Required practical 18 · Physics · Physics Paper 2, both tiers

Force and extension of a spring

Investigate the relationship between force and extension for a spring.

The exam trap. Extension is new length minus original length. Plotted the other way round, the gradient is 1/k.

Variables

Independent (you change): Force (weight) on the spring
Dependent (you measure): Extension of the spring
Control (you keep the same): The same spring
Reading the length at eye level from the same point
Adding weights gently

Hang the spring from the clamp and measure its unstretched length against the vertical ruler.
Why The original length is needed to calculate extension.
Add a 1 N weight and measure the new length at eye level.
Why Eye level avoids parallax error.
Calculate extension = new length − original length.
Why Extension is the change in length, not the length.
Repeat, adding 1 N at a time up to about 6 N.
Why A range of forces shows the pattern and the limit of proportionality.
Plot force against extension, with units on both axes.
Why The graph shows where the relationship stops being linear.
Find the spring constant k = F ÷ e from the gradient of the straight part.
Why On a force–extension graph, the gradient is k.

Hazard	How to reduce the risk
Springs can snap back and masses can fall.	Wear eye protection and keep feet clear; use a tray or cushion under the masses.

Up to 4.0 N the extension rises 2.5 cm per newton: proportional, k = 4.0 ÷ 0.100 = 40 N/m.
Beyond 4.0 N the limit of proportionality is exceeded.

Plotting length instead of extension.
Instead Extension = length − original length.
Leaving the quantity or unit off an axis.
Instead Label both axes with the quantity and unit: force in N, extension in cm.
Using the gradient of an extension–force graph as k.
Instead k is the gradient of force (y) against extension (x); the other way round gives 1/k.