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TRANSCRIPT
Questions to assess Practical Skills
Q1.
(a) The image below shows a full-size photograph of a double-slit interference pattern, using a laser.
Determine the fringe width w using a ruler to take measurements from the image above.
You may use a hand-lens to help you make this measurement.
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(3)
(b) Calculate the uncertainty in the value of w measured in part (a).
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(2)
(c) In the experiment shown in the diagram below, the fringe pattern in the image in part (a) is produced.
s = 0.60 ± 0.02 mm
D = 1.500 ± 0.002 m
Using these data and your answers to part (a) and part (b), determine
(i) the wavelength of the laser light used
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(1)
(ii) the percentage uncertainty in this value of wavelength
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(1)
(iii) the absolute uncertainty in this value of wavelength.
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(1)
(Total 8 marks)
Q2.
A student carries out an experiment to determine the diameter of a cylindrical wire based on the theory of Young’s double−slit experiment, using the arrangement shown in Figure 1.
Figure 1
The wire is mounted vertically in front of a single narrow slit which is illuminated by monochromatic light. The wire produces a shadow between points P and Q on a glass slide covered with tracing paper. The light diffracts as it passes the wire. Points A and B act as coherent sources causing interference fringes to be seen between P and Q.
The student uses a metre ruler to measure the distances L and D shown in Figure 1. Figure 2 shows the pattern of interference fringes between P and Q. The student takes readings from a vernier scale to indicate the positions of the centres of two of the fringes.
Figure 2
The student’s measurements are shown in Table 1.
Table 1
L/mm
D/mm
R1/mm
R2/mm
46
395
8.71
11.16
(a) Determine the spacing of the interference fringes w using Figure 1 and the data in Table 1.
Give your answer to an appropriate number of significant figures.
w ___________________ m
(2)
(b) Determine the diameter d of the wire.
wavelength of the monochromatic light = 589.3 nm
d = ___________________ m
(2)
(c) Estimate the number of interference fringes seen between P and Q.
number of interference fringes = ___________________
(3)
(d) The student uses a micrometer screw gauge to confirm his result for d.
Describe a suitable procedure that the student should carry out before using the micrometer to ensure that the measurements are not affected by systematic error.
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(2)
(e) To reduce the impact of random error, the student takes several measurements of the diameter at different points along the wire so that he can calculate a mean value for d.
These measurements are shown in Table 2.
d/mm
0.572
0.574
0.569
0.571
0.566
0.569
Use the data from Table 2 to determine the percentage uncertainty in the student’s result for d.
percentage uncertainty = ___________________ %
(2)
(Total 11 marks)
Q3.
This question is about an experiment to measure the wavelength of microwaves.
A microwave transmitter T and a receiver R are arranged on a line marked on the bench.
A metal sheet M is placed on the marked line perpendicular to the bench surface.
Figure 1 shows side and plan views of the arrangement.
The circuit connected to T and the ammeter connected to R are only shown in the plan view.
Figure 1
The distance y between T and R is recorded.
T is switched on and the output from T is adjusted so a reading is produced on the ammeter as shown in Figure 2.
Figure 2
M is kept parallel to the marked line and moved slowly away as shown in Figure 3.
Figure 3
The reading decreases to a minimum reading which is not zero.
The perpendicular distance x between the marked line and M is recorded.
(a) The ammeter reading depends on the superposition of waves travelling directly to R and other waves that reach R after reflection from M.
State the phase difference between the sets of waves superposing at R when the ammeter reading is a minimum.
Give a suitable unit with your answer.
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(1)
(b) Explain why the minimum reading is not zero when the distance x is measured.
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(1)
(c) When M is moved further away the reading increases to a maximum then decreases to a minimum.
At the first minimum position, a student labels the minimum n = 1 and records the value of x.
The next minimum position is labelled n = 2 and the new value of x is recorded.
Several positions of maxima and minima are produced.
Describe a procedure that the student could use to make sure that M is parallel to the marked line before measuring each value of x.
You may wish to include a sketch with your answer.
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(2)
(d) It can be shown that
where λ is the wavelength of the microwaves and y is the distance defined in Figure 1.
