Forces, Movement, Shape, and Momentum
5 marks · NormalA spring has an unstretched length of 7.0 cm. The table below shows how the length of the spring changes as different forces are applied.
| Force (N) | Length (cm) |
|---|---|
| 0 | 7.0 |
| 2 | 7.5 |
| 4 | 8.1 |
| 6 | 8.7 |
| 8 | 9.2 |
Complete the following column to show the extension of the spring for each force.
| Force (N) | Extension (cm) |
|---|---|
| 0 | |
| 2 | |
| 4 | |
| 6 | |
| 8 |
Plot a graph of force (y-axis) against extension (x-axis). (Describe the shape of the graph.)
Does this spring obey Hooke’s law over the range of forces shown? Explain your answer.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) 0 N: 0.0 cm, 2 N: 0.5 cm, 4 N: 1.1 cm, 6 N: 1.7 cm, 8 N: 2.2 cm
(b) Graph is a straight line passing through the origin; force is proportional to extension. (Shape: straight line.)
(c) Yes, the spring obeys Hooke's law over this range because force is proportional to extension (straight line graph through origin).
Common mistakes: Subtracting from wrong length for extension
Show mark scheme and worked solution
Marking points
A1 (a) · 1 mark · All extensions correct (0.0, 0.5, 1.1, 1.7, 2.2 cm).
M1 (b) · 1 mark · Graph plotted with correct axes (force/extension), all points correctly marked.
A2 (b) · 1 mark · Correct description of the graph's shape (straight line through origin).
E1 (c) · 1 mark · Clear statement on whether Hooke's law is obeyed, using data/graph evidence.
A3 (c) · 1 mark · Explanation linked to proportionality/graph (must mention straight line through origin or proportionality).
Worked solution
a) Extension = new length - original length (7.0 cm):
| Force (N) | Extension (cm) |
|---|---|
| 0 | 0.0 |
| 2 | 0.5 |
| 4 | 1.1 |
| 6 | 1.7 |
| 8 | 2.2 |
b) Graph points to plot: (0.0, 0), (0.5, 2), (1.1, 4), (1.7, 6), (2.2, 8). Points form a straight line through the origin. Shape: straight line.
c) Yes, because the graph is a straight line through the origin, showing force and extension are proportional—so the spring obeys Hooke's law over this range.