AQA A Level Physics Paper 3 Section A: Practical skills and data analysis November 2020 question paper 7408/3A

A simple pendulum performs oscillations of period T in a vertical plane.

Figure 1 shows views of the pendulum at the equilibrium position and at the instant of release. Figure 1 also shows a rectangular card marked with a vertical line.

The card can be used as a fiducial mark to reduce uncertainty in the measurement of T.

Annotate Figure 1 to show a suitable position for the fiducial mark. Explain why you chose this position.

The period of the pendulum is constant for small-amplitude oscillations. Figure 2 shows an arrangement used to determine the maximum amplitude that can be considered to be small, by investigating how T varies with amplitude.

Describe a suitable procedure to determine A_R, the amplitude of the pendulum as it is released. You may add detail to Figure 2 to illustrate your answer.

Figure 3 shows some of the results of the experiment.

Estimate, using Figure 3, the expected percentage increase in T when A_R increases from 0.35 m to 0.70 m. Show your working.

In another experiment the pendulum is released from a fixed amplitude. The amplitudes A_n of successive oscillations are recorded, where n = 1, 2, 3, 4, 5....

Table 1 shows six sets of readings for the amplitude A₅.

Determine the result that should be recorded for A₅. Go on to calculate the percentage uncertainty in this result.

Table 2 shows results for A_n and the corresponding value of ln(A_n / m) for certain values of n.

Complete Table 2.

Plot on Figure 4 a graph of ln(A_n / m) against n.

It can be shown that

where A₀ is the amplitude of release of the pendulum δ is a constant called the damping factor.

Explain how to find δ from your graph. You are not required to determine δ.

Figure 5 shows apparatus used to investigate the bending of a beam.

The beam is placed horizontally on rigid supports. The distance L between the supports is 80 cm.

A travelling microscope is positioned above the midpoint of the beam and focused on the upper surface.

Figure 6 shows an enlarged view of both parts of the vernier scale.

The smallest division on the fixed part of the scale is 1 mm.

What is the value of the vernier reading R₀ in mm? Tick (✓) one box.

Figure 7 shows the beam bending when a hanger of mass 0.050 kg is suspended from the midpoint.

The microscope is refocused on the upper surface and the new vernier reading R is recorded. The vertical deflection s of the beam is equal to (R – R₀).

The total mass m suspended from the beam is increased in steps of 0.050 kg. A value of s is recorded for each m up to a value of m = 0.450 kg. Further values of s are then recorded as m is decreased in 0.050 kg steps until m is zero.

Student A performs the experiment and observes that values of s during unloading are sometimes different from the corresponding values for loading.

State the type of error that causes the differences student A observes.

Student B performs the experiment using a thinner beam but with the same width and made from the same material as before.

Discuss one possible advantage and one possible disadvantage of using the thinner beam.

Figure 8 shows the best-fit line produced using the data collected by student A.

where E is the Young modulus of the material of the beam and η is a constant.

Deduce in s⁻² the order of magnitude of η.

E = 1.14 GPa

Student C performs a different experiment using the same apparatus shown in Figure 5 on page 10. A mass M is suspended from the midpoint of the beam. The vertical deflection s of the beam is measured for different values of L.

Figure 9 shows a graph of the results for this experiment.

Figure 9 shows that log₁₀(s / m) varies linearly with log₁₀(L / m).

State what this shows about the mathematical relationship between s and L. You do not need to do a calculation.

Deduce, using Figure 9, the value of s when L = 80 cm.

Determine M using Figure 8.

Figure 10 shows a partly-completed circuit used to investigate the emf ε and the internal resistance r of a power supply.

The resistance of P and the maximum resistance of Q are unknown.

Figure 10

Complete Figure 10 to show a circuit including a voltmeter and an ammeter that is suitable for the investigation.

Describe

• a procedure to obtain valid experimental data using your circuit

• how these data are processed to obtain ε and r by a graphical method.

Figure 11 shows a different experiment carried out to confirm the results for ε and r.

Initially the power supply is connected in series with an ammeter and a 22 Ω resistor. The current I in the circuit is measured.

The number n of 22 Ω resistors in the circuit is increased as shown in Figure 11. The current I is measured after each resistor is added.

It can be shown that

Figure 12 on page 22 shows a graph of the experimental data.

Figure 12

Show that ε is about 1.6 V.

Figure 13 shows the circuit when four resistors are connected.

Show, using Figure 12, that the current in the power supply is about 0.25 A.

Deduce, for the circuit shown in Figure 13,

• the potential difference (pd) across the power supply

Figure 14 shows the plots for n = 1 and n = 14

Three additional data sets for values of n between n = 1 and n = 14 are needed to complete the graph in Figure 14.

Suggest which additional values of n should be used. Justify your answer.

The experiment is repeated using a set of resistors of resistance 27 Ω.

The relationship between n and I is now

Show on Figure 14 the effect on the plots for n = 1 and n = 14 You do not need to do a calculation.