The student plots the graph shown in Figure 4.
The student estimates the uncertainty in each value of to be 0.025 m and adds error bars to the graph.
Determine
• the maximum gradient Gmax of a line that passes through all the error bars
• the minimum gradient Gmin of a line that passes through all the error bars.
Gmax = ____________________
Gmin = ____________________
(3)
(e) Determine λ using your results for Gmax and Gmin.
λ = ____________________ m
(2)
Figure 4
(f) Determine the percentage uncertainty in your result for λ.
percentage uncertainty in λ = ____________________ %
(3)
(g) Explain how the graph in Figure 4 can be used to obtain the value of y.
You are not required to determine y.
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(2)
(h) Suppose that the data for n = 13 had not been plotted on Figure 4.
Add a tick (✔) in each row of the table to identify the effect, if any, on the results you would obtain for Gmax, Gmin, λ and y.
Result
Reduced
Not affected
increased
Gmax
Gmin
λ
y
(4)
(Total 18 marks)
Q4.
A student aligns the longer edge of a rectangular glass block along a line LR, as shown in Figure 1.
The student marks the outline of the block and directs a ray along PQ.
The student marks the direction of the emergent ray then removes the block and marks a line perpendicular to LR where PQ and LR intersect.
The student then marks the points W, X, Y and Z that are defined in Figure 2.
(a) Show that the refractive index n of the block is given by the equation
You may wish to use the equation
where θ1 and θ2 are the angles shown in Figure 3.
You may also wish to illustrate your answer with a diagram.
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(2)
(b) The student repeats the procedure for different directions of the incident ray PQ. The student measures XZ, WX, YZ and WY for each direction of PQ.
State and explain how the student can use these results to obtain a value of n by a graphical method.
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(2)
(c) The student used a block with dimensions 114 mm × 65 mm × 19 mm to perform the experiment.
The student’s data are shown in the table below.
WX/mm
WY/mm
XZ/mm
YZ/mm
130
78
113
44
103
75
80
38
90
73
63
33
81
71
49
27
75
69
38
22
67
66
15
10
Explain whether the range of measurements made by the student is suitable.
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(3)
(Total 7 marks)
Q5.
Figure 1 shows how the refractive index n of a type of glass varies with the wavelength of light λ passing through the glass. The data for plotting the graph were determined by experiment.
Figure 1
(a) A student says that Figure 1 resembles that of the decay of radioactive atomic nuclei with time and that it shows half-life behaviour.
Comment on whether the student is correct.
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(1)
(b) The dispersion D of glass is defined as the rate of change of its refractive index with wavelength. At a particular wavelength D= .
Determine D at a wavelength of 400 nm. State an appropriate unit for your answer.
D ____________________ unit __________
(3)
(c) It is suggested that the relationship between n and λ is of the form
where a and b are constants. The data plotted in Figure 1 are given in the table below.
λ / nm
n
300
1.6060
350
1.6048
400
1.6040
450
1.6035
500
1.6030
550
1.6028
600
1.6025
You are to determine a using a graph of n against
.
Make any calculations that you need to in order to plot your graph. The columns in the table are for you to use to calculate and tabulate the derived data that you need.You may not need all the columns.
(3)
(d) Plot your graph on Figure 2. The values of n are provided on the y-axis.
Figure 2
(3)
(e) Use your graph to determine a.
(1)
(f) State the significance of a.
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(1)
(g) Another suggestion for the relationship between n and λ is that
n=cλd
where c and d are constants.
Explain how d can be determined graphically. Do not attempt to carry out this analysis.
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(3)
(Total 15 marks)
Q6.
The diagram shows the arrangement of apparatus in an experiment to measure the wavelength of red light emitted by a laser. The light is incident on a double-slit so that an interference pattern is produced on the screen.
A student sets up the apparatus and measures the fringe width w of the interference pattern and the distance D between the double-slit and screen.
The student makes further measurements of w using the same laser but with different values of D and different slit spacing s.
The student’s results are shown in the table below
D/m
1.000
0.70
1.03
0.900
0.70
0.93
0.800
0.70
1.14
0.84
1.000
1.00
1.00
0.76
0.800
1.00
0.80
0.62
0.600
1.00
0.60
0.50
(a) Complete the table above.
