What it shows
A spring stretches in proportion to the load, and a mass hanging on it bobs up and down with a period that depends on the mass and the spring constant. The two experiments give the same spring constant.
The science
Hooke’s law says that the extension is proportional to the load for small loads: F = k x, where k is the spring constant. When a mass m is pulled down and released, the restoring force F = −k x produces simple harmonic motion with period T = 2π √(m / k). So T² = (4π² / k) m, a straight line through nearly the origin; the small offset comes from the spring’s own mass, which adds about one third of its mass to m. The two methods should give the same k.
Materials
Cost: under Rs 200. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A soft spring from a hardware shop or a short section of a Slinky (a pen spring is too stiff)
- A stand, a clamp or a hook fixed to a shelf
- A weight hanger and a set of 20 g or 50 g masses (washers or coin bags)
- A metre rule fixed upright behind the spring
- A phone stopwatch
- A kitchen scale to check the masses
- Graph paper
Safety
For this project: Keep the load light and your face away from the spring in case it snaps back. An adult should check the stand.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
7 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Hang the spring from the clamp, with the ruler beside it, and note the pointer position of the bottom coil with the empty hanger.
Add masses 20 g at a time up to 200 g and record the extension for each load in a table.
Plot load (in newtons, mass × 9.8) against extension and find the spring constant k from the slope; the line should be straight.
Now set the hanger with 100 g, pull it down 2 cm and release it, and time 20 oscillations; calculate the period T.
Repeat for 150, 200, 250 and 300 g, timing 20 oscillations for each.
Plot T² against the mass m and find the slope, which equals 4π² / k.
Calculate k from the slope and compare it with the static value from the first graph.
What you should see
The load-extension graph is a straight line for small loads and the dynamic graph of T² against m is a straight line that cuts the axis slightly to the left of zero. The two spring constants agree to within about 10 percent.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1State Hooke’s law.
Within the elastic limit, the extension of a spring is directly proportional to the applied force.
2What is the period of a mass on a spring?
T = 2π √(m / k).
3Why does the T² graph not pass exactly through the origin?
The spring itself has mass, which adds about a third of its mass to the oscillating load.
4What happens to T if the amplitude is made larger?
It stays the same for simple harmonic motion, as long as the spring is within its elastic limit.
Take it further
Join two identical springs in series and then in parallel and show the effective k halves or doubles.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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