FOCUSED REVIEW
Focused Review: Springs and Elastic Potential Energy — Foundational
Reinforce the highest-leverage ideas about restoring force, elastic potential energy, turning points, and energy transformations.
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 Foundational 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: Foundational
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
Force Direction
Use equilibrium to identify the restoring-force direction.
A spring is stretched to the right. Which way does the spring force point?
Reveal Answers
Left, toward equilibrium.
Why it works: The restoring force points opposite the displacement.
ACTIVITY 2
Stored Energy
Compare equal-magnitude stretch and compression.
Does +x or −x store more spring energy when |x| is the same?
Reveal Answers
Neither; the energies are equal.
Why it works: Us = ½kx² depends on x².
ACTIVITY 3
Turning Point
Recall the speed at maximum deformation.
What is the instantaneous speed at maximum compression or extension?
Reveal Answers
Zero.
Why it works: Maximum deformation 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
Restoring Force and Equilibrium
For an ideal spring, Fs = −kx. The force points toward equilibrium, grows with |x|, and vanishes at x = 0.
Example: stretch right → force left. Sensei Note: the negative sign describes direction, not a negative magnitude.
KEY CONCEPT 2
Elastic Energy and Energy Exchange
A deformed spring stores Us = ½kx². As an ideal spring returns toward equilibrium, spring energy decreases while kinetic energy can increase.
Example: doubling |x| quadruples Us. Sensei Note: equal stretch and compression store equal energy.
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
Turning Point to Equilibrium
Track energy as the spring relaxes.
A block moves from maximum compression toward equilibrium on a frictionless surface. What happens to Us and K?
Reveal Answers
Us decreases and K increases.
Why it works: Mechanical energy is transferred from the spring into motion.
PRACTICE 3
Focused Setup Strategy
Separate force-direction reasoning from energy reasoning.
At equilibrium, is spring force zero? Is the block necessarily at rest?
Reveal Answers
The spring force is zero; the block need not be at rest.
Why it works: x = 0 makes Fs = 0, while kinetic energy can be maximum.
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
Force vs. Energy
Identify which quantity changes sign.
When displacement changes from +x to −x, which changes sign: Fs or Us?
Reveal Answers
Fs changes sign; Us does not.
Why it works: Force is directional; spring energy depends on x².
QUICK CHECK 2
Maximum Extension
Identify the turning-point condition.
At maximum extension, what is the speed?
Reveal Answers
Zero.
Why it works: The object reverses direction at a turning point.
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
Spring Energy Depends on x²
Us = ½kx², so equal-magnitude stretch and compression store equal energy.
KEY TAKEAWAY 3
Use Turning Points and Equilibrium as Anchors
At maximum deformation v = 0; at equilibrium Fs = 0 and spring energy is minimum.
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 →