Final answer:
The sign of work is determined by the angle between the force and displacement vectors; work is positive if they are in the same direction, negative if opposite, and zero if perpendicular.
Step-by-step explanation:
The sign of work (W) is determined entirely by the angle between the direction of the force and the direction of displacement. In physics, the formula for calculating work is W = Fd cos θ, where W is work, F is the magnitude of the force on the system, d is the magnitude of the displacement of the system, and θ is the angle between the force vector F and the displacement vector d.
If the force and displacement are in the same direction, the cosine of the angle is 1, and the work done is positive. If the force and displacement are in opposite directions (angle between 90° and 180°), the cosine of the angle is negative, and the work done is negative. When the force is perpendicular to the displacement (angle is 90°), the cosine of the angle is 0, and the work done is zero. This relationship outlines the interplay between force direction, displacement, and the work performed.