(1)
(b) Complete the graph below by plotting the two remaining points and drawing a best fit straight line.
(2)
(c) (i) Determine the gradient of the graph above.
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(3)
(ii) Determine the wavelength of the red laser light used in this experiment.
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(1)
(d) (i) Theory suggests that the graph above should go through the origin.
State and explain what this suggests about the relationship between w and .
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(2)
(ii) The student discovers that the best fit line drawn in the graph does not go through the origin.
Determine, using information from the graph above, the value of w corresponding to .
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(2)
(iii) The graph suggests a systematic error in a measurement.
Identify the measurement.
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(1)
(e) The interference pattern produced on the screen is much brighter in the centre of the screen than at the edges.
State what causes this effect.
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(1)
(Total 13 marks)
Q7.
In this experiment you will investigate how the time between two pendulums moving in phase depends on their relative lengths.
No description of the experiment is required. You should devote your time to making and recording observations, and giving only the specific information requested.
You are provided with the apparatus shown in the diagram.
(a) (i) Adjust the horizontal separation of the strings, s, by moving clip A so that, with each pendulum bob at the same height above the floor, the longer pendulum has a length, L, of about 1.00 m.
(ii) Adjust the height of clamp C until the distance, y, defined in the diagram, is about 0.20 m. Ensure that the part of the string between clip B and the clamped circuit board is vertical.
(iii) Measure and record the distances, s, y and L.
(b) (i) Displace and release one of the pendulums so that it performs small-amplitude oscillations in a plane which is parallel to the edge of the bench. Set the other pendulum in motion so that it performs oscillations in a plane that is parallel to the edge of the bench.
(ii) Start the stopwatch at the instant when the two pendulum motions are seen to be exactly in phase.
(iii) Measure and record, T, which is the time until the pendulums are next seen to move exactly in phase.
(iv) By adjusting clamp C and ensuring that the values of s and L remain unchanged, measure and record further values of T, which correspond to four larger values of y.
(c) (i) Plot a graph of on the vertical axis against on the horizontal axis.
(ii) Measure and record the gradient, G, of your graph.
(iii) Evaluate .
(16)
(d) (i) Describe the measures that you took to ensure that the part of the string between clip B and the clamped circuit board was vertical.
(ii) Describe and explain the factors you considered when choosing your additional values for y.
(iii) A student suggests that in order to extend the enquiry, additional measurements of T should be made using values of y that were much smaller than 20.0 cm. Discuss briefly whether you think that such additional readings would improve the quality of the evidence obtained from the experiment.
(6)
(Total 22 marks)
Q8.
In an attempt to investigate how the resistance of a filament lamp varies with current through the lamp, a student obtains the results shown in the table.
voltage/V
0.50
1.50
3.00
4.50
6.00
12.00
current/A
0.51
1.25
2.00
2.55
2.95
4.00
resistance/Ω
(a) Complete the table by calculating the corresponding values of resistance.
(2)
(b) (i) On the grid below plot a graph of resistance against current for the filament lamp.
(ii) Use your graph to estimate the resistance of the filament lamp when no current flows through the lamp.
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(iii) Use your graph to determine the change in the resistance of the filament when the current increases
from 0 to 1.0 A, _________________________________________________
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from 1.0 A to 2.0 A ______________________________________________
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(iv) Calculate the power dissipated in the lamp filament when the current through the filament is 1.0 A and 2.0 A.
1. ____________________________________________________________
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2. ____________________________________________________________
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(8)
(c) Using information from part (b)(iv), explain why the change in resistance of the filament is less for a current change of 0 to 1.0 A than for a current change of 1.0 A to 2.0 A. Do not attempt any calculation.
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(2)
(Total 12 marks)
Q9.
(a) (i) Describe how you would make a direct measurement of the emf ɛ of a cell, stating the type of meter you would use.
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(1)
(ii) Explain why this meter must have a very high resistance.
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(1)
(b) A student is provided with the circuit shown in the diagram below.
The student wishes to determine the efficiency of this circuit.
