1. **State the problem:** A learner performed a Hooke's Law experiment with a spring and measured mass and loaded spring length. We need to: - (a) Calculate applied force and extension. - (b) Plot applied force against extension. - (c) Find the spring constant from the graph. - (d) Determine if the spring reached its elastic limit and explain. 2. **Calculate applied force for each mass:** Using $F=mg$, with $g = 9.8$ m/s$^2$: - For 0 kg: $F=0\times 9.8=0$ N - For 0.02 kg: $F=0.02 \times 9.8=0.196$ N - For 0.04 kg: $F=0.04 \times 9.8=0.392$ N - For 0.06 kg: $F=0.06 \times 9.8=0.588$ N - For 0.08 kg: $F=0.08 \times 9.8=0.784$ N - For 0.10 kg: $F=0.10 \times 9.8=0.98$ N 3. **Calculate extension for each load:** Extension is the increase in length from 11 cm, converted to mm: - At 0 kg: $11$ cm, extension $= (11 - 11)\times 10=0$ mm - At 0.02 kg: $12.1$ cm, extension $= (12.1 - 11)\times 10=11$ mm - At 0.04 kg: $13.2$ cm, extension $= (13.2 - 11)\times 10=22$ mm - At 0.06 kg: $14.3$ cm, extension $= (14.3 - 11)\times 10=33$ mm - At 0.08 kg: $15.4$ cm, extension $= (15.4 - 11)\times 10=44$ mm - At 0.10 kg: $16.5$ cm, extension $= (16.5 - 11)\times 10=55$ mm 4. **Completed Table C2.1:** | Mass (kg) | Length (cm) | Applied Force (N) | Extension (mm) | |-----------|-------------|------------------|----------------| | 0 | 11 | 0 | 0 | | 0.02 | 12.1 | 0.196 | 11 | | 0.04 | 13.2 | 0.392 | 22 | | 0.06 | 14.3 | 0.588 | 33 | | 0.08 | 15.4 | 0.784 | 44 | | 0.10 | 16.5 | 0.98 | 55 | 5. **Plotting the graph (b):** Plot applied force (N) on the y-axis and extension (mm) on the x-axis using the table values. 6. **Determine spring constant (c):** Hooke's Law states $F = kx$, so $k = \frac{F}{x}$. Using any data except zero extension, for example at 55 mm: $$k = \frac{0.98}{55} \approx 0.0178$$ N/mm Convert to N/m: $$k = 0.0178 \times 1000 = 17.8 \text{ N/m}$$ 7. **Did the spring reach the elastic limit? (d)(i):** No. 8. **Explain (d)(ii):** The graph of force versus extension is a straight line passing through origin indicating proportionality; if the spring had passed the elastic limit, the graph would curve or flatten. Thus within this range, the spring obeys Hooke's Law and has not reached its elastic limit.