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Exam Review: Topic 01 – Measurement
Practice Test: 33 marks (43 minutes)
Additional Problem: 11 marks (16 minutes)
1.
Reagan IB Physics
Which of the following contains one fundamental and one derived unit?
A.
B.
C.
D.
ampere
ampere
joule
joule
kilogram
coulomb
newton
coulomb
(1)
2.
The current, I, through a resistor is measured with a digital ammeter to be 0.10 A. The
uncertainty in the calculated value of I2 will be
A.
1 %.
B.
2 %.
C.
5 %.
D.
20 %.
3.
Which of the following will reduce random errors in an experiment?
A.
Using an instrument having a greater precision
B.
Checking the calibration of the instrument used
C.
Checking for zero error on the instrument used
D.
Repeating readings
4.
A body accelerates from rest with a uniform acceleration a for a time t. The uncertainty in a is 8
% and the uncertainty in t is 4 %. The uncertainty in the speed is
A.
32 %.
B.
12 %.
C.
8 %.
D.
2 %.
5.
The length of each side of a sugar cube is measured as 10 mm with an uncertainty of ±2 mm.
Which of the following is the absolute uncertainty in the volume of the sugar cube?
A. ±6 mm3
B. ±8 mm3
C. ±400 mm3
D. ±600 mm3
6.
The time taken for a stone dropped from rest to fall vertically through 16 m is 2.0 s. Based on
these measurements, what is the best estimate for the acceleration of free fall?
A. 4.0 m s–2
B. 8.0 m s–2
C. 9.8 m s–2
D. 10 m s–2
7.
Which of the following lists only two vector quantities?
A.
mass, energy, work
B.
momentum, work, speed
C.
weight, force, acceleration
D.
momentum, energy, displacement
8.
Which of the following is equivalent to the joule?
A. N m2
B. N m–2
C.
(1)
(1)
(1)
(1)
(1)
(1)
kg m s–2
D.
kg m2 s–2
(1)
9.
3
3
A volume is measured to be 52 mm . This volume in m is
A. 5.2 × 103 m3.
B. 5.2 × 101 m3.
C. 5.2 × 10–1 m3.
D.
5.2 × 10–8 m3.
(1)
10.
Two cars, X and Y, are travelling towards a junction.
The velocity of car X is VX and car Y is VY.
Which of the following vectors represent the velocity of
Y relative to X?
(1)
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Exam Review: Topic 01 – Measurement
11.
Reagan IB Physics
In an experiment to measure the acceleration of free fall at the surface of the Earth the
following results were obtained.
Acceleration of free fall / m s–2
7.69
7.70
7.69
7.68
7.70
The results are
A.
accurate and precise.
B.
inaccurate but precise.
C.
accurate but imprecise.
D.
inaccurate and imprecise.
(1)
12.
Which of the following is a valid statement?
A.
A measurement that is not precise can be accurate.
B.
A measurement that is precise is always accurate.
C.
A measurement that is not precise will always be inaccurate.
D.
Repeated measurements will always increase accuracy and precision.
(1)
13.
Data analysis question.
The speed v of waves on the surface of deep water depends only on the wavelength λ of the
waves. The data gathered from a particular region of the Atlantic Ocean are plotted below.
The uncertainty in the speed v is ±0.30 m s–1 and the uncertainty in λ is too small to be shown
on the diagram.
(a)
State, with reference to the graph,
(i)
why v is not directly proportional to λ.
...........................................................................................................................
(1)
(ii)
the value of v for λ = 39 m.
...........................................................................................................................
(1)
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Exam Review: Topic 01 – Measurement
(b)
Reagan IB Physics
It is suggested that the relationship between v and λ is of the form
v= a λ
where a is a constant. To test the validity of this hypothesis, values of v2 against λ are
plotted below.
(i)
Use your answer to (a)(ii) to show that the absolute uncertainty in v2 for a
wavelength of 39 m is ±5 m2 s–2.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(ii)
2
2 –2
The absolute uncertainty in v for a wavelength of 2.5 m is ±1 m s . Using this
value and the value in (b)(i), construct error bars for v2 at the data points for
λ = 2.5 m and 39 m.
(1)
(iii) State why the plotted data in (b)(ii) suggest that it is likely that v is proportional to
λ .
...........................................................................................................................
(1)
(iv)
Use the graph above to determine the constant a.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(v)
Theory shows that a =
k
. Determine a value for k.
2π
...........................................................................................................................
(1)
(Total 11 marks)
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Exam Review: Topic 01 – Measurement
14.
Reagan IB Physics
This question is about electrical resistance of the metal mercury.
The resistance R of a sample of mercury was measured as a function of the temperature T of the
sample. The sample was cooled and data points were taken at temperature intervals of 0.2 K.
The uncertainties in R and T are too small to be shown on the graph.
The hypothesis is that resistance is proportional to absolute temperature for temperatures
greater than 4.5 K.
(a)
(i)
Suggest whether the data supports the hypothesis.
...........................................................................................................................
(1)
(ii)
Draw a line of best fit through the data.
(2)
(b)
State the value of R for which the rate of change of resistance of the sample with
temperature is least.
......................................................................................................................................
(1)
(c)
At a temperature TC the resistance suddenly becomes zero.
(i)
Use the graph to determine the possible range of the temperature TC.
...........................................................................................................................
(1)
(ii)
State, to the correct number of significant figures, the value of TC and its
uncertainty.
...........................................................................................................................
...........................................................................................................................
(2)
(iii)
Outline how the temperature TC could be measured more precisely.
...........................................................................................................................
