1.
Which of the following contains one fundamental and one derived unit?
A.
ampere
kilogram
B.
ampere
coulomb
C.
joule
newton
D.
joule
coulomb
(Total 1 mark)
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 %.
(Total 1 mark)
3.
Data analysis question.
The photograph below shows a magnified image of a dark central disc surrounded by concentric
dark rings. These rings were produced as a result of interference of monochromatic light.
The graph below shows how the ring diameter D varies with the ring number n.
The innermost ring corresponds to n = 1. The corresponding diameter is labelled in the
photograph. Error bars for the diameter D are shown.
(a)
State one piece of evidence that shows that D is not proportional to n.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(1)
(b)
On the graph above, draw the line of best-fit for the data points.
(2)
(c)
Theory suggests that D2 = kn.
A graph of D2 against n is shown below. Error bars are shown for the first and last data
points only.
(i)
Using the first graph, calculate the percentage uncertainty in D2, of the ring n = 7.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(ii)
Based on the second graph, state one piece of evidence that supports the
relationship D2 = kn.
...........................................................................................................................
...........................................................................................................................
(1)
(iii)
Use the second graph to determine the value of the constant k, as well as its
uncertainty.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(4)
(iv)
State the unit for the constant k.
...........................................................................................................................
...........................................................................................................................
(1)
(Total 11 marks)
4.
Data analysis question.
The photograph below shows a magnified image of a dark central disc surrounded by concentric
dark rings. These rings were produced as a result of interference of monochromatic light.
The graph below shows how the ring diameter D varies with the ring number n.
The innermost ring corresponds to n = 1. The corresponding diameter is labelled in the
photograph. Error bars for the diameter D are shown.
(a)
State one piece of evidence that shows that D is not proportional to n.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(1)
(b)
On the graph opposite, draw the line of best-fit for the data points.
(2)
(c)
It is suggested that the relationship between D and n is of the form
D = cnp
where c and p are constants.
Explain what graph you would plot in order to determine the value of p.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(3)
(d)
Theory suggests that p =
1
and so D2 = kn (where k = c2).
2
A graph of D2 against n is shown below. Error bars are shown for the first and last data
points only.
(i)
Using the first graph, calculate the percentage uncertainty in D2, of the ring n = 7.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(ii)
Based on the second graph, state one piece of evidence that supports the
relationship D2 = kn.
...........................................................................................................................
...........................................................................................................................
(1)
(iii)
Use the second graph to determine the value of the constant k, as well as its
uncertainty.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(4)
(iv)
State the unit for the constant k.
...........................................................................................................................
...........................................................................................................................
(1)
(Total 14 marks)
5.
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
(Total 1 mark)
6.
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 %.
(Total 1 mark)
7.
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)
(b)
It is suggested that the relationship between v and λ is of the form
v= a 
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)
The absolute uncertainty in v2 for a wavelength of 2.5 m is ±1 m2 s–2. 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
.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(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)
8.
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)
Draw a best-fit line for the data.
(1)
(b)
State, with reference to the line you have drawn in (a),
(i)
why v is not directly proportional to λ.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(1)
(ii)
the value of v for λ = 39 m.
...........................................................................................................................
(1)
(c)
It is suggested that the relationship between v and λ is of the form
v= a 
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 (b)(ii) to show that the absolute uncertainty in v2 for a
wavelength of 39 m is ±5 m2 s–2.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(ii)
The absolute uncertainty in v2 for a wavelength of 2.5 m is ±1 m2 s–2. Using this
value and the value in (c)(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 (c)(ii) suggest that it is likely that v is proportional to
.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(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 12 marks)
9.
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
(Total 1 mark)
10.
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
(Total 1 mark)
11.
This question is about electrical resistance.
The graph shows the variation with temperature T of the resistance R of an electrical
component.
(a)
A student hypothesizes that the resistance is inversely proportional to the temperature.
