Net work

Also called Total work, Work done by the net force

The signed sum of the work done on a system by every force exerted on it. The work-energy theorem equates the change in kinetic energy to net work, not to the work done by any one force on its own.

The CED puts the word in brackets so it cannot be missed. Essential knowledge 3.2.A.4: the work-energy theorem states that the change in an object's kinetic energy is equal to the sum of the work (net work) being done by all forces exerted on the object. The AP Physics 1 and AP Physics 2 sheets print it as

\Delta K = \sum W_i = \sum F_{\parallel,i}\, d_i

and the two Physics C sheets print the same $\Delta K = \sum W_i$ alongside the integral form of work.

The error this term exists to prevent. A block is pulled across a rough floor. You compute $W = Fd\cos\theta$ for the pull, set it equal to $\Delta K$ , and the answer is wrong, because friction was also doing work. Only when a single force acts is one force's work the same number as the net work.

The sum is algebraic, not a magnitude sum. Work is a scalar that carries a sign, so a negative term subtracts. Drag a crate across a floor at constant speed and the pull does positive work, kinetic friction does an equal negative work, the net work is zero, and $\Delta K = 0$ even though neither individual work was small.

Zero net work does not mean nothing happened. It means the kinetic energy came back to where it started. Energy still moved, some of it into thermal energy: 3.2.A.4.iii adds that the energy dissipated by friction is typically equated to the force of friction times the length of the path over which the force is exerted.

Two routes get you the number, summing each force's work or working from the net force, and the work-energy theorem guide sets both out with worked cases.

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