In everyday language we say a student doing homework or a person standing for hours holding a heavy bag is working hard. In physics, the word work has a much narrower, precise meaning. Work is said to be done only when a force acts on an object and the object moves in the direction of (or along the line of) that force. If there is no force, or no displacement, then no work is done, no matter how tired you feel.
Two conditions must both be satisfied for work to be done:
- A force must act on the object.
- The object must undergo a displacement (it must move).
When a constant force $F$ acts on an object and moves it through a displacement $s$ in the direction of the force, the work done is the product of the two:
$W=Fs$
Here $F$ is the force in newtons (N), $s$ is the displacement in metres (m), and $W$ is the work in joules (J). When the force and displacement are not in the same direction but make an angle $\theta$ with each other, only the component of force along the displacement does work, so $W=Fs\cos\theta$. For Class 9 we mostly use the simple case where force and motion are along the same line, i.e. $\theta=0$ and $\cos\theta=1$.
The SI unit of work is the joule (J), named after James Prescott Joule. One joule is the work done when a force of 1 newton moves an object through a distance of 1 metre in the direction of the force, so $1\,\text{J}=1\,\text{N}\times1\,\text{m}$. Lifting a 100 g apple (weight roughly 1 N) up by 1 m takes about 1 J of work.
Work is a scalar quantity — it has magnitude but no direction. However, its value can be positive, negative or zero depending on the angle between force and displacement:
- Positive work — force has a component in the direction of motion ($\theta$ between $0^{\circ}$ and $90^{\circ}$). Example: pushing a box forward; gravity on a falling stone.
- Negative work — force acts opposite to motion ($\theta$ between $90^{\circ}$ and $180^{\circ}$). Example: friction slowing a moving trolley; gravity on a ball thrown upward.
- Zero work — either there is no displacement, or the force is perpendicular to the displacement ($\theta=90^{\circ}$). Example: a coolie carrying a load on his head and walking on level ground does no work against gravity, because the upward force and the horizontal motion are at right angles.
This is why simply pushing hard against a fixed wall — with great effort but zero displacement — counts as zero work in physics, even though your muscles tire.