Use data from the graph to show whether the hypothesis is supported.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(3)
(b)
A second student suggests that the relationship is of the form
lg R = a +
b
T
where a and b are constants.
The student plots the graph below. Error bars have been included for the sake of clarity.
(i)
Explain how the graph drawn could be used as evidence to support the student’s
suggestion.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(ii)
Use the graph to determine the constants a and b.
b: .......................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
a: .......................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(4)
(iii)
Using your answers to (b)(ii), determine a value for the resistance of the
component at a temperature of 260 K.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(Total 11 marks)
12.
This question is about electrical resistance.
The graph shows the variation with temperature T of the resistance R of an electrical
component.
(a)
A student hypothesizes that the resistance is inversely proportional to the temperature.
Use data from the graph to show whether the hypothesis is supported.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(3)
(b)
A second student suggests that the relationship is of the form
lg R = a +
b
T
where a and b are constants.
The student plots the graph below. Error bars have been included for the sake of clarity.
(i)
Explain how the graph drawn could be used as evidence to support the student’s
suggestion.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(ii)
Use the graph to determine the constants a and b.
b: .......................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
a: .......................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(4)
(iii)
Using your answers to (b)(ii), determine a value for the resistance of the
component at a temperature of 260 K.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(Total 11 marks)
13.
The current in a resistor is measured as 2.00 A ± 0.02 A. Which of the following correctly
identifies the absolute uncertainty and the percentage uncertainty in the current?
Absolute uncertainty
Percentage uncertainty
A.
± 0.02 A
±1 %
B.
± 0.01 A
± 0.5 %
C.
± 0.02 A
± 0.01 %
D.
± 0.01 A
± 0.005 %
(Total 1 mark)
14.
Data analysis question.
Gillian carried out an experiment to investigate the craters formed when steel balls are dropped
into sand. To try and find the relationship between the diameter of the crater and the energy of
impact of steel balls of the same diameter, she dropped a steel ball from different heights h into
sand and measured the resulting diameter d of the crater. The data are shown plotted below.
(a)
The uncertainty in the measurement of d is ±0.40 cm; the uncertainty in h is too small to
be shown. Draw error bars for the data point (0.2, 0.047) and the data point (2.0, 0.10).
(2)
(b)
Draw a best-fit line for the data points.
(2)
(c)
The original hypothesis, made by Gillian, was that the diameter of the crater is directly
proportional to the energy of impact of the steel balls. Explain why the data does not
support this hypothesis.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(3)
(d)
Since Gillian’s data did not support her hypothesis, she researched to find alternative
hypotheses. She found that there are two theories used to predict a relationship between d
and h. In order to find which theory is best supported by the data, she processed the data
in two separate ways. The processed data are shown below.
(i)
Draw a line of best-fit on each graph.
(2)
(ii)
State and explain which theory is best supported by the student’s data.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(Total 11 marks)
15.
Data analysis question.
Gillian carried out an experiment to investigate the craters formed when steel balls are dropped
into sand. To try and find the relationship between the diameter of the crater and the energy of
impact of steel balls of the same diameter, she dropped a steel ball from different heights h into
sand and measured the resulting diameter d of the crater. The data are shown plotted below.
(a)
The uncertainty in the measurement of d is ±0.40 cm; the uncertainty in h is too small to
be shown. Draw error bars for the data point (0.2, 0.047) and the data point (2.0, 0.10).
(2)
(b)
Draw a best-fit line for the data points.
(2)
(c)
The original hypothesis, made by Gillian, was that the diameter of the crater is directly
proportional to the energy of impact of the steel balls. Explain why the data does not
support this hypothesis.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(3)
(d)
Since Gillian’s data did not support her hypothesis, she researched to find alternative
hypotheses. She found that there are two theories used to predict a relationship between d
and h.
1
1
Theory 1 predicts that d = const (h) 3 and theory 2 predicts that d = const (h) 4 .
