Practical Analysis | Edexcel A-Level Physics A2

[Maximum number: 11]

A student investigated the damping of a rotational pendulum using the apparatus shown.

Figure for Question 1 — Edexcel A-Level Physics A2

When the metal rod is rotated through an angle and released, the rod performs angular oscillations about a vertical axis through the wire. The plastic sheets dampen the oscillations as they move through the air.

(a)

The student displaced the metal rod by a large angle. He recorded the maximum displacement angle every 10 oscillations.

n	$\theta/^{\circ}$
10	124
20	82
30	55
40	37
50	25
60	16

Figure for Question (a) — Edexcel A-Level Physics A2

[ 11 ]

(i)

Plot a graph of $\ln\theta$ against n on the grid opposite. Use the additional column for your processed data.

[ 5 ]

(ii)

Determine the value of $\lambda$ from the graph.

[ 3 ]

Using a large triangle on the best-fit line gives a gradient of about -0.0405. Since the gradient is $-\lambda$ ,

$\lambda\approx0.041$

(to 2 or 3 significant figures, with no unit).

(iii)

The student claimed that the initial displacement angle was greater than $180^{\circ}$ . Deduce whether this claim is correct.

[ 3 ]

From $\ln\theta=\ln\theta_0-\lambda n$ ,

$\ln\theta_0=\ln\theta+\lambda n=3.2+(0.041)(50)=5.25,$

so $\theta_0=e^{5.25}=191^{\circ}$ . This is greater than $180^{\circ}$ , so the claim is correct.

[Maximum number: 3]

A ball rolls along a U-shaped track. The ball oscillates in a vertical plane as shown.

Figure for Question 2 — Edexcel A-Level Physics A2

A student determined the time period T for different values of the distance D. She obtained the results shown in the table.

She predicts that for these oscillations

$T\propto\sqrt{D}.$

Show that her results are consistent with this prediction.

Table for Question 2 — Edexcel A-Level Physics A2

Use of $T=k \sqrt{ } D$

Or
$T^{2}=k D$

Three relevant calculations shown

[minimum 2 s.f.]

Comment consistent with comparing calculations [dependent MP2]

[Accept other valid routes]

Example of calculation
$k=0.78 / \sqrt{ } 0.235=1.61$ $k=0.94 / \sqrt{ } 0.335=1.62$ $k=1.09 / \sqrt{ } 0.445=1.63$

As these values are consistent the prediction is correct.

[Maximum number: 12]

A student investigated the damped oscillations of a pendulum using the apparatus shown.

The paper cone acted as a damper.
The student displaced the cone and allowed the pendulum to oscillate.
He measured the amplitude A every 5 oscillations and recorded the value to the nearest 5 mm.

Figure for Question 3 — Edexcel A-Level Physics A2

(a)

Give two reasons why it would not be appropriate to record A to the nearest mm.

[ 2 ]

(b)

The relationship between A and the number of oscillations n is

A=A_0 e^- n

where A_0 is the initial amplitude and is a constant.

[ 10 ]

(i)

The student recorded the following results.

Plot a graph of A against n on the grid opposite.
Use the additional column for your processed data.

Table for Question (i) — Edexcel A-Level Physics A2

[ 5 ]

(ii)

Determine the value of from the graph.

Table for Question (ii) — Edexcel A-Level Physics A2

[ 3 ]

(iii)

Explain why the value of A_0 determined from the graph may not be the true value of A_0.

[ 2 ]

[Maximum number: 5]

A student investigated the damping of a rotational pendulum using the apparatus shown.

Figure for Question 4 — Edexcel A-Level Physics A2

When the metal rod is rotated through an angle and released, the rod performs angular oscillations about a vertical axis through the wire. The plastic sheets dampen the oscillations as they move through the air.

The student displaced the metal rod by a large angle. He recorded the maximum displacement angle every 10 oscillations.

n	$\theta/^{\circ}$
10	124
20	82
30	55
40	37
50	25
60	16

Plot a graph of $\ln\theta$ against n on the grid opposite. Use the additional column for your processed data.

