middle (see-saw, scissors, crowbar).
- Class II: load in the middle (bottle opener, wheelbarrow, nutcracker). MA is always more than 1.
- Class III: effort in the middle (tongs, your forearm, fishing rod). MA is less than 1, but you gain speed and control.
Pulley
A single fixed pulley (like at a well) has MA = 1. It does not reduce the force, but it lets you pull down to lift up, which is easier. A single movable pulley hangs with the load and has an ideal MA of 2. Joining pulleys in a block and tackle gives a larger MA.
No machine gives free work. When effort is smaller, you must move it through a longer distance. Friction always wastes a little energy, so real output work is less than input work.
Try it at home
Lever test: Put a pencil under a 30 cm ruler as a fulcrum. Place a few coins at one end. Press the other end with one finger. Now slide the pencil closer to the coins and press again. Which felt easier? Predict first, then check. (Answer: fulcrum near the load needs less effort.)
Power test: Walk up a flight of stairs and time it. Then walk up fast and time it again. Work = your weight (mass × 10) × height of the stairs. Divide by each time to find your power in watts.
Key formulas and definitions
- W = F × s (joule, J)
- KE = ½ m v²
- PE = m g h
- PE + KE = constant (no friction)
- P = W ÷ t (watt, W)
- 1 kWh = 3.6 × 10⁶ J
- MA = load ÷ effort
- Lever: load × load arm = effort × effort arm
Worked examples
1. A force of 20 N pushes a crate 3 m along the floor. Find the work done.
W = F × s = 20 × 3 = 60 J.
2. A 2 kg ball moves at 6 m/s. Find its kinetic energy.
KE = ½ m v² = ½ × 2 × 6² = ½ × 2 × 36 = 36 J.
3. A 2 kg ball is lifted to a height of 4 m (g = 10 m/s²). Find its potential energy.
PE = m g h = 2 × 10 × 4 = 80 J.
4. A 2 kg ball is dropped from 5 m. Find its KE and speed just before hitting the ground (g = 10).
PE at top = 2 × 10 × 5 = 100 J. All of it becomes KE, so KE = 100 J. ½ × 2 × v² = 100, so v² = 100, v = 10 m/s.
5. A student of mass 50 kg climbs 3 m of stairs in 6 s. Find her power (g = 10).
W = m g h = 50 × 10 × 3 = 1500 J. P = W ÷ t = 1500 ÷ 6 = 250 W.
6. A 1500 W heater runs for 2 hours a day for 30 days. Find the energy used in kWh and the cost at ₹8 per unit.
Energy per day = 1.5 kW × 2 h = 3 kWh. For 30 days = 90 kWh. Cost = 90 × 8 = ₹720.
7. A 600 N load is 1.5 m from the fulcrum of a lever. The effort is 4.5 m from the fulcrum. Find the effort and the MA.
600 × 1.5 = E × 4.5, so E = 900 ÷ 4.5 = 200 N. MA = 600 ÷ 200 = 3.
8. The speed of a car doubles. By how many times does its kinetic energy change?
KE ∝ v². New KE = ½ m (2v)² = 4 × ½ m v². So KE becomes 4 times.
Common mistakes
- Saying work is done when you hold a heavy bag still. No movement means W = 0.
- Forgetting to square the speed in KE = ½mv². Doubling v makes KE four times, not two times.
- Mixing up watt and watt hour. Watt is power (J/s); kWh is energy.
- Thinking a machine gives more work out than you put in. It only reduces force by making you move farther.