Physics 9702/52 October/November 2019: question paper and mark scheme
Cambridge AS & A Level Physics (9702), Paper 5 Planning, Analysis and Evaluation, October/November 2019. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
A student is investigating the maximum height reached by a light plastic ball when it is launched vertically from a compressed spring, as shown in Fig. 1.1.
final position of ball
h
initial position of ball
spring
Fig. 1.1
It is suggested that the maximum height h of the ball and the compression x of the spring are related by the equation
4rr 3tgh 1
= kx 2
3 2 where r is the radius of the ball, t is the density of the ball, g is the acceleration of free fall and k is the spring constant of the spring.
Design a laboratory experiment to test the relationship between h and x.
Explain how your results could be used to determine a value for t.
You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to:
• 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
x is the independent variable and h is the dependent variable or vary x and measure/determine h 1
keep r and/or k constant 1
Methods of data collection
labelled diagram of workable experiment including: 1
• labelled spring
• upper ball vertically (by eye) above the spring and at least one of the balls labelled
• vertical (by eye) rule at least from top of spring to position of upper ball
method to determine x, e.g. use a rule/calipers to measure original and final length of spring and find the difference 1
use of micrometer/calipers/rule to measure diameter of ball 1
method to determine h described, e.g. 1
measure the distance between the top of the ball at maximum height and the top of the ball on the spring
or
measure the distance between the bottom of the ball at maximum height and the bottom of the ball on the spring
Method of analysis
plot a graph of h against x2 1
(or lg h against lg x)
relationship valid if a straight line through (0,0) 1
(for lg h against lg x straight line with gradient = 2)
3k 1
ρ= 3
8 πr g × gradient
3k
for lg h against lg x, ρ= 3 y −intercept
8πgr × 10
1 Additional detail including safety considerations
D1 use large box/cage to collect ball (to prevent ball rolling on floor/bouncing) 6
or
reasoned method to avoid draughts, e.g. switch off fans, close windows, use a screen
D2 expression to determine k from relevant experiment, e.g. k = mg / x or gradient of F–x graph
D3 stand on bench with clamped rule vertically to measure vertical distance
D4 method to ensure clamped rule to measure h is vertical, e.g.
correctly positioned set square indicated at right angles between the rule and the horizontal surface
or
plumb line shown in appropriate position
D5 r = d / 2 when diameter measured
D6 repeat diameter measurement in different directions and find average
D7 repeat experiment for each value of x and determine average h
D8 method to securely fix spring to the bench e.g. tape/G-clamp
D9 experiment to determine k, e.g. place mass m on the spring and measure compression x
D10 video (camera) shown level (by eye) with elevated ball and description of play back frame by frame or slow motion
A student is investigating how the resistance of a thermistor varies with temperature. The thermistor is placed in water, as shown in Fig. 2.1.
to electrical circuit
beaker water
thermistor
heat
Fig. 2.1
The thermistor is connected to a battery with electromotive force (e.m.f.) E and negligible internal resistance. The current I in the thermistor is measured. The resistance R of the thermistor is then determined using the expression
E
R= .
I
The experiment is repeated for different temperatures of the water.
It is suggested that the resistance R of the thermistor and the thermodynamic temperature T are related by the equation
R = pT q
where p and q are constants.
(a) A graph is plotted of lg R on the y-axis against lg T on the x-axis.
Determine expressions for the gradient and the y-intercept.
gradient = ……
y-intercept = ……
[1]
(b) The value of E is 9.4 ± 0.1 V.
Values of T, I and lg T are given in Fig. 2.2.
T/K I / mA R / 103 Ω lg (T / K) lg (R / 103 Ω)
303 1.0 ± 0.1 2.481
313 1.6 ± 0.1 2.496
323 2.4 ± 0.1 2.509
333 3.7 ± 0.1 2.522
343 5.5 ± 0.1 2.535
353 8.7 ± 0.1 2.548
Fig. 2.2
Calculate and record values of R / 103 Ω and lg (R / 103 Ω) in Fig. 2.2.
Include the absolute uncertainties in R / 103 Ω and lg (R / 103 Ω). [4]
(c) (i) Plot a graph of lg (R / 103 Ω) against lg (T / K).
Include error bars for lg (R / 103 Ω). [2]
(ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2]
(iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer.
gradient = …… [2]
1.1
1.0
lg (R / 103 Ω)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
2.48 2.49 2.50 2.51 2.52 2.53 2.54 2.55
lg (T / K)
(iv) Determine the y-intercept of the line of best fit. Do not determine the absolute uncertainty.
y-intercept = …… [1]
(d) Using your answers to (a), (c)(iii) and (c)(iv), determine the values of p and q. You need not be concerned with units. Do not include the absolute uncertainties.
p = ……
q = ……
[2]
(e) Using your answers to (d), determine the thermodynamic temperature T when the resistance of the thermistor is 15 kΩ.
T = …… K [1]
[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) gradient = q 1
and
y-intercept = lg p
2(b)
R / 103 Ω lg (R / 103 Ω)
9.4 or 9.40 0.97 or 0.973
5.9 or 5.88 0.77 or 0.771 or 0.769
3.9 or 3.92 0.59 or 0.591 or 0.593
2.5 or 2.54 0.40 or 0.398 or 0.405
1.7 or 1.71 0.23 or 0.230 or 0.233
1.1 or 1.08 0.04 or 0.041 or 0.033
Values of R as above. 1
Values of lg R as above. 1
Uncertainties in R from (±0.9 to ±1.2) to (±0.02 to ±0.03) 1
and
row 2 between ±0.40 and ±0.50
and
row 4 between ±0.09 and ±0.10.
Uncertainties in lg R consistent with uncertainties in R e.g. from ±0.05 to ±0.01. 1
2(c)(i) Six points plotted correctly. 1
Must be accurate to the nearest half a small square. Diameter of points must be less than half a small square.
Error bars in lg R plotted correctly. 1
All error bars must be plotted. Length of bar must be accurate to less than half a small square and symmetrical.
2(c)(ii) Line of best fit drawn. 1
Upper end of line should pass between (2.500, 0.70) and (2.502, 0.70) and lower end of line should pass between
(2.528, 0.30) and (2.532, 0.30).
Do not accept line from first to last point.
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 from the line of best fit into ∆y / ∆x. 1
Distance between data points must be greater than half the length of the drawn line.
Gradient must be negative.
uncertainty = gradient of line of best fit – gradient of worst acceptable line 1
or
uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient)
2(c)(iv) y-intercept determined by substitution of correct point from the line of best fit into y = mx + c. 1
2(d) p determined from y-intercept. 1
p (= 10y-intercept) = 10(c)(iv)
q = answer to (c)(iii) and given to 2 or 3 significant figures. 1
2(e) T determined from (d) or (c)(iii) and (c)(iv) with correct substitution shown. 1
R q 15
T =q =
p p
or
lg 15 − lg p 1.176 − lg p
lg T = =
q q
lg 15 − y -intercept 1.176 − (c)(iv)
lg T = =
gradient (c)(iii)
1.176 −(c)(iv)
(c)(iii)
T = 10
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On this page, free: the mark scheme for AS & A Level Physics 9702/52, October/November 2019 (9702_w19_ms_52), and the question paper (9702_w19_qp_52), to read or download, with each question's marking points written out underneath.
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Physics 9702/52 for October/November 2019 is out of 30 marks, with 1 hour 15 minutes to answer it.
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