Physics 9702/53 May/June 2023: question paper and mark scheme
Cambridge AS & A Level Physics (9702), Paper 5 Planning, Analysis and Evaluation, May/June 2023. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
A wooden cube of mass A is placed on an inclined plane. The cube is attached to a cylinder of mass B using string that passes over a pulley, as shown in Fig. 1.1.
pulley string
cube
cylinder plane horizontal surface θ
Fig. 1.1 (not to scale)
The angle between the plane and the horizontal surface is θ. Initially the cylinder is held at rest.
The cylinder is released. The time for the cylinder to fall a distance d is t.
It is suggested that t is related to θ by the relationship
2d = – AH sinθ – KA t2 (A + B) (A + B) where H and K are constants.
Plan a laboratory experiment to test the relationship between t and θ.
Draw a diagram showing the arrangement of your equipment.
Explain how the results could be used to determine values for H and K.
In your plan you should include:
● the procedure to be followed
● the measurements to be taken
● the control of variables
● the analysis of the data
● any safety precautions to be taken.
Diagram
…… [15]
Mark scheme
1 Defining the problem
θ is the independent variable and t is the dependent variable or vary θ and measure t 1
keep d constant 1
Methods of data collection
labelled diagram of workable experiment including: 1
plane supported by stand / support
stand/support on bench/floor/horizontal surface
minimum of two labels from cube, cylinder, (inclined) plane, method of support, bench/floor/horizontal surface, pulley,
string
diagram showing method to measure d, e.g. 1
clamped vertical rule near cylinder
or
drawn rule on plane used to measure d
or
distance d marked on plane and rule used to determine d
use a protractor to measure θ 1
or
use a rule(r) to measure appropriate lengths for a trigonometric calculation
use a timer/stop-watch to measure t or light gates connected to a timer to measure t 1
1 Method of Analysis
1 1 1
plot a graph of 2
against sin θ or equivalent (e.g. sin θ against 2 )
t t
Do not accept logarithms.
2d ( A + B ) × gradient 1
H =−
A
1 2d ( A + B )
(for sin θ against :H =− )
t 2
A × gradient
2d ( A + B ) × y -intercept 1
K =−
A
1
(for sin θ against : K = −H × y -intercept )
t2
1 Additional detail including safety considerations 6
D1 Safety precaution linked to falling cylinder, e.g. use of cushion/sand box to collect cylinder/prevent damage to
cylinder/floor/bench/injury
D2 protractor correctly positioned on diagram
or
appropriate trigonometric relationship for marked lengths
D3 keep A and B constant
D4 use a (top-pan) balance to measure A and B
D5 correct positioning of light gates to determine t, e.g. two light gates either end of distance d, connected to a timer
or
correct position of video camera with timer in frame of the video to determine t
D6 method to release cylinder/cube, e.g. cube held by set square, set square moved to release cube.
D7 reasoned method to keep d constant as θ changes, e.g.
(when measuring d by position of cylinder) adjust the length of the string or adjust the position of vertical marks or
adjust the position of the vertical rule or initial position of the cube
or
(when measuring d by position of cube) use fixed marks on the plane or ruler placed on the plane with d measured
between the marks
D8 method to increase t for cylinder to fall, e.g. use large d to increase t
D9 repeat measurements of t for the same θ and average t
D10 relationship valid if a straight line is produced (not passing through the origin)
Do not accept straight line passing through the origin.
A student investigates the discharge of capacitors in the circuit shown in Fig. 2.1.
CP CQ
V
R
Fig. 2.1
The capacitors have capacitances CP and CQ.
The student closes the switch to charge the capacitors and then records the maximum reading V0 on the voltmeter.
The switch is opened and a stop‑watch is started. The capacitors discharge through the resistor and the reading on the voltmeter decreases. When the reading on the voltmeter is V the time t is recorded. The discharge of the capacitors is repeated and the mean time T is calculated.
The experiment is repeated for different values of CP and CQ.
For each combination of CP and CQ, the combined capacitance C is calculated.
It is suggested that C and T are related by the equation
ln V = – T
V0 CR where R is the resistance of the resistor.
(a) A graph is plotted of T on the y‑axis against C on the x‑axis.
