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AP Physics | Spring Force and Energy Stored in a Spring

Overview
Ready to master springs for AP Physics? In this video, Ashish walks you step by step through spring force (Hooke’s law) and elastic potential energy so you can solve any F = kx or U = 1/2 kx^2 problem with confidence. We cover direction of force, equilibrium, work–energy with integrals, area under F–x graphs, and the most common AP mistakes to avoid. 💡📈

What you’ll learn

1. Hooke’s Law: how and why F = kx
2. Restoring force direction and sign conventions
3. Spring constant k: units, measuring k, and interpreting slope on F–x graphs
4. Work done by or on a spring and when signs flip
5. Deriving U = 1/2 kx^2 from W = ∫F dx
6. Using area under F–x graphs as energy
7. Equilibrium and choosing reference levels for energy
8. AP-style tips for setups with gravity, two springs, and ramps

Chapters
00:00 Welcome and learning goals 🎯
00:40 Hooke’s law F = kx: intuition and definitions
02:15 Restoring force direction and sign conventions
04:05 Spring constant k: units, how to measure, F–x slope
06:10 From work to energy: ∫ kx dx → 1/2 kx^2
07:50 Triangle area under F–x = stored energy
09:00 Equilibrium and zero-energy reference
10:00 Common AP mistakes and how to avoid them
12:00 Exam-style examples: compress, stretch, mixed systems
15:00 Quick lab plan: measuring k from data
17:00 FRQ strategy: justify, graph, units, and checks
18:30 Recap and practice problems

Key formulas used
Hooke’s law: Fspring = −kx (direction opposite displacement)
Magnitude often quoted as F = kx
Elastic potential energy: U = 1/2 kx^2
Work–energy link: ΔU = −Wby spring and Won spring = +ΔU
Graph method: Energy stored = area under F–x from 0 to x = 1/2 kx^2

Common AP pitfalls to avoid

1. Dropping the minus sign in F = −kx when discussing direction
2. Using kx instead of 1/2 kx^2 for energy
3. Mixing up “work by” vs “work on” the spring
4. Forgetting units: N for force, N/m for k, J for energy
5. Using Δx as (xf − xi) directly in energy without computing final minus initial energies

Quick derivation (why 1/2 kx^2)
Start with F = kx (magnitude). Work to stretch from 0 to x: W = ∫0→x kx dx = 1/2 kx^2. This equals the elastic potential energy stored in the spring. Simple triangle area under the F–x line gives the same result.

Mini practice (try these after the video)

1. A 300 N/m spring is stretched 0.08 m. Find U. Then find work done by you.
2. A spring stores 0.45 J at x = 0.10 m. Find k.
3. Two springs in parallel with k1 = 200 N/m and k2 = 300 N/m are compressed 0.05 m. Find total energy stored.

Who this is for
AP Physics 1 and AP Physics C students who want a clean, mistake-free way to do spring problems fast and accurately. Teachers can use the chapters as a mini lesson plan. 🧠✅

Call to action
If this helped, like the video, subscribe to PhyFix, and share with a friend who needs a quick win on springs. Comment your score on the mini practice and I’ll reply with a solution outline. 🔔

About the instructor
By Ashish | PhyFix
WhatsApp: +91 8684901516
Website: [https://freedemoclasses.netlify.app/](https://freedemoclasses.netlify.app/)

Keywords
AP Physics, Hooke’s law, spring force, spring constant, elastic potential energy, 1/2 kx^2, work energy theorem, F x graph, area under curve, restoring force, equilibrium, AP Physics review, AP FRQ tips, measure k, slope of F x graph

Hashtags
#APPhysics #HookesLaw #SpringForce #ElasticEnergy #PhysicsTutorial #PhyFix