Figure 20 shows a child on a playground toy - AQA - GCSE Physics - Question 9 - 2021 - Paper 1

To investigate the properties of the spring:

1. Set up the apparatus: Secure a clamp stand to a table and attach the spring to it using a clamp.
2. Add weights: Hang weights on the spring and record the force applied to the spring.
3. Measure extension: For each weight added, measure the extension of the spring from its original length.
4. Repeat measurements: Gradually increase the weight in increments and measure the corresponding extension up to the maximum weight.
5. Risk assessment: Ensure the clamp is secure to prevent it from falling. Use safety goggles to avoid injuries from falling weights.

The correct equation that links extension (e), force (F), and spring constant (k) is:

$F = k imes e$

To determine the spring constant (k) from the data in Figure 21, use the formula:

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

If we assume the values from the graph, for example, a force (F) of 5 N and extension (e) of 0.125 m, then:

$k = \frac{5}{0.125} = 40 \, N/m$

Figure 21 supports the student's conclusion by demonstrating a linear relationship between the force applied to the spring and its extension. As more weight is added, the spring stretches proportionally, indicating that the extension directly correlates with the applied force, hence confirming the observation about proportionality.

To calculate the elastic potential energy (E_e) stored in the spring, we can use the formula:

$E_e = \frac{1}{2} k e^2$

Given:

• Spring constant, $k = 13 \, N/m$
• Extension, $e = 20 \, cm = 0.20 \, m$, we substitute these values:

$E_e = \frac{1}{2} imes 13 imes (0.20)^2 = \frac{1}{2} \times 13 \times 0.04 = 0.26 \, J$