Work by a Constant Force
For a constant force, work is the scalar product of force and displacement, so its sign is set by the angle between those vectors and not by force magnitude alone.
Why this shows up in the exam
Forces on straight paths · Work by gravity or normal reaction · Comparing angled pulls
Learn the idea
Work selects the component of force along displacement. A force transfers energy only through the part that points along the actual displacement; a perpendicular push changes direction but does no work.
🧠 Memory hook: Dot force with displacement, not with velocity unless finding power.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- W = F . s = Fs cos(theta) — constant force over displacement s
- W_net = sum W_i — work contributions add as scalars
How to approach it
- 1Draw force and displacement vectors
- 2Take their dot product with signs
- 3Check the result has units of joules
Common slip-ups that cost marks
- •Using Fs without cos(theta)
- •Treating work as a vector
- •Assigning zero work whenever a force exists
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A 2 kg body speeds up from 3 m/s to 7 m/s. What net work is done on it?
More from Work, Energy and Power
Work and its calculation
Work is the energy transferred by a force acting over a distance, and can be calculated using the dot product, area under a force-displacement graph, or for variable and constant forces.
Conservation of energy
The law of conservation of energy states that energy cannot be created or destroyed, only transformed, including cases with energy loss and efficiency considerations.
Work-energy theorem
The work-energy theorem states that the net work done on an object equals the change in its kinetic energy, and applies to both constant and variable forces.
Conservative and non-conservative forces
Conservative forces, like gravity and spring force, conserve mechanical energy, while non-conservative forces, like friction, dissipate energy as heat.
Elastic potential energy
Elastic potential energy is the energy stored in a stretched or compressed spring, proportional to the square of its displacement.
Power
Power is the rate at which work is done or energy is transferred, and can be calculated as the product of force and velocity at any instant.