The photograph shows some metal washers - Edexcel - A-Level Physics - Question 11 - 2023 - Paper 3

To obtain a more accurate mean value for $t$, the student could stack the washers when measuring their thickness. By doing this, the measurement technique would increase the total thickness being measured, which helps reduce the relative percentage uncertainty in the measurement. Additionally, measuring multiple washers would also help in calculating a more reliable average.

To find the area $A$ of a washer, we use:
$A = \frac{\pi}{4} (d_f + d_i)(d_f - d_i)$
Mean values are given as:
$d_f = 4.52 \, \text{cm} \, \text{±} \, 0.02 \, \text{cm}$
$d_i = 2.53 \, \text{cm} \, \text{±} \, 0.02 \, \text{cm}$
First, calculate $A$:
$A = \frac{\pi}{4} (4.52 + 2.53)(4.52 - 2.53)$
Calculating the values:
$A = \frac{\pi}{4} (7.05)(1.99) \approx \frac{\pi}{4} (14.0195) \approx 11.0249 \, \text{cm}^2$
Now, to find the percentage uncertainty:
The uncertainties are combined by the rule of sums and differences:
$\left( \frac{u_d}{d} \right) = \frac{0.02}{4.52} + \frac{0.02}{2.53} \approx 0.00443 + 0.00791 = 0.01234$
So the total uncertainty in $A$ is:
$u_A = A \times 0.01234 \approx 11.0249 imes 0.01234 \approx 0.1365$
Therefore, the percentage uncertainty is:
$\frac{u_A}{A} \times 100\% \approx \frac{0.1365}{11.0249} \times 100\% \approx 1.24\%$
This confirms that the percentage uncertainty is about 3%, assuming rounding and significant figures.

To deduce whether the washers are made from iron or steel, we first need to find the density using the mass and volume relation. The mean mass of a washer is given as 32.0 g.
To find the volume $V$ of the washer, we can use the area calculated previously:
The density formula is:
$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$
Assuming the volume of the washer calculated earlier is approximately ( V ), we can find the density:
If we assume the washers are cylindrical,
The volume can be approximated as:
$V = A \times t$
We will take $t = 4 mm = 0.4 cm$:
$V \approx 11.0249 \, \text{cm}^2 \times 0.4 \, \text{cm} \approx 4.40996 \, \text{cm}^3$
Thus, the density calculation would be:
$\text{Density} = \frac{32.0 \, g}{4.40996 \, cm^3} \approx 7.25 \, g/cm^3$
The calculated density (7.25 g/cm³) falls between the densities of iron (6.6 g/cm³) and steel (7.9 g/cm³), indicating that the washers are more likely made from steel, as they are heavier than those made of pure iron.