In this circuit, useful power is dissipated in the external resistor. The total power input is the power produced by the battery.
Efficiency =
The efficiency can be determined using two readings from a voltmeter.
(i) Show that the efficiency = where ɛ is the emf of the cell
and V is the potential difference across the external resistor.
(1)
(ii) Add a voltmeter to the diagram and explain how you would use this new circuit to take readings of ɛ and V.
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(2)
(c) Describe how you would obtain a set of readings to investigate the relationship between efficiency and the resistance of the external resistor. State any precautions you would take to ensure your readings were reliable.
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(2)
(d) State and explain how you would expect the efficiency to vary as the value of R is increased.
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(2)
(Total 9 marks)
Q10.
A signal generator is connected to an oscilloscope, as shown in Figure 1.
Figure 1
The Y-voltage gain and time-base settings of the oscilloscope are shown in Figure 2.
Figure 2
When switch S is open (off) the oscilloscope displays the waveform shown in Figure 3.
When S is closed (on) the oscilloscope displays the waveform shown in Figure 4.
(a) Determine the peak-to-peak voltage V of the waveform shown in Figure 4.
V = ____________________ V
(1)
(b) Determine the frequency f of the waveform shown in Figure 4.
f = ____________________ Hz
(2)
Figure 3
Figure 4
(c) Figure 5 shows the signal generator connected in series with a resistor R and a capacitor C.
Figure 5
The oscilloscope is connected across the capacitor.
The Y-voltage gain and time-base settings are still the same as shown in Figure 2.
When S is closed (on) the oscilloscope displays the waveform shown in Figure 6.
Figure 6
Determine the time constant of the circuit in Figure 5.
time constant = ____________________ s
(2)
(d) A student suggests that setting the time-base to 0.2 ms division–1 might reduce uncertainty in the determination of the time constant.
State and explain any possible advantage or disadvantage in making this suggested adjustment.
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(3)
(e) The student connects an identical resistor in parallel with R and uses the oscilloscope to display the waveform across C.
Draw on Figure 7 the waveform you expect the student to see.
The waveform of Figure 6 is shown as a dashed line to help you show how the waveform changes.
Figure 7
Explain the change in the waveform.
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(2)
(f) Figure 8a is a graph of voltage against time showing the output of the signal generator. Figure 8b shows the voltage across C during the same time interval.
The student interchanges the positions of R and C and connects the oscilloscope across R.
Complete Figure 8c to draw the voltage across R during the time interval.
Figure 8a
Figure 8b
Figure 8c
(2)
(g) State and explain what changes, if any, the student needs to make to the settings of the oscilloscope so the waveform across R is fully displayed.
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(2)
(Total 14 marks)
Q11.
A student investigates the variation of electric potential with distance along a strip of conducting paper of length l and of uniform thickness. The strip tapers uniformly from a width 4w at the broad end to 2w at the narrow end, as shown in Figure 1. A constant pd is applied across the two ends of the strip, with the narrow end at positive potential, Vl, and the broad end at zero potential. The student aims to produce a graph of pd against distance x, measured from the broad end of the strip.
Figure 1
(a) Draw a labelled circuit diagram which would be suitable for the investigation.
(2)
(b) The student obtained some preliminary measurements which are shown below.
pd, V/V
0
2.1
4.5
7.2
Distance, x/m
0
0.100
0.200
0.300
By reference to the physical principles involved, explain why the increase of V with x is greater than a linear increase.
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(4)
(c) The potential, V, at a distance x from the broad end is given by
V = k – 1.44Vl ln (2l – x),
where Vl is the potential at the narrow end, and k is a constant.
(i) The student’s results are given below. Complete the table.l = 0.400 m
distance x/m
potential V/V
(2l – x)/m
ln (2l – x)
0.100
2.1
0.700
– 0.357
0.200
4.5
0.270
6.4
0.330
8.3
0.360
9.3
0.380
10.1
(ii) Plot a graph of V against ln (2l – x) and explain whether or not it confirms the equation.
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(iii) Use the graph to calculate Vl.
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(10)
(Total 16 marks)
Q12.
This question is about the determination of the resistivity of a wire.
