Work

Work is how a force feeds energy into a moving object. In general it is the force accumulated along the path, W = ∫F·dr; when the force is constant over a straight displacement this collapses to the shortcut W = Fd cosθ. Only the part of the force pointing along the motion counts, which is why the angle matters. A force straight along the path does the full Fd; a force at a right angle does nothing; a force pulling backward does negative work and drains energy away.

Three things about work get mangled here. Dropping the angle and writing W = Fd for a force that pushes partly sideways, when only the along-the-motion part counts: W = Fd cosθ. Multiplying one force by the distance even as the force changes with position, when a varying force needs the area under the force-versus-position graph — for a spring, W = ½kx². And treating work as always positive, when a force that opposes the motion, like friction or gravity on the way up, does negative work and drains energy away.