Law
Hooke’s Law
For an ideal spring: \(F=-kx\). The restoring force points opposite displacement from equilibrium.
- Meaning of \(k\)
- Equilibrium position
- Direction/sign conventions
Work & Energy · Physics
Elastic Potential Energy (Springs)
Springs store energy when stretched or compressed: \(U_s=\tfrac12 kx^2\).
This topic includes
Subtopics to master
Connect Hooke’s law to stored energy and solve multi-spring energy problems.
Energy
Spring Potential Energy Function
From \(F=-kx\), the stored energy is \(U_s=\tfrac12 kx^2\) (relative to \(x=0\)).
- Where the \(x^2\) comes from
- Work–energy connection
- Graph \(U(x)\)
Systems
Multiple Springs
Combine springs in series/parallel (intro) and track total energy stored across elements.
- Equivalent stiffness idea
- Energy in each spring
- Common setups
Meaning
Energy Storage and Release
A spring trades energy between \(U_s\) and kinetic energy; this powers launches and oscillations (preview).
- Release from compression
- Energy transfer picture
- Real-world examples
Practice
Practice & Exercises
Solve energy problems with springs: compute \(U_s\), speeds, and compression distances.
- \(U_s=\tfrac12 kx^2\) drills
- Work vs energy interpretation
- Spring launch problems
- Multi-spring energy bookkeeping
- Concept checks (signs, equilibrium)
Bridge
Toward Energy Conservation
With only conservative forces (springs + gravity), \(K+U_s+U_g\) is conserved — a powerful solving tool.
- When conservation applies
- Energy diagrams preview
- Next topics link