Describe briefly how to use the apparatus in Fig. 3.1 to find the diameter of the glass ball. Add a labelled diagram of the arranged apparatus to support your explanation.
Obtain $x$ and $y$ from Fig. 3.3.
Calculate the true lengths $X$ and $Y$ in metres, rounded to the nearest mm.
Calculate the force $F_2$ applied to the clay by the ball, using the equation $F_2 = \frac{3Y}{X}$. Show your working.
Measure, then note down, the diameter of the smaller indentation $d_1$ and the diameter of the larger indentation $d_2$.
Use Fig. 3.5 to plot the data listed in Table 3.1.
On Fig. 3.5, draw the best-fit curve through the plotted points.
Use Fig. 3.5 to determine the surface areas $A_1$ and $A_2$ of the modelling clay inside the indentations with diameters $d_1$ and $d_2$ recorded in part (c). Show on your graph how you arrive at your answers.
A second student states that $A_2 = kA_1$ and $F_2 = kF_1$, where $k$ is a constant, $F_1 = 3.0\,\text{N}$ and $F_2$ is your answer to part (b)(iii). Using your values of $F_2$, $A_1$ and $A_2$ from parts (b)(iii) and (d)(iii), calculate two values of $k$. Write your answers to a suitable number of significant figures.
If two values of $k$ are within $10\%$ of each other, they are treated as the same within experimental uncertainty. Explain whether these results support the student’s claim.
In another laboratory, students obtain different values of $A_1$ and $A_2$ even though they use the same apparatus arrangement. Identify two variables that should be controlled so that similar values of $A_1$ and $A_2$ are obtained when using modelling clay.