Figure 9 shows a spring standing on a table - Edexcel - GCSE Physics Combined Science - Question 4 - 2020 - Paper 1

The reduction in the length of the spring can be determined by first measuring the original length of the spring without any weights. Then, after adding a known weight, measure the new length of the spring. The reduction in length can be calculated by subtracting the new length from the original length.

1. Use a ruler with smaller millimeter divisions for more accurate measurements.
2. Repeat the experiment multiple times and calculate an average to minimize errors.

The reduction in length eventually reaches a limit because the spring coils become fully compressed, preventing further elongation.

To calculate the spring constant k, use the formula:

$k = \frac{F}{x}$

where F is the force applied (0.50 N) and x is the extension (13 mm, converted to 0.013 m).

Substituting the values: $k = \frac{0.50}{0.013} \approx 38.46 \, N/m.$ Thus, the spring constant k is approximately 38.5 N/m.

To find the extension of the spring, use the formula for work done in extending a spring:

$E = \frac{1}{2} k x^2$

Rearranging the formula gives: $x^2 = \frac{2E}{k}$

Substituting given values, where E = 0.14 J and k = 175 N/m:

$x^2 = \frac{2 \times 0.14}{175}$

Calculating this gives: $x^2 = \frac{0.28}{175} \approx 0.0016$

Therefore, taking the square root: $x \approx 0.04 \, m$ The extension of the spring is therefore 0.04 m.