Spring Force and Coupled Motion
For an ideal spring operating within its linear elastic limit, the restoring force is F_s = -kx, where x is measured from the natural length, and the stored elastic potential energy is U_s = kx^2/2.
Why this shows up in the exam
Spring calibration · Coupled blocks · Maximum extension
Learn the idea
An ideal spring exerts -kx and stores kx squared over two. Spring deformation couples blocks and pulleys; maximum extension need not mean zero acceleration.
🧠 Memory hook: Force is kx; energy is 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 = -k x — Hooke law
- U_s = (1/2)k x² — spring energy
- Delta K+Delta U_g+Delta U_s=0 — conservative balance
How to approach it
- 1Define deformation
- 2Write constraints
- 3Choose force or energy method
Common slip-ups that cost marks
- •Using kx as energy
- •Zero acceleration at turning point
- •Ignoring pulley ratios
🌟 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 block moves on a horizontal rough surface with coefficient of kinetic friction 0.2. A horizontal force of 10 N acts on it. Take g = 10 m/s^2. What is its acceleration?
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