Calculating work in non-trivial situations

If a constant force F pushes an object in the same direction as the object moves, for a distance d, then the work done by the force on the object is simple:

Example: a constant force in direction of motion

But real life is rarely so simple. You need to know how to deal with more complicated situations. Let's take a look at several ...

The magnitude of the force changes as the object moves

There's no way to avoid integration when this happens.

The force is not in same direction as the motion.

The basic idea here is to find the component of the force which acts along the direction of motion.

guide to finding the component of force along direction of motion
Example: Constant force NOT in direction of motion
The need for "the-component-of-force-in-the-same-direction-as-motion" occurs so frequently that physicists have a special shorthand notation to describe it: the dot product.
a brief description of the dot product
a problem in which the dot products helps a LOT

But what if the direction of the force, or the object, CHANGES as the object moves?

Example: Constant force, changing direction of motion

solution in PDF format
Solution in GIF format: Part 1 Part 2

Your turn: multiple forces and changing direction of motion