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

To determine the reduction in length when weights are added, first measure the original length of the spring without any weights. Then, progressively add weights and measure the new lengths after each addition. Finally, subtract the new length from the original length to find the reduction.

1. Use a ruler with smaller divisions for more accurate measurements of the spring length.
2. Ensure that the measurements are taken at eye level to avoid parallax error.

The reduction in length reaches a limit because the coils of the spring become fully compressed when the maximum load is applied, preventing any further extension.

Given the force of 0.5 N results in an extension of 13 mm (0.013 m), the spring constant k is calculated using Hooke's law:

$k = \frac{F}{x} = \frac{0.5 \, N}{0.013 \, m} \approx 38.46 \, N/m$

Using the work-energy principle, the work done on a spring is given by:

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

Substituting the given values:

$0.14 = \frac{1}{2} \cdot 175 \cdot x^2$

Rearranging gives:

$x^2 = \frac{0.14 \cdot 2}{175} \\ \approx 0.0016$

Thus, evaluating gives:

$x \approx 0.04 \, m$