Spring Force and Elastic Energy
For an ideal Hooke-law spring measured from natural length, F_s=-kx and U_s=(1/2)kx^2; spring constants combine according to their physical connection.
Why this shows up in the exam
Spring-block speed and compression · Cut or combined spring problems · Elastic energy sharing
Learn the idea
An ideal spring stores energy quadratically in deformation. Doubling a spring deformation doubles its force but quadruples the stored energy, while cutting or combining springs changes the effective stiffness.
🧠 Memory hook: Force uses kx; stored energy uses half kx squared.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- F_s = -kx — Hooke-law restoring force
- U_s = (1/2)kx² — elastic potential energy
- 1/k_series = sum(1/k_i) — springs in series
- k_parallel = sum k_i — springs in parallel
How to approach it
- 1Define each spring deformation
- 2Find effective stiffness if needed
- 3Apply force balance or energy consistently
Common slip-ups that cost marks
- •Using total length instead of deformation
- •Forgetting the square in spring energy
- •Combining series springs as parallel
🌟 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.