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

To improve the accuracy of the mean value for $t$, the student could stack multiple washers on top of each other and measure the combined thickness, thereby increasing the total thickness measured. This method reduces the impact of measurement errors by increasing the distance being measured, leading to a more reliable mean.

First, we calculate the area $A$ using the formula: $A = \frac{\pi}{4} (d_f + d_i)(d_f - d_i)$ Substituting the values:

• $d_f = 4.52 \, cm\pm0.02 \, cm$
• $d_i = 2.53 \, cm\pm0.02 \, cm$

Calculating the area:

• $d_f - d_i = 4.52 - 2.53 = 1.99 \, cm$
• $d_f + d_i = 4.52 + 2.53 = 7.05 \, cm$
• Therefore: $A = \frac{\pi}{4} (7.05)(1.99) \approx 11.0712 \, cm^2$ The uncertainties for the sums and differences can be calculated and multiplied accordingly: $u(A) = A \times \sqrt{\left(\frac{u(d_f)}{d_f}\right)^2 + \left(\frac{u(d_i)}{d_i}\right)^2}$ Substituting the uncertainties and calculating: The approximate calculation results in:\n- $\text{Percentage Uncertainty} \approx \frac{u(A)}{A} \times 100 \approx 3\%$.

To determine whether the washers are made of iron or steel, we first need to find their density using the mean mass and the volume calculated from the dimensions. The mean mass of a washer is given as 32.0 g.

• Using the density formula: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$
• Volume $V$ can be calculated as: $V = A \times t$ where $t$ is in cm, converting 4 mm to 0.4 cm. Using the previously calculated area $A \approx 11.0712 \, cm^2$ and: $V \approx 11.0712 \times 0.4 \approx 4.42848 \, cm^3$

Calculating the density: $\text{Density} \approx \frac{32.0 \, g}{4.42848 \, cm^3} \approx 7.22 \, g/cm^3$

Since the density of steel ranges from 7.6 g/cm³ to 7.9 g/cm³ and that of iron ranges from 6.6 g/cm³ to 7.6 g/cm³, the calculated density suggests that the washers are made from steel.