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Paper 3 9702 Problems.pdf
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3 A student has been asked to determine the linear acceleration of a toy car as it moves down a slope. He sets up the apparatus as shown in Fig.3.1.
The
time t to move from rest through a distance d is found for
different values of d. A graph of d (y-axis) is plotted
against t2 (x-axis) as shown in Fig.3.2.
t 2 / s2
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(a) Theory suggests that the graph is a straight line through the origin.
Name the feature on Fig.3.2 that indicates the presence of (i) random error,
...................................................................................................................................
(ii) systematic error.
...................................................................................................................................
[2]
(b) (i) Determine the gradient of the line of the graph in Fig.3.2.
gradient = ........................................... [2]
(ii)
Use your answer to (i) to
calculate the acceleration of the toy down the slope. Explain your
working.
acceleration = ........................................ ms–2 [3]
Answer all the questions in the spaces provided.
1 (a) (i) Define density.
...................................................................................................................................
...................................................................................................................................
(ii) State the base units in which density is measured.
...................................................................................................................................
[2] (b) The speed v of sound in a gas is given by the expression
where p is the pressure of the gas of density ρ. γ is a constant.
Given that p has the base units of kgm−1s−2, show that the constant γ has no unit.
[3]
2 A student uses a metre rule to measure the length of an elastic band before and after stretching it.
The lengths are recorded as
length of band before stretching, L0 = 50.0 ± 0.1 cm length of band after stretching, LS = 51.6 ± 0.1 cm.
Determine
(a) the change in length (LS− L0), quoting your answer with its uncertainty,
(LS− L0) = ……………………………………… cm [1]
9702/2/O/N/02
(LS− L0)
(b)
the fractional change in length, 
,
L0
fractional change = ………………………………. [1]
(c) the uncertainty in your answer in (b).
uncertainty
= ………………………………… [3]
9702/2/O/N/02
Answer all the questions in the spaces provided.
1 A simple pendulum may be used to determine a value for the acceleration of free fall g. Measurements are made of the length L of the pendulum and the period T of oscillation.
The values obtained, with their uncertainties, are as shown.
T = (1.93 ± 0.03) s L = (92 ± 1) cm
(a) Calculate the percentage uncertainty in the measurement of
(i) the
period T, uncertainty = ............................................ %
[1] (ii) the length L. uncertainty = ............................................
% [1]
(b) The relationship between T, L and g is given by
42L g = T 2 .
Using your answers in (a), calculate the percentage uncertainty in the value of g.
uncertainty = ............................................ % [1]
(c) The values of L and T are used to calculate a value of g as 9.751 m s–2.
(i) By reference to the measurements of L and T, suggest why it would not be correct to quote the value of g as 9.751 m s–2.
..................................................................................................................................
............................................................................................................................
[1]
(ii) Use your answer in (b) to determine the absolute uncertainty in g.
Hence state the value of g, with its uncertainty, to an appropriate number of
significant figures.
g = .......................... ± ........................ m s–2 [2]
Answer all the questions in the spaces provided.
1 A student takes readings to measure the mean diameter of a wire using a micrometer screw gauge.
(a) Make suggestions, one in each case, that the student may adopt in order to (i) reduce a systematic error in the readings,
...................................................................................................................................
...................................................................................................................................
(ii) allow for a wire of varying diameter along its length,
...................................................................................................................................
...................................................................................................................................
(iii) allow for a non-circular cross-section of the wire.
...................................................................................................................................
...................................................................................................................................
[3]
(b)
The mean diameter of the wire is found to be 0.50 ±
0.02mm. Calculate the percentage uncertainty in
(i) the diameter,
uncertainty = …………………………………. %
(ii) the area of cross-section of the wire.
uncertainty = …………………………………. %
[2]
For
Examiner’s Use Answer all
the questions in the spaces provided.
1 (a) Distinguish between systematic errors and random errors.
systematic errors ............................................................................................................. .......................................................................................................................................... random errors ..................................................................................................................
..................................................................................................................................... [2]
(b) A cylinder of length L has a circular cross-section of radius R, as shown in Fig. 1.1.
The volume V of the cylinder is given by the expression
V = πR2L .
The volume and length of the cylinder are measured as
V = 15.0 ± 0.5 cm3
L = 20.0 ± 0.1 cm.
Calculate the radius of the cylinder, with its uncertainty. radius = ........................ ± ........................ cm [5]
![L S − L 0 ) = ……………………………………… cm [1] 9702/2/O/N/02 (](https://fs.znanio.ru/d5af0e/fa/c4/dae8fc83d6ae70330bb35dcd81c62fab0d.jpg)
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