Work

Work is done when energy is transferred from one entity to another through the application of force. Specifically, work occurs when a force acts on an object that undergoes displacement from one position to another. The amount of work depends on both the force applied and how far the object moves in the direction of that force.

Work is calculated using the dot product of force and displacement vectors. Only the component of force parallel to the displacement contributes to work done. Mathematically, this is expressed as the product of force magnitude, displacement magnitude, and the cosine of the angle between them, ensuring that perpendicular force components do not contribute to work.

When a force is constant in both magnitude and direction, the work done depends only on the starting and ending positions, not the path between them. The integral of force with respect to displacement yields the same result regardless of the route taken. This path independence is a key property of work under constant force conditions.

In the SI system, work is measured in Newton-meters (N·m), also called joules. In the English system, work is measured in foot-pounds (ft·lb). Both units represent force multiplied by distance, reflecting the fundamental definition that work equals force times displacement in the direction of motion.

For variable forces, work is calculated by dividing the displacement into infinitesimal segments and computing the dot product of force and displacement for each segment, then summing all increments. This approach applies to situations like spring compression or expansion, where force varies with position. The work done by a spring force is determined by integrating the force function over the displacement path.

Work is the mechanism by which energy is transferred between objects. When a force does work on an object, it transfers energy to that object, changing its state of motion or position. This energy transfer is fundamental to understanding how forces affect objects and is central to the work-energy theorem.

On curved paths, the force and displacement components vary at different points. Work is calculated by expressing force components as functions of position along the path and integrating these components with respect to displacement. The physical concept remains the same: calculate work for tiny displacements and add them up along the entire curved trajectory.