Hooke's Law Lab

Hooke's Law Lab: Measuring Spring Constants

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Springs are everywhere—in pens, mattresses, car suspensions, and trampolines. What makes springs so useful is their predictable behavior: stretch them a little, they pull back a little; stretch them more, they pull back more. This simple relationship, discovered by Robert Hooke in 1660, forms the foundation for understanding elastic materials and energy storage [1].

This lab lets you explore Hooke's Law firsthand by hanging various masses on springs, measuring extensions, and determining spring constants from your data.

The Physics of Springs

Hooke's Law

Robert Hooke observed that the force exerted by a spring is proportional to how much it's stretched or compressed from its natural length [1]:

$F = kx$

where:

• F = restoring force (N) — the force the spring exerts
• k = spring constant (N/m) — a measure of the spring's stiffness
• x = extension or compression (m) — displacement from natural length

The negative sign (often written F = -kx) indicates that the spring force opposes the displacement—pull it, and it pulls back; push it, and it pushes back.

Elastic Potential Energy

A stretched or compressed spring stores energy. This elastic potential energy is given by [2]:

$E_e = \frac{1}{2}kx^2$

Notice the x² term: doubling the extension quadruples the stored energy!

Key Relationships

Learning Objectives

After completing this lab, you should be able to:

1. Apply Hooke's Law to calculate spring force from extension
2. Determine the spring constant experimentally from F vs x data
3. Interpret the slope of a Force vs Extension graph
4. Calculate elastic potential energy stored in a spring
5. Explain the difference between soft and stiff springs
6. Predict how changing mass affects extension (at equilibrium)

Exploration Activities

Activity 1: Verify Hooke's Law

Objective: Confirm that force is proportional to extension.

Procedure:

1. Select "Soft (50 N/m)" spring
2. Add masses in 0.2 kg increments from 0.2 to 1.0 kg
3. Record force (F = mg) and extension for each mass
4. Plot F vs x—should be a straight line through the origin
5. Click "Fit Line" to find the slope

Expected result: Slope ≈ 50 N/m (the spring constant)

Activity 2: Compare Spring Stiffness

Objective: Understand how spring constant affects behavior.

Procedure:

1. Add 0.5 kg mass to each spring type (Soft, Medium, Stiff)
2. Record extension for each
3. Calculate k = F/x for each

Analysis: Which spring extends most? Which stores most energy?

Activity 3: Determine Unknown Spring Constant

Objective: Practice experimental determination of k.

Procedure:

1. Select "Unknown" spring
2. Add at least 5 different masses
3. Record F and x for each
4. Plot F vs x and use "Fit Line"
5. Report your measured value of k

Challenge: Calculate your percentage error once you reveal the actual value.

Activity 4: Energy Investigation

Objective: Explore elastic potential energy.

Procedure:

1. Set up any spring with 0.5 kg
2. Note the elastic PE shown
3. Double the mass to 1.0 kg
4. Compare the new elastic PE to the original

Question: Did PE double? Why or why not? (Hint: E ∝ x² and x ∝ m)

Real-World Applications

Reference Data: Common Spring Constants

Challenge Questions

Level 1 (Basic):

1. A spring with k = 100 N/m is stretched 0.15 m. What force does it exert?

Level 2 (Intermediate): 2. A 2 kg mass hangs from a spring in equilibrium, causing a 0.08 m extension. Find k.

Level 3 (Advanced): 3. How much energy is stored in a spring (k = 250 N/m) compressed 0.12 m?

Level 4 (Challenge): 4. Two springs (k₁ = 100 N/m, k₂ = 200 N/m) are connected in series. What is the effective spring constant?

Level 5 (Extension): 5. A 0.5 kg mass oscillates on a spring with k = 50 N/m. What is the period of oscillation? (T = 2π√(m/k))

Common Mistakes to Avoid

Frequently Asked Questions

Q: What happens if you stretch a spring too far? A: Beyond the elastic limit, Hooke's Law no longer applies. The spring permanently deforms (plastic deformation) and won't return to its original length [2].

Q: Why is the slope of F vs x equal to k? A: From F = kx, rearranging gives F/x = k. On a graph of F (y-axis) vs x (x-axis), the slope Δy/Δx = ΔF/Δx = k [1].

Q: Does Hooke's Law apply to compression as well as extension? A: Yes! The formula works for both cases. Compression is a negative extension, and the force is in the opposite direction (still opposing the displacement) [1].

Q: Why does elastic PE depend on x² rather than x? A: Energy is work done, which is force × distance. But force varies with distance (F = kx), so we integrate: W = ∫F dx = ∫kx dx = ½kx² [2].

Q: What's the difference between spring constant and stiffness? A: They're essentially the same concept. A higher spring constant means a stiffer spring—it takes more force to stretch it by a given amount.

References

[1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics, 10th Edition. Wiley. Chapter 7: Kinetic Energy and Work.

[2] Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers, 10th Edition. Cengage Learning. Chapter 7: Energy of a System.

[3] Knight, R. D. (2016). Physics for Scientists and Engineers: A Strategic Approach, 4th Edition. Pearson.

[4] Young, H. D., & Freedman, R. A. (2019). University Physics with Modern Physics, 15th Edition. Pearson.

About the Data

Spring constant values for real-world applications are approximate and vary with specific designs. The physics equations follow standard notation from university physics textbooks.

Citation Guide

To cite this simulation in academic work:

Simulations4All. (2025). Hooke's Law Lab [Interactive simulation]. Simulations4All Educational Platform. Retrieved from https://simulations4all.com/simulations/hookes-law-lab

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