Figure 1 shows a micrometer screw gauge that is used to measure the diameter of the wire.
Figure 1
(a) State the resolution of the main scale on the micrometer in Figure 1.
resolution = __________________mm
(1)
(b) Determine the distance between the anvil and the spindle of the micrometer in Figure 1. State any assumption you make.
distance = ___________________mm
(2)
(c) A student must also determine the length L of the wire between clips P and Q that will be connected into a circuit.
Figure 2 shows the metre ruler being used to measure L.
Figure 2
Determine L
L = ________________________ mm
(1)
(d) Calculate the percentage uncertainty in your result for L.
percentage uncertainty = ___________________ %
(2)
(e) State and explain what the student could have done to reduce uncertainty in the reading for L.
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(1)
(f) The student intends to make measurements that will allow her to determine the resistance of one metre of the wire. She uses an ohm-meter to measure the resistance R for different lengths L of the wire. The student’s measurements are shown in the table below.
L/cm
R/Ω
81.6
8.10
72.2
7.19
63.7
6.31
58.7
5.85
44.1
4.70
Determine the value that the student should record for the resistance per metre of the wire.
Use the additional column in the table above to show how you arrived at your answer.
resistance of one metre of wire = ________________ Ω
(2)
(g) Determine the resistivity of the wire. Give a suitable unit for your answer.
mean diameter of the wire = 0.376 mm
resistivity = ________________ unit = ____________
(4)
(Total 13 marks)
Q13.
The circuit in Figure 1 shows a sinusoidal ac source connected to two resistors, R1 and R2, which form a potential divider. Oscilloscope 1 is connected across the source and oscilloscope 2 is connected across R2.
Figure 1
(a) Figure 2 shows the trace obtained on the screen of oscilloscope 1. The time base of the oscilloscope is set at 10 m/s per division and the voltage sensitivity at 15 V per division.
Figure 2
For the ac source, calculate
(i) the frequency,
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(ii) the rms voltage.
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(4)
(b) The resistors have the following values: R1 = 450 Ω and R2 = 90 Ω.Calculate
(i) the rms current in the circuit,
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(ii) the rms voltage across R2.
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(2)
(c) Oscilloscope 2 is used to check the calculated value of the voltage across R2. The screen of oscilloscope 2 is identical to that of oscilloscope 1 and both are set to the same time base. Oscilloscope 2 has the following range for voltage sensitivity: 1 V per div., 5 V per div., 10 V per div. and 15 V per div.State which voltage sensitivity would give the most suitable trace. Explain the reasons for your choice.
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(3)
(Total 9 marks)
Q14.
This question is about capacitor charging and discharging.
A student designs an experiment to charge a capacitor using a constant current. The figure below shows the circuit the student designed to allow charge to flow onto a capacitor that has been initially discharged.
The student begins the experiment with the shorting lead connected across the capacitor as in the figure above. The variable resistor is then adjusted to give a suitable ammeter reading. The shorting lead is removed so that the capacitor begins to charge. At the same instant, the stop clock is started.
The student intends to measure the potential difference (pd) across the capacitor at 10 s intervals while adjusting the variable resistor to keep the charging current constant.
The power supply has an emf of 6.0 V and negligible internal resistance. The capacitor has a capacitance of 680 µF. The variable resistor has a maximum resistance of 100 kΩ.
(a) The student chooses a digital voltmeter for the experiment. A digital voltmeter has a very high resistance.
Explain why it is important to use a voltmeter with very high resistance.
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(1)
(b) Suggest one advantage of using an analogue ammeter rather than a digital ammeter for this experiment.
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(1)
(c) Suggest a suitable full scale deflection for an analogue ammeter to be used in the experiment.
full scale deflection = ____________________
(2)
(d) The diagram shows the reading on the voltmeter at one instant during the experiment. The manufacturer gives the uncertainty in the meter reading as 2%.
Calculate the absolute uncertainty in this reading.
uncertainty = ____________________V
(1)
(e) Determine the number of different readings the student will be able to take before the capacitor becomes fully charged.
number = ____________________
(3)
(f) The experiment is performed with a capacitor of nominal value 680 µF and a manufacturing tolerance of ± 5