Work & Energy

Force & Newton's Laws answered why things move; this lesson asks how much got done and how fast. Where Speed & Motion measured how quickly position changes, here we measure how much work a force performs and how quickly it performs it.

Work: force times distance

Pushing an object a distance along the direction of the force is what physics calls doing work:

$W = F \times s$

measured in joules (J). Mind the words "along the direction": carrying a shopping bag while walking, your arm pulls straight up while the bag moves horizontally — the arm does no work on the bag.

Worked example: dragging a box

Dragging a box 3 m along the floor with a horizontal force of 50 N: $W = F \times s = 50 \times 3 = 150$ J. With only 25 N of strength over the same 3 m, the work is $25 \times 3 = 75$ J — half the force, half the work.

Kinetic and potential energy

Energy comes in two most familiar forms:

Kinetic energy: the energy of moving, growing with both speed and mass: $E_k = \frac{1}{2}mv^2$ ;
Potential energy: energy stored by position. Lift an object and it stores gravitational potential energy:

$E_p = mgh$

Worked example: a lifted ball

Raising a 2 kg ball to a height of 5 m (with g = 9.8 N/kg): $E_p = mgh = 2 \times 9.8 \times 5 = 98$ J. Those 98 J are exactly the work you did — and the energy the ball now stores.

Conservation: the form changes, the total does not

Let go of the ball. It loses height, so potential energy drains away; it gains speed, so kinetic energy builds up. The decrease on one side equals the increase on the other — an instant before landing, all 98 J of potential energy have turned into kinetic energy (ignoring air resistance). Energy never appears or disappears from nothing; it only changes form, and the total stays fixed. That is conservation of energy: a ledger that allows no debt, with every entry in plain sight.

Power: how fast the work gets done

Two people each do 600 J of work; one finishes in 20 seconds, the other needs 10 minutes. Who works harder? Power measures the rate of doing work:

$P = \frac{W}{t}$

measured in watts (W), where 1 W = 1 J/s.

Worked example: power

600 J of work done in 20 seconds: $P = 600 \div 20 = 30$ W. A bulb rated at 40 W converts 40 J of electrical energy into light and heat every second; a rice cooker at several hundred watts converts energy far faster.

Quick quiz

1. A force of 50 N pushes an object 3 m along its direction. How much work is done?
2. A 2 kg ball is lifted to a height of 5 m (g = 9.8). How much potential energy is stored?
3. 600 J of work is done in 20 seconds. What is the power?