Work-Energy Theorem
For a particle of constant mass, the total work by all forces between two states equals K_f minus K_i, whether or not individual forces are conservative.
Why this shows up in the exam
Finding speed after a displacement · Using a given v(x) relation · Stopping-distance calculations
Learn the idea
Net work equals the change in translational kinetic energy. Instead of solving for acceleration at every instant, add the work of all forces and compare the starting and ending speeds.
🧠 Memory hook: Net work changes speed-squared energy.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- W_net = Delta K — particle work-energy theorem
- K = (1/2)mv² — translational kinetic energy
- W_net = (1/2)m(v_f²-v_i²) — constant-mass endpoints
How to approach it
- 1Choose initial and final states
- 2Sum work by every relevant force
- 3Set the sum equal to K_f-K_i
Common slip-ups that cost marks
- •Using only one force instead of net work
- •Dropping the initial kinetic energy
- •Applying momentum conservation to a non-isolated interval
🌟 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.