Work and Energy: Forces, Motion, and Tension

Study Notes

Work is associated with a force and a displacement in physics.
For work to be done, the force must act through a distance.
Three methods to find work done by a force:
- Work done by a constant force
- Work done by a variable force
- Work done by the area under force and displacement graph

Work done on a system by a constant force is the product of the magnitude F of the force, the magnitude r of the displacement of the point of application of the force, and cos θ, where θ is the angle between the force and displacement vectors: W = F∆r cos θ
A force does no work on an object if the force does not move through a displacement.
Work is a scalar, even though it is defined in terms of two vectors, a force and a displacement.
SI unit of work is the newton·meter (N·m or kg·m2/s2).

If the force varies with position, the x component Fx of the force is approximately constant over a small interval.
The work done can be calculated by integrating Fx with respect to x over the path taken by the particle: W = ∫Fxdx

The force exerted by a spring on a block varies with the block's position x relative to the equilibrium position x = 0.
The work done by the spring can be calculated by integrating the force with respect to x: W = ∫Fdx.

This method is used when force and displacement are either parallel or antiparallel.
The area of the graph gives the magnitude of the work done.
If force and displacement have the same sign, work done is positive; if they have opposite signs, work done is negative.

Examples of calculating work done by a constant force, variable force, and spring force.
Example of finding the total work done by a force over a certain distance.