Final answer:
The work done by a force acting on a body is calculated using the formula W = F · d cos θ. In Hooke's law systems, such as springs, work done is (1/2)kx², equating to stored potential energy. When the force and displacement are perpendicular, no work is done.
Step-by-step explanation:
To find the work done by a force P acting on a body displaced from point A to point B, we can use the formula W = F · d cos θ, where W is the work done, F is the magnitude of the force, d is the displacement, and θ is the angle between the force and the displacement vector. If the force is constant and directed along the displacement, or we are considering only the component of the force that is along the displacement, the work done is simply the product of the force's component in the direction of movement and the displacement (Fd cos θ).
When a system is deformed, such as stretching a spring that follows Hooke's law (where force is proportional to the displacement), the work done can be calculated as (1/2)kx², where k is the spring constant and x is the deformation. This work is equivalent to the energy stored in the system as potential energy.
In cases where the force is not aligned with the displacement, such as a charged particle moving in an electric field, we may find situations where no work is done because the force and displacement are perpendicular to each other.