Springs and Hooke's Law
Hang weights on a spring one at a time and watch it stretch, bounce and settle, while a graph of pull against stretch is drawn point by point. Within the spring's limit the points fall on a straight line: double the pull and the stretch doubles, and the slope of the line gives the spring's stiffness. Keep adding weight and the line bends, and when the weights come off the spring stays longer than it started. Compare one spring, two joined end to end and two side by side, and change the stiffness, the weights and the limit.
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What you can adjust
- Spring constant
- 5 – 100 N/m
- Mass of each weight
- 50 – 500 g
- Number of weights
- 1 – 12
- Arrangement
- 0 – 2
- Elastic limit of each spring
- 2 – 20 N
How stiff each spring is: the pull in newtons needed to stretch it by 1 metre. At 25 N/m a pull of 1 N stretches it by 4 cm. A very soft spring stops taking weights once it would stretch past 60 cm (120 cm for two in series).
The mass of each weight hung on the spring. A 100 g weight pulls down with a force of about 0.98 N.
How many weights are added, one after another. Each one adds a point to the graph.
Two identical springs end to end stretch twice as far for the same pull, so they act like one spring of half the stiffness. Side by side they share the pull, so they act like one spring of twice the stiffness.
The pull on one spring beyond which it no longer springs back fully. Past this point the graph bends, and the spring stays stretched when the weights come off. Set it above the total weight to see a spring that stays within its limit.
About this simulation
What it shows
A spring hangs from a support and weights are added one at a time. After each one the spring bounces a little and settles, and its stretch is read from a ruler in centimetres. A graph of the pull against the stretch gains a point each time.
The key idea
Within its limit a spring stretches in proportion to the pull: double the force and the extension doubles, so the points fall on a straight line and its slope is the spring constant. Pull past the limit of proportionality and the line bends, and the spring no longer returns to its old length when the weights come off.
Try this
Run the defaults: the line bends after the sixth weight and the spring ends 3.8 cm longer. Set Elastic limit of each spring to 10 and it springs back fully. Try Two in series.
A simple model: here the limit of proportionality and the elastic limit are the same point; in real springs the elastic limit comes slightly later. The springs are light, the weights hang still between bounces, and the bend past the limit follows a smooth made-up curve rather than a measured one. The bounce is slowed down so it is easy to see. Two springs side by side are treated as sharing the pull equally, so their limit is twice that of one. Weights stop being added once the stretch would pass 60 cm (120 cm for two in series), so a soft spring with heavy weights may hold fewer than you chose.