In physics, work is done when a force moves an object. If the force stays the same, we simply multiply force by distance. But often, the force changes as the object moves. This is called a variable force.

The Force-Displacement Graph

To find the work done by a changing force, we use a graph. We draw force on the vertical axis (y-axis) and displacement (distance moved) on the horizontal axis (x-axis). This is known as a Force-Displacement graph. The shape formed by the line on the graph represents how the force changes as the object moves from one point to another.

Calculating Work as Area

The golden rule for this topic is that the work done equals the area under the graph. If the line is a straight diagonal, the shape is often a triangle or a rectangle. You simply calculate the area of those shapes using basic geometry. For example, the area of a triangle is 1/2 × base × height. That value tells you exactly how much work was performed by the changing force.

Handling Irregular Shapes

Sometimes, the force changes in a curved way, creating an irregular shape on the graph. To find the area here, we break the space under the curve into very thin vertical strips. Each strip is treated like a tiny rectangle. By adding the areas of all these tiny rectangles together, we get the total work done. In advanced math, this process is called integration.

Real-World Example: Stretching a Spring

Think about stretching a metal spring. The more you pull, the harder the spring pulls back against you. Because the force required to stretch it increases as you go further, this is a perfect example of a variable force. If you draw this on a graph, it creates a triangle. Finding the area of that triangle gives you the energy stored in the spring as work.

• Force is measured in Newtons (N).
• Displacement is measured in meters (m).
• Work is measured in Joules (J).
• Total Work = Area under the Force-Displacement curve.