Elastic Stores and the Square Law in a Spring

Lab Brief #6

🎯 Your mission

Run the experiment. Find out what really happens.

⚡ The twist

The opposite of what you expect is often what happens.

What you'll learn

Up to its limit of proportionality, a spring's extension is proportional to the force applied, F = kx, and the energy stored is the area under that force-extension graph, ½kx². Because area grows with the square of extension, stretching a spring twice as far stores four times the energy, not twice. That is why a bow drawn to full length delivers so much more than one drawn halfway, and why a car bumper is designed to crumple over a long distance rather than a short one.

Key words

Hooke's law
Up to the limit of proportionality, the extension of a spring is proportional to the force applied.
elastic store
Energy held in a stretched or compressed object, equal to the area under its force-extension graph.

Make a hypothesis first

Predict: what happens if you double the force?

Say your guess out loud — then find out if you were right.

Get ready

🧰 What you need

steel spring
slotted masses
clamp stand
ruler
graph paper

Get ready

⚠️ Safety first

Wear eye protection — a spring stretched past its limit can fly loose.
Clamp the stand to the bench and keep feet from under the hanging masses.

Step 1 of 4 · Read

Think about what you just learned: say what "Hooke's law" and "elastic store" mean in your own words before you start.

Step 2 of 4 · Do

Hang masses on a spring in 0.5 N steps and record the extension each time. Plot force against extension, find the gradient k, and calculate the stored energy at half extension and at full extension to check the four-fold ratio.

Step 3 of 4 · Observe

Record what actually happened, including anything that did not match what you expected.

Step 4 of 4 · Record

Write a conclusion that answers the question this lesson opened with, and state your uncertainty.

Question 1 of 3

Stretching a spring twice as far stores:

How sure are you?😐 maybe

Question 2 of 3

Hooke's law holds only up to the:

How sure are you?😐 maybe

Question 3 of 3

On a force-extension graph, the energy stored is shown by:

How sure are you?😐 maybe

Mind = blown

🎢 You feel weightless on a roller coaster because you and the seat are falling at the same speed.

Nice work!

You got 0 of 3 right.

All lessons

🎯

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✨ More to explore

🌍 Where you see this in real life: You use this every time you flip a light switch, ride a bike, or kick a ball.

🏆 Stretch challenge (try it this week): Time how long a small ball rolls down something, then change the slope and try again.

👨‍👩‍👧 For the dinner table: “Show me something at home that uses this kind of energy.”

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