In order to test which theory her data supports, she plotted a graph of lg(d) against lg(h).
The plot produced a straight line that could be drawn through all the error bars.
The graph includes the lines of maximum and minimum gradients based on the first error
bar for the first non-zero data point and the last error bar. The last error bar is too small to
be shown. State and explain if the original data support theory 1 or theory 2.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(4)
(Total 11 marks)
16.
An object falls for a time of 0.25 s. The acceleration of free fall is 9.81 m s–2. The displacement
is calculated. Which of the following gives the correct number of significant digits for the
calculated value of the displacement of the object?
A.
1
B.
2
C.
3
D.
4
(Total 1 mark)
17.
Data analysis question.
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)
(ii)
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
hypothesis he plotted a graph of v2 against n as shown below.
Explain how the graph verifies the hypothesis that v is proportional to
n.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(3)
(Total 11 marks)
18.
Two lengths, a and b, are measured to be 51±1 cm and 49±1 cm respectively. In which of the
following quantities is the percentage uncertainty the largest?
A.
a+b
B.
a–b
C.
a×b
D.
a
b
(Total 1 mark)
19.
Data analysis question.
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)
(ii)
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 above to show that this hypothesis is incorrect.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(3)
(d)
n . To verify this
hypothesis he plotted a graph of lg v against lg n as shown below.
Another student hypothesized that v might be proportional to
Show that the graph verifies the hypothesis that v is proportional to
n.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(4)
(Total 12 marks)
20.
A volume is measured to be 52 mm3. This volume in m3 is
A.
5.2 × 103 m3.
B.
5.2 × 101 m3.
C.
5.2 × 10–1 m3.
D.
5.2 × 10–8 m3.
(Total 1 mark)
21.
The masses and weights of different objects are independently measured. The graph is a plot of
weight versus mass that includes error bars.
These experimental results suggest that the
A.
measurements show a significant systematic error but small random error.
B.
measurements show a significant random error but small systematic error.
C.
measurements are precise but not accurate.
D.
weight of an object is proportional to its mass.
(Total 1 mark)
22.
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)
23.
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)
24.
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.
(Total 1 mark)
25.
This question is about liquid flow.
The diagram shows a storage container for liquids.
The container is filled from above. The distance between the base of the container and the
ground is h0.
The container, which is initially empty, is then filled at a constant rate. The height h of the
liquid surface above the ground is measured as a function of time t. The results of the
measurements are shown plotted below.
(a)
Draw a best-fit line for the data.
(1)
(b)
State and explain whether h is directly proportional to t for the periods
(i)
t = 0 to t = 120 s.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(1)
(ii)
t > 120 s.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(1)
(c)
Use data from the graph to determine the value of h0.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(2)
(d)
The area of the base of the container is 1.8 m2. Deduce that the volume of liquid entering
the storage container each second is approximately 0.02 m3 s–1.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(3)
(e)
The container is completely filled after 850 s. Calculate the total volume of the container.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(1)
(f)
It is hypothesized that for t > 400 s the relation between t and h is of the form
h = ktn
where k and n are constants.
(i)
Outline how, using a graphical technique, you would verify this hypothesis.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(ii)
Explain how you would determine the value of n.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(1)
(g)
The empty container is now filled at half the rate in (d). Using the axes, sketch a graph to
show the variation of h with t in the range t = 0 to t = 900 s.
(2)
(Total 14 marks)
26.
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.
(Total 1 mark)
27.
Data analysis question.
The frequency f of the fundamental vibration of a standing wave of fixed length is measured for
different values of the tension T in the string, using the apparatus shown.
In order to find the relationship between the speed v of the wave and the tension T in the string,
the speed v is calculated from the relation
v=2fL
where L is the length of the string.
The data points are shown plotted on the axes below. The uncertainty in v is ±5 m s–1 and the
uncertainty in T is negligible.
(a)
Draw error bars on the first and last data points to show the uncertainty in speed v.
