Aim
To investigate the relationship between the stretching force and the extension of a spring and to determine the spring constant.
Variables
- Manipulated: Stretching force, F (the weight of the load)
- Responding: Extension of the spring, x
- Constant: The same spring
Apparatus & materials
- Steel spring
- Retort stand and clamp
- Slotted masses with a hanger
- Half-metre rule
- Pointer
- G-clamp
Procedure
- Suspend the spring from the clamp and attach a pointer to its lower end, next to a vertical half-metre rule.
- With no load, record the initial pointer reading.
- Hang a 50 g load (weight 0.5 N) on the spring and record the new pointer reading.
- Calculate the extension x = new reading − initial reading.
- Add loads in steps up to about 250 g, recording the reading each time; then remove the loads to check the spring returns.
- Record the force F and the extension x for each load.
Tabulating results
Record the stretching force F in N and the extension x in cm (or mm). Head each column with the quantity and unit and keep the decimal places consistent.
The graph
Plot F (y-axis) against x (x-axis). A straight line through the origin shows F is directly proportional to x, obeying Hooke's law; the line curves beyond the elastic limit.
Analysis
By Hooke's law F = kx, so the gradient of the F against x graph gives the spring constant k. The straight-line region shows the spring obeys Hooke's law.
Precautions
- Add and remove loads gently and wait for the spring to settle before reading.
- Read the pointer at eye level to avoid parallax error.
- Do not exceed the elastic limit of the spring.
Force and Motion II · Graph skills
Sample results and what they show
Example data for a steel spring (the initial pointer reading has already been subtracted to give the extension):
- Force F = 0.5 N, extension x = 2.0 cm
- F = 1.0 N, x = 4.0 cm
- F = 1.5 N, x = 6.0 cm
- F = 2.0 N, x = 8.0 cm
- F = 2.5 N, x = 10.0 cm
Each time the force goes up by 0.5 N the extension goes up by 2.0 cm, so the extension is a constant multiple of the force. This is the signature of a spring obeying Hooke’s law: the extension is directly proportional to the stretching force within the elastic limit.
When you take the loads off and the pointer returns to its starting reading, the spring is still elastic, which tells you that you never went past the elastic limit during the readings.
Reading the graph and finding the answer
Plot force F (y-axis) against extension x (x-axis). The points fall on a straight line through the origin, which confirms F is directly proportional to x.
The gradient of this line is the spring constant k. Draw a large triangle using two widely spaced points on the best-fit line, for example (0.020 m, 0.5 N) and (0.100 m, 2.5 N).
Convert the extension to metres first:
k = ΔF ÷ Δx = (2.5 − 0.5) N ÷ (0.100 − 0.020) m = 2.0 N ÷ 0.080 m = 25 N m⁻¹
So the spring constant is 25 N m⁻¹, meaning 25 N is needed for every 1 m of extension. The straight part of the graph is the region where Hooke’s law holds; if you overload the spring the line curves upward beyond the elastic limit.
Marks examiners look for
For the practical marks: add and remove each load gently and wait for the spring to stop bobbing before reading, read the pointer against the rule at eye level to avoid parallax error, and do not exceed the elastic limit so the spring returns to its original length.
For the Paper 3 science-process-skill marks, state the variables clearly: the manipulated variable is the stretching force F, the responding variable is the extension x, and the fixed variable is the same spring throughout. Tabulate F in N and x in cm (or m) with a unit in every column heading and a consistent number of decimal places.
Draw axes with even scales, plot the points sharply, and draw a single thin best-fit line. When you find k from the gradient, show the triangle, the coordinates and the unit.
A good conclusion links the straight line through the origin back to the aim: the spring obeys Hooke’s law.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)