Points to Ponder

Saying "calculate the work done" is vague. You must always specify which force (or group of forces) is doing the work, and over which displacement of the body. The context should make this clear.

Work is a scalar, but unlike mass or kinetic energy (which are always positive scalars), work can be positive or negative. For example, friction or viscous drag always does negative work on a moving body because the force opposes the displacement.

By Newton's Third Law, the mutual forces between two bodies are equal and opposite: $\vec{F}_{12} + \vec{F}_{21} = 0$. However, the work done by these two forces, $W_{12} + W_{21}$, does not always cancel to zero. It may sometimes cancel, but this is not guaranteed.

You can often calculate the work done by a force even if you don't know the force's exact nature. This is done by using the Work-Energy theorem, as shown in Example 5.2 of the textbook.

The Work-Energy theorem is not a new, independent law; it is a scalar form of Newton's Second Law. The principle of conservation of mechanical energy is itself a consequence of the Work-Energy theorem when only conservative forces act.

The Work-Energy theorem holds true in all inertial frames. It can also be applied in non-inertial frames, provided you include the work done by pseudo forces when calculating the net work on the body.

The potential energy for a conservative force is always defined up to an arbitrary additive constant. You are free to choose the zero point. For gravitational potential energy $mgh$, the zero is usually taken at the ground. For spring potential energy $\frac{1}{2}kx^2$, the zero is at the spring's equilibrium position.

Not every force in mechanics has an associated potential energy. Friction is a key example: its work over a closed path is non-zero, so no potential energy function can be defined for it.

During a collision: …