(1)
(b)
The original hypothesis is that the speed is directly proportional to the tension T.
Explain why the data do not support this hypothesis.
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(2)
(c)
It is suggested that the relationship between speed and tension is of the form
v=k T
where k is a constant.
To test whether the data support this relationship, a graph of v2 against T is plotted as
shown below.
The best-fit line shown takes into account the uncertainties for each data point.
The uncertainty in v2 for T = 3.5 N is shown as an error bar on the graph.
(i)
State the value of the uncertainty in v2 for T = 3.5 N.
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(1)
(ii)
At T = 1.0 N the speed v = 27 ± 5 m s–1. Calculate the uncertainty in v2.
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(3)
(d)
Use the graph in (c) to determine k without its uncertainty.
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(4)
(Total 11 marks)
28.
Data analysis question.
The frequency f of the fundamental vibration of a standing wave of fixed length is measured for
different values of the tension T in the string, using the apparatus shown.
In order to find the relationship between the speed v of the wave and the tension T in the string,
the speed v is calculated from the relation
v=2fL
where L is the length of the string.
The data points are shown plotted on the axes below. The uncertainty in v is ±5 m s–1 and the
uncertainty in T is negligible.
(a)
Draw error bars on the first and last data points to show the uncertainty in speed v.
(1)
(b)
The original hypothesis is that the speed is directly proportional to the tension T.
Explain why the data do not support this hypothesis.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(2)
(c)
It is suggested that the relationship between speed and tension is of the form
v=k T
where k is a constant.
To test whether the data support this relationship, a graph of v2 against T is plotted as
shown below.
The best-fit line shown takes into account the uncertainties for each data point.
The uncertainty in v2 for T = 3.5 N is shown as an error bar on the graph.
(i)
State the value of the uncertainty in v2 for T = 3.5 N.
...........................................................................................................................
...........................................................................................................................
(1)
(ii)
At T = 1.0 N the speed v = 27 ± 5 m s–1. Calculate the uncertainty in v2.
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(3)
(d)
Use the graph in (c) to determine k without its uncertainty.
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(4)
(Total 11 marks)
29.
The density of a metal cube is given by the expression ρ 
M
where M is the mass and V is the
V
volume of the cube. The percentage uncertainties in M and V are as shown below.
M
12 
V
4.0 
The percentage uncertainty in the calculated value of the density is
A.
3.0 .
B.
8.0 .
C.
16 .
D.
48 .
(Total 1 mark)
30.
The volume V of a cylinder of height h and radius r is given by the expression
V = r2h.
In a particular experiment, r is to be determined from measurements of V and h. The
uncertainties in V and in h are as shown below.
V
7 
h
3 
The approximate uncertainty in r is
A.
10 .
B.
5 .
C.
4 .
D.
2 .
(Total 1 mark)
31.
This question is about the electrical power available from a wind turbine.
The maximum electrical power generated by a wind turbine, Pout , was measured over a range of
incident wind speeds, vin.
The graph below shows the variation with vin of Pout. Uncertainties for the data are not shown.
(a)
It is suggested that Pout is proportional to
(i)
vin .
Draw the line of best-fit for the data points.
(1)
(ii)
State one reason why the line you have drawn does not support this hypothesis.
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(1)
(iii)
The uncertainty in the power at 15 m s–1 is 5 . Draw an error bar on the graph to
represent this uncertainty.
(2)
(b)
The theoretical relationship between the available power in the wind, Pin, and incident
wind speed is shown in the graph below.
Using both graphs,
(i)
determine the efficiency of the turbine for an incident wind speed of 14 m s–1.
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(3)
(ii)
suggest, without calculation, how the efficiency of the turbine changes with
increasing wind speed.
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(3)
(c)
Outline one advantage and one disadvantage of using wind turbines to generate electrical
energy.
Advantage:
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Disadvantage: ...................................................................................................
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(2)
(Total 12 marks)