Grade 11 asked what forces DO to motion. Grade 12 asks what they COST. The currency is work, and its unit is the joule: $1\ \mathrm{J} = 1\ \mathrm{N \cdot m}$, one newton pushing through one metre. Read aloud: W equals F d cos theta. Letter by letter — $W$ is the work in joules, $F$ is the constant force in newtons, $d$ is the displacement in metres, and $\theta$ (Greek theta) is the angle between the force and the direction of travel. Whichever one the question leaves blank is what you solve for.

House rule for this chapter, stated once: W is work. Weight gets written $F_g = mg$, the way SPH4U writes it, because two different $W$'s in one chapter is a wound nobody needs.

The cosine is the whole idea. Only the part of the force lying ALONG the path does work. Pull straight along and $\cos 0^\circ = 1$ — full price. Pull at $60^\circ$ and $\cos 60^\circ = 0.5$ — half of your force is going sideways and buys nothing. Push at $90^\circ$ and $\cos 90^\circ = 0$: carry a heavy bag across a level room and, in physics' strict accounting, you do zero work on it. Your shoulder disagrees; the ledger does not. And when the force points BACKWARD along the path, $\cos 180^\circ = -1$ — friction's signature move, and the reason work can be negative.