force / N extension / cm 3 2.0 6 4.0 9 6.0 The table gives the extension of a spring for three loads. Assuming the spring obeys Hooke's law, what load would...
Question 1 Report
| force / N | extension / cm |
|---|---|
| 3 | 2.0 |
| 6 | 4.0 |
| 9 | 6.0 |
The table gives the extension of a spring for three loads. Assuming the spring obeys Hooke's law, what load would give an extension of 8.0 cm?
Answer Details
The data in the table show a linear pattern: every additional 3 N of force produces an additional 2.0 cm of extension. This means the spring constant is:
\[ k = \frac{F}{x} = \frac{3}{2.0} = 1.5 \text{ N/cm} \]
Since the spring obeys Hooke's law, this ratio remains constant. To find the force that produces 8.0 cm of extension:
\[ F = k \times x = 1.5 \times 8.0 = 12 \text{ N} \]
Alternatively, you can extend the pattern in the table: 3 N gives 2.0 cm, 6 N gives 4.0 cm, 9 N gives 6.0 cm, so 12 N gives 8.0 cm. Each step adds 3 N for every 2.0 cm. The key principle is that under Hooke's law, force and extension are directly proportional, so you can scale up using the same ratio.
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