FOCUSED REVIEW
Focused Review: Springs and Elastic Potential Energy — Algebra-Based
Reinforce the highest-leverage equations and quantitative setups for spring force, spring energy, work, and conservation of energy.
TIME
Approximately 15 minutes
BEST FOR
Targeted reinforcement
FINISH WITH
A readiness check
After this focused review, you’ll be able to...
analyze springs and elastic potential energy using the Algebra-Based treatment with confidence.
Choose how you want to review
Course Alignment
This Physics Sensei Unit Review reinforces the unit below. Use it to review core ideas, prepare for homework, or refresh before a quiz or exam.
RESOURCE: Physics Sensei Unit Review
UNIT: Springs and Elastic Potential Energy
TREATMENT: Algebra-Based
COURSE LEVEL: Introductory college physics
BEST USED
✓ After learning the unit
✓ Before starting homework
✓ Before a quiz or exam
Physics Sensei is an independent educational resource organized around physics concepts, problem-solving strategies, and guided review.
Your Review Plan
Complete these six stages in order. Each stage builds on the previous one and prepares you for the final readiness check.
6 Stages • Approximately 15 minutes.
Warm-Up Check
Before you begin, take a moment to see what you already remember. Do not worry about getting everything right. This is only a starting point.
ACTIVITY 1
Hooke’s Law
Calculate a restoring-force magnitude.
A 300 N/m spring is stretched 0.040 m. Find |Fs|.
Reveal Answers
12 N.
Why it works: |Fs| = k|x| = 300(0.040).
ACTIVITY 2
Elastic Energy
Calculate stored energy.
A 200 N/m spring is compressed 0.10 m. Find Us.
Reveal Answers
1.0 J.
Why it works: Us = ½kx².
ACTIVITY 3
Turning Point
Identify the zero-speed state.
What is v at maximum compression?
Reveal Answers
0 m/s.
Why it works: Maximum compression is a turning point.
Ready to strengthen your understanding?
You've refreshed what you already know. Next, you'll reinforce the essential concepts that will help you solve problems with confidence. Need to see the learning path again?
Core Concepts
Reinforce the two highest-leverage relationships, then use them in representative situations.
KEY CONCEPT 1
Hooke’s Law and Elastic Energy
Use Fs = −kx for force and Us = ½kx² for stored energy.
Example: doubling x doubles force magnitude but quadruples spring energy. Sensei Note: keep force direction and energy sign reasoning separate.
KEY CONCEPT 2
Spring Work and Mechanical Energy
Spring work satisfies Ws = −ΔUs. For a frictionless horizontal system, K + Us is constant.
Example: ½kA² = ½mv² + ½kx². Sensei Note: choose states before substituting numbers.
Ready to apply these ideas?
You've reinforced the essential concepts. Now it's time to put them into practice by working through guided examples and building your problem-solving confidence. Need a quick reminder?
Guided Practice
Apply the reinforced ideas to two representative situations, then use the strategy card to check your setup.
PRACTICE 2
Speed at Equilibrium
Convert spring energy to kinetic energy.
A 0.50 kg block is released from rest after compressing a 200 N/m spring by 0.10 m. Find v at equilibrium.
Reveal Answers
2.0 m/s.
Why it works: ½kx² = ½mv², so v = x√(k/m).
PRACTICE 3
Focused Setup Strategy
Choose energy terms before calculating.
If vertical position changes, which potential-energy term joins Us?
Reveal Answers
Ug = mgy.
Why it works: Include every conservative potential that changes between the selected states.
Ready to check your understanding?
You've practiced the essential skills with guidance. Now it's time to solve a few short problems on your own and confirm you're ready to move forward. Need a quick reminder?
Confidence Check
You've rebuilt the key ideas and practiced them with guidance. Now try these short questions on your own to check your understanding before moving on.
QUICK CHECK 1
Energy Scaling
Use proportional reasoning.
If x doubles, what happens to Us?
Reveal Answers
It quadruples.
Why it works: Us ∝ x².
QUICK CHECK 2
Spring Work Sign
Use Ws = −ΔUs.
A spring moves toward equilibrium. Is Ws positive or negative?
Reveal Answers
Positive.
Why it works: Spring potential energy decreases, so −ΔUs is positive.
How did it go?
You've checked your understanding. Take one final look at the essential ideas before deciding what to do next. Need a quick reminder?
Summary
Before moving on, take one final look at the most important ideas from this review.
KEY TAKEAWAY 2
Connect Work to Potential Energy
Ws = −ΔUs.
KEY TAKEAWAY 3
Solve by Initial and Final States
Write the energy equation, eliminate zero terms, then solve.
Ready for your next step?
You've reviewed the essential ideas one last time. Now choose the resource that best matches how confident you feel. Need a quick reminder?
Next Step
Great work!
You've completed this review. Choose the next resource that best matches how confident you feel.
I'm Still Unsure
Review the key ideas and examples again.
Review Again →
I Need More Practice
Continue with additional practice for this topic.
Go to Practice →
I'm Ready
Continue to the next recommended resource.
Continue →