Determine an expression for the gradient.
gradient = …… [1]
(b) Values of CP , CQ and t are given in Table 2.1.
Table 2.1
CP / 10– 4 F CQ / 10– 4 F C / 10– 4 F t/s t/s T/s
2.2 1.5 12.9 14.5
2.2 3.3 21.1 19.7
2.2 5.6 23.7 24.9
3.3 1.5 15.3 16.9
5.6 1.5 19.0 17.6
5.6 3.3 30.9 32.1
The relationship between C, CP and CQ is
CPCQ
C= .
CP+CQ
Calculate and record values of C / 10– 4 F and T / s in Table 2.1.
Include the absolute uncertainties in T. [2]
(c) (i) Plot a graph of T / s against C / 10– 4 F.
Include error bars for T. [2]
(ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines. [2]
(iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer.
gradient = …… [2]
34
32
T/s
30
28
26
24
22
20
18
16
14
12
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
C / 10– 4 F
(d) The values of V0 and V are:
V0 = (4.8 ± 0.1) V
V = (2.4 ± 0.1) V.
Calculate ln V . Include the absolute uncertainty in ln V .
V0 V0
ln V = …… [1]
V0
(e) (i) Using your answers to (a), (c)(iii) and (d), determine the value of R. Include an appropriate unit.
R = …… [2]
(ii) Determine the percentage uncertainty in R.
percentage uncertainty in R = ……% [1]
(f) The experiment is repeated. Determine the value of C that gives a value of T of 60.0 s. Include the absolute uncertainty in your answer.
C = …… F [2]
[Total: 15]
To avoid the issue of disclosure of answer‑related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series.
Mark scheme
2(a) V 1
gradient = −R ln
V0
2(b) 1
C / 10–4 F T/s
0.89 or 0.892 13.7 ± 0.8
1.3 or 1.32 20.4 ± 0.7
1.6 or 1.58 24.3 ± 0.6
1.0 or 1.03 16.1 ± 0.8
1.2 or 1.18 18.3 ± 0.7
2.1 or 2.08 31.5 ± 0.6
Values of C and T correct as shown above.
Absolute uncertainties in T correct as shown above. 1
2(c)(i) Six points from (b) plotted correctly. 1
Must be within half a small square. Diameter of points must be less than half a small square.
Error bars in T plotted correctly. 1
All error bars to be plotted. Total length of bar must be accurate to less than half a small square and symmetrical.
2(c)(ii) Straight line of best fit drawn. 1
Do not accept line from top point to bottom point.
Points must be balanced.
Line must pass between (1.42, 22.0) and (1.45, 22.0) and between (1.95, 30.0) and (2.00, 30.0)
Worst acceptable line drawn (steepest or shallowest possible line that passes through all the error bars). 1
All error bars must be plotted.
2(c)(iii) Gradient determined with clear substitution of data points into Δy / Δx. 1
Distance between data points must be greater than half the length of the drawn line.
Gradient of worst acceptable line determined with clear substitution of data points into Δy / Δx. 1
uncertainty = (gradient of line of best fit – gradient of worst acceptable line)
or
uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient)
2(d) – 0.69 or – 0.693 and ± 0.06 1
2(e)(i) R determined using gradient and R given to 2 or 3 significant figures. 1
gradient (c)(iii)
R=− =
V (d)
ln
V0
R correctly determined using gradient and SI unit with correct power of ten for R (e.g. Ω). 1
2(e)(ii) Percentage uncertainty in R with method shown. 1
V
Δ ln
V0 Δgradient
percentage uncertainty = + × 100
gradient
ln V
V0
or
Correct substitution for max/min methods.
2(f) C determined to a minimum of 2 significant figures from (c)(iii) or (d) and (e)(i) with correct substitution. 1
T 60.0
C= =
gradient gradient
or
−T −60.0
C= =
V (e)(i) × (d)
−R ln
V0
Absolute uncertainty in C determined with correct method used: 1
Using gradient to determine C:
Δgradient
ΔC = ×C
gradient
Allow using R to determine C:
V
Δ ln
V0 (e)(ii)
ΔC = + ×C
100
ln V
V0
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Physics 9702/53 for May/June 2023 is out of 30 marks, with 1 hour 15 minutes to answer it.
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