A student investigates the indentation made by a glass ball in the surface of modelling clay.

1. (a)Describe briefly how to use the apparatus in Fig. 3.1 to determine the diameter of the glass ball. [Figure 3.1] Draw a labelled diagram of the arranged apparatus to help your explanation.[2]
2. (b)(i)The student uses the glass ball to make an indentation in a piece of modelling clay. Fig. 3.2 shows the apparatus used. [Figure 3.2] A 300 g mass with weight F₁ = 3.0N is placed on a wooden strip directly above the glass ball. The mass is left in place for one minute and then removed. The student repeats the experiment with the ball on a different part of the clay and the 300 g mass hanging at the end of the wooden strip as shown in Fig. 3.3. [Figure 3.3 (drawn to a scale of 1:5)] The lengths x and y in Fig. 3.3 are shown to a scale of 1:5. The actual lengths X and Y are five times larger. Measure x and y on Fig. 3.3.[1]
3. (b)(ii)Calculate the actual lengths X and Y in metres to the nearest mm.[1]
4. (b)(iii)Calculate the force F2, exerted on the clay by the ball, using the equation: F2 = 3Y / X Show your working.[1]
5. (c)When the ball presses into the surface of the clay, it makes a small circular mark. This mark is called an indentation. Fig. 3.4 shows the indentations made by the glass ball in the surface of the clay. The indentations are drawn full size. [Figure 3.4 (drawn full size)] The smaller indentation is made by the mass positioned as shown in Fig. 3.2. The larger indentation is made by the mass positioned as shown in Fig. 3.3. Measure and record the diameter of the smaller indentation d₁ and the diameter of the larger indentation d₂.[1]
6. (d)(i)The graph in Fig. 3.5 shows the relationship between the diameter of the indentation and the surface area of the modelling clay inside the indentation for this glass ball. [Figure 3.5] On Fig. 3.5, plot the data shown in Table 3.1. [Table 3.1][1]
7. (d)(ii)On Fig. 3.5, draw the best-fit curve.[1]
8. (d)(iii)Use Fig. 3.5 to determine the surface areas A₁ and A₂ of the modelling clay inside the indentations with diameters d₁ and d₂ recorded in (c). Show on your graph how you arrive at your answers.[1]
9. (e)(i)Another student claims that: A₂ = kA₁ and F₂ = kF₁ where k is a constant, F₁ = 3.0N and F₂ is your answer to (b)(iii). Using your values of F₂, A₁ and A₂ from (b)(iii), and (d)(iii), calculate two values of k. Record your answers to a suitable number of significant figures.[2]
10. (e)(ii)Values of k are assumed to be the same within the limits of experimental accuracy if they are within 10% of each other. Explain whether these results show that the student's claim is correct.[1]
11. (f)Students in another laboratory obtain different values of A₁ and A₂ using the same arrangement of the apparatus. Identify two variables that should be controlled to ensure similar values of A₁ and A₂ when using modelling clay.[2]

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