Hooke's law GCSE physics lesson: F = k e, springs and the force–extension graph

Hooke's law: a student's results

A student hung a spring from a clamp beside a vertical ruler, with a pointer at its bottom, and added 100 g masses. With nothing on it the spring was 6.0 cm long; with 100 g, 200 g, 300 g and 400 g it was 10.9, 15.8, 20.7 and 25.6 cm long. Use g = 9.8 N/kg.

1. With 300 g on it, what was the spring's extension, in cm?
2. What force does 300 g pull the spring with, in newtons?
3. Why does the student read the pointer with their eye level with it?
   1. So the reading isn't shifted by looking from above or below
   2. So the spring stretches further
   3. So the masses hang still
4. With 400 g the force is 3.92 N. Use that reading to find the spring constant, in N/m.
5. Plotted with force up and extension along, the readings make a straight line through the ___. Its gradient is the ___.
6. Predict the spring's extension with 250 g on it, in cm.
7. With 600 g the spring was 40.0 cm long, and with all the masses off it stayed 7.5 cm long. What happened?
   1. It went past its limit: it stretched more than F = k e says and was deformed inelastically
   2. It obeyed Hooke's law all the way and was deformed elastically
   3. Nothing: a spring always comes back a little longer

Hooke's law and springs: practice

Show your working on paper. Use g = 9.8 N/kg. Turn centimetres into metres and grams into newtons first. The stretch is optional.

Diagnostic question: choose and explain

1. A spring is 12 cm long. A weight hung on it stretches it to 18 cm long. Its spring constant is 50 N/m. What is the weight?
   1. 9 N
   2. 3 N
   3. 300 N
   4. 6 N

Practice questions

1. A spring has a spring constant of 40 N/m. What force stretches it by 0.05 m, in newtons?
2. A force of 6 N stretches a spring of spring constant 120 N/m. What is its extension, in metres?
3. A force of 4.5 N stretches a spring by 9 cm. What is its spring constant, in N/m?
4. A 250 g mass hangs on a spring of spring constant 35 N/m. What is the spring's extension, in cm?
5. Which of these is elastic deformation?
   1. A ruler bent a little that springs back straight
   2. A paper clip bent into a new shape
   3. A lump of modelling clay squashed flat
   4. A spring stretched so far it stays longer
6. A spring's force–extension graph is a straight line through the origin, then it curves. What does the curve show?
   1. The spring has gone past its limit of proportionality: F = k e no longer works
   2. The spring has become stiffer
   3. The spring constant has doubled
7. A spring hangs from a clamp with a mass on it. Why does stretching it need two forces?
   1. One force alone would just move the spring: the clamp pulls up on its top while the weight pulls down on its bottom
   2. One force stretches it and the other makes it go back afterwards
   3. It doesn't: the weight stretches it and the clamp does nothing
8. A spring of spring constant 80 N/m is stretched by 0.15 m. How much energy does it store, in joules?
9. A spring of spring constant 200 N/m is stretched by 4 cm. How much energy does it store, in joules?
10. A spring stretched by 10 cm stores 0.5 J. What is its spring constant, in N/m?
11. Stretch: a spring of spring constant 25 N/m reaches its limit of proportionality at an extension of 40 cm. What is the largest mass, in grams, it can hold and still obey Hooke's law? Then try it on the live spring.

Support: Write three lines before any F = k e: the extension (stretched length − original length), the extension in metres, and the force in newtons (W = m g for a mass).

Hooke's law: exit

Write the extension in metres before using F = k e.

1. A spring is 8.0 cm long. With a 2.0 N weight on it, it is 13.0 cm long. What is its spring constant, in N/m?
2. How long is the spring with a 3.0 N weight on it, in cm?

Exit check

Lengths, not extensions: shows who takes the extension and turns it into metres.

A spring is 8.0 cm long. With a 2.0 N weight on it, it is 13.0 cm long.

Hooke's law and springs

Use g = 9.8 N/kg. Write the extension in metres and the force in newtons before using a formula. Questions 4 and 5 are about the energy stored.