(1)
(d)
Outline two reasons why you could not use the data to determine an accurate value for R
at room temperature.
......................................................................................................................................
......................................................................................................................................
(2)
(Total 10 marks)
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Exam Review: Topic 01 – Measurement
Reagan IB Physics
Additional Problem
15.
A student performs an experiment with a paper toy that rotates as it falls slowly through the air.
After release, the paper toy quickly attains a constant vertical speed as measured over a fixed
vertical distance.
The aim of the experiment was to find how the terminal speed of the paper toy varies with its
weight. The weight of the paper toy was changed by using different numbers of paper sheets in
its construction.
The graph shows a plot of the terminal speed v of the paper toy (calculated from the raw data)
and the number of paper sheets n used to construct the toy. The uncertainty in v for n = 1 is
shown by the error bar.
(a)
The fixed distance is 0.75 m and has an absolute uncertainty of 0.01 m. The percentage
uncertainty in the time taken to fall through the fixed distance is 5 %.
(i)
Calculate the absolute uncertainty in the terminal speed of the paper toy for n = 6.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
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Exam Review: Topic 01 – Measurement
(ii)
Reagan IB Physics
On the graph, draw an error bar on the point corresponding to n = 6.
(1)
(b)
On the graph, draw a line of best-fit for the data points.
(1)
(c)
The student hypothesizes that v is proportional to n. Use the data points for n = 2 and
n = 4 from the graph opposite to show that this hypothesis is incorrect.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(3)
(d)
Another student hypothesized that v might be proportional to
n . To verify this
2
hypothesis he plotted a graph of v against n as shown below.
Explain how the graph verifies the hypothesis that v is proportional to
n.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(3)
(Total 11 marks)
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Exam Review: Topic 01 – Measurement
Mark Scheme
1.
B
2.
D
13.
(a)
(i)
(ii)
(b)
(i)
3.
4.
D
B
Reagan IB Physics
5.
6.
D
B
7.
8.
D
D
9.
10.
D
D
the graph is not linear/a straight line (going through the
error bars) / does not go through origin;
11.
12.
B
A
1
7.7 m s–1; (N.B. line is drawn for candidate, answer must be correct)
1
⎛ 0.3 ⎞
% uncertainty in v = ⎜
= ⎟ = 3.9%;
⎝ 0.7 ⎠
doubles 3.9% (allow ECF from (a)(ii)) to obtain %
uncertainty in v2(= 7.8%);
absolute uncertainty (= ±[0.078 × 59.3]) = 4.6;
(= ±5 m2 s–2)
3
or
calculates overall range of possible value as 7.4 – 8.0; (allow ECF)
squares values to yield range for v2 of 54.8 to 64; (allow ECF)
so error range becomes 9.2 hence ±4.6; (must see this value to
2 sig fig or better to award this mark)
(ii)
(iii)
1
square) and
2
last-but-one point (±2.5 squares); (judge by eye)
1
a straight-line/linear graph can be drawn that goes through origin;
1
correct error bars added to first point (±
(iv) uses triangle to evaluate gradient; (triangle need not be
shown if read-offs clear, read-offs used must lie on
candidate’s drawn line)
to arrive at gradient value of 1.5 ± 0.2; (unit not required)
recognizes that gradient of graph is a2 and evaluates
a = 1.2 ± 0.2
1
( m 2 s −1 );
3
or
candidate line drawn through origin and one data point read;
correct substitution into v2 = a2λ; (a2 does not need to be
evaluated for full credit)
a = 1.2 ±
1
0.2( m 2 s −1 );
1
square.
2
Award [1 max] if one or two data points used and no line drawn.
Award [2 max] if line does not go through origin – allow
(v)
k = 9.4 m s–2; (allow ECF from (b)(iv))
1
[11]
14.
(a)
(i)
(ii)
(b)
no
the graph is not linear / not a straight line;
a straight horizontal line through the initial points along the T axis;
a smooth curve through the remaining points (T = 4.4 K to 7.0 K);
The straight line and curve do not need to be joined.
R = 0 Ω;
Do not apply unit mark.
1
2
1
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Exam Review: Topic 01 – Measurement
(c)
4.2 – 4.4 K;
1
(ii)
4.3 K;
±0.1 (K);
Allow ECF from (c)(i).
2
(iii)
(d)
Reagan IB Physics
(i)
more sensitive thermometer / thermometer with a finer
graduated scale / by taking resistance measurements at
smaller temperature intervals;
Award [0] for electronic digital thermometer only.
the data are for low temperatures well below room temperature;
no reason to assume the trend will continue to room temperature;
the data shows R varying sharply at TC and another such transition
might take place below room temperature;
mercury is a liquid at room temperature;
Award any other sensible answer.
1
2 max
[10]
15.
(a)
(i)
(ii)
(b)
⎛ 0.01 ⎞
percentage uncertainty in distance = ⎜
= ⎟ 1.3%;
⎝ 0.75 ⎠
percentage uncertainty in v = (5 + 1.3 =) 6.3 %;
absolute uncertainty in n = 6 point is (0.40 × 0.063 =) 0.025 m s–1;
overall length of error bar drawn correct to within half a
small square;
Consistent with (a) (i).
3
1
any reasonable smooth curve/straight-line passing through error bars
1
(c)
tests for
v
n
or ;
n
v
v
v
= 0.12 for n = 2 and
= 0.085 for n = 4; (both needed)
n
n
hypothesis incorrect because two values should be equal.
(d)
3
(if v ∝ n )v 2 ∝ n ;
graph of v2 against n is a straight-line;
that goes through the origin;
3
[11]
8/6