9.7 - Force & Extension (Hooke's Law)

The experiment

Aim

To find out how the weight hung on a spring affects how far it stretches, to find the spring's spring constant, and then to use the graph as a way of weighing an unknown object.

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Background

• The extension is the increase in length from the spring's natural length, its length with nothing hanging on it.
• Hooke's law says the extension is directly proportional to the force. While it holds, $F=ke$, where $F$ is the force in N, $e$ is the extension in m, and $k$ is the spring constant in N/m. A stiff spring has a large spring constant.
• Hooke's law only holds up to the limit of proportionality. Past it, the graph curves.
• Stretching a spring also stores energy in its elastic potential energy store.
• You can't measure the spring constant directly, but you can measure the spring's length as the weight on it increases.
• So in this practical you find the extension for each weight and plot extension against weight. The graph gives the spring constant, and can then weigh an unknown object, as a spring balance does.

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Variables

• Independent variable - The weight hung on the spring.
• Dependent variable - The extension of the spring.
• Control variables - The spring, the position of the ruler, and the pointer read against it.

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Method

1. Set up - Hang the spring from a clamp stand, and clamp a metre ruler upright beside it with the zero of the scale level with the top of the spring.
2. Fit a pointer - Tape a splint to the bottom of the spring, horizontal and resting against the scale.
3. Measure the natural length - With no weight on the spring, read the pointer against the ruler.
4. Add the weights - Hook on the 1.0 N base of the weight stack and read the length, then add weights 1 N at a time up to 10 N, reading the length each time.
5. Work out the extensions - Take the natural length off each reading.
6. Plot the graph - Extension on the y-axis against weight on the x-axis, with a line of best fit.
7. Weigh an unknown object - Hang it on the spring, measure its extension, and read its weight off the graph. Check the answer with a newtonmeter.

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Safety

• Eye protection - A spring stretched too far can snap back.
• Stop the stand tipping - Clamp a heavy weight to its base, and put a tray under the masses.
• Stand, don't sit - So you can move away if the masses fall.

Worked example - Spring constant and energy stored

A student set the zero of the ruler level with the top of a spring, and recorded its length as they added weights 1 N at a time.

They then hung an unknown object on the spring, which stretched it by 10.0 cm.

Find the spring constant, the limit of proportionality, and the energy stored at 4.0 N, then find the weight of the unknown object.

Common exam questions

Question 1

Why is the zero of the ruler set level with the top of the spring?

So that every reading on the ruler is the length of the spring itself, which makes the extension easy to work out.

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Question 2

Why is the pointer taped on horizontally, so that it can't slip?

If the pointer twists or slides, the reading changes for a reason that has nothing to do with the weight on the spring.

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Question 3

How do you convert a mass marked in grams into the weight it applies?

Change it to kilograms, then use weight = mass × gravitational field strength. A 100 g mass is 0.1 kg, so it pulls with about 1 N.

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Question 4

A spring extends by 0.04 m when a weight of 10 N is hung on it. Calculate the spring constant.

k = F ÷ e = 10 ÷ 0.04 = 250 N/m.

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Question 5

Graphs of extension against weight are drawn for a stiff spring and a loose spring. Which line is steeper?

The loose spring's. It stretches further for the same weight, so its extension rises faster. A stiffer spring gives a shallower line and a larger spring constant.