[Maximum number: 3]

A student investigated the damped oscillations of a pendulum using the apparatus shown.

The paper cone acted as a damper.
The student displaced the cone and allowed the pendulum to oscillate.
He measured the amplitude A every 5 oscillations and recorded the value to the nearest 5 mm.

Figure for Question 5 — Edexcel A-Level Physics A2

The relationship between A and the number of oscillations n is

A=A_0 e^- n

where A_0 is the initial amplitude and is a constant.

Determine the value of from the graph.

Table for Question 5 — Edexcel A-Level Physics A2

[Maximum number: 6]

A student used the apparatus shown to investigate the time taken for a hollow cylinder to roll down a ramp.

Figure for Question 6 — Edexcel A-Level Physics A2

(a)

Two students each carried out this procedure for another value of $\Delta h$ . They recorded the following times for the same value of $\Delta h$ .

Table for Question (a) — Edexcel A-Level Physics A2

Compare the accuracy and precision of the data that each student collected.

[ 4 ]

(b)

The relationship between t and the acceleration of free fall g is given by

t² = 4s² / (gΔh)

where s is the distance along the ramp between the start line and the finish line.
The student recorded the following values.

t = 2.44 s ± 0.04 s
s = 80.0 cm ± 0.1 cm
Δh = 43 mm ± 1 mm

[ 2 ]

(i)

Deduce whether the value of g is accurate.

[ 2 ]

The lower limit is $10.0(100-5.9)/100=9.4\,\mathrm{m\,s^{-2}}$ . The accepted value $9.81\,\mathrm{m\,s^{-2}}$ lies within the uncertainty range, so the result is accurate. Equivalently, the percentage difference $1.9\%$ is less than the percentage uncertainty $5.9\%$ .

[Maximum number: 2]

A student added small lead spheres to a test tube. The student placed the test tube in a small beaker of water. The test tube floated as shown.

Figure for Question 7 — Edexcel A-Level Physics A2

The student gave the test tube a small vertical displacement. The test tube then oscillated vertically.

The student replaced the water with another liquid. The period is given by $T=\sqrt{\frac{16\pi m}{D^2\rho g}},$ where D is the test-tube diameter, m is the mass of the test tube and spheres, and $\rho$ is the liquid density.

The density of glycerol is $1260\,\mathrm{kg\,m^{-3}}$ . Deduce whether the liquid could be glycerol.

The upper limit is $1190(1+0.041)=1239\,\mathrm{kg\,m^{-3}}$ , below $1260\,\mathrm{kg\,m^{-3}}$ . Therefore the liquid may not be glycerol.

[Maximum number: 3]

A student added small lead spheres to a test tube. The student placed the test tube in a small beaker of water. The test tube floated as shown.

Figure for Question 8 — Edexcel A-Level Physics A2

The student gave the test tube a small vertical displacement. The test tube then oscillated vertically.

The student replaced the water with another liquid. The period is given by $T=\sqrt{\frac{16\pi m}{D^2\rho g}},$ where D is the test-tube diameter, m is the mass of the test tube and spheres, and $\rho$ is the liquid density.

Show that the percentage uncertainty in $\rho$ is about $4\%$ .

Because $\rho\propto D^{-2}T^{-2}$ , $%U(\rho)=2\frac{0.01}{2.38}\times100+2\frac{0.01}{0.61}\times100=4.12\%,$ about $4\%$ .

[Maximum number: 2]

A student investigated the properties of a spring using the apparatus shown.

Figure for Question 9 — Edexcel A-Level Physics A2

The student determined the time period T of the oscillations of the mass-spring system.

The student displaced the mass downwards. He released the mass so that the mass oscillated vertically. He used a stopwatch to measure the time for multiple oscillations.

Determine the percentage uncertainty in the mean value of T.

Percentage uncertainty =

Edexcel A-Level Physics A2 6.5 Analysis Questions

Exam points

Covered syllabus points

Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question (iii)

Question 2

Question 3

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question 4

Question 5

Question 6

Question (a)

Question (b)

Question (i)

Question 7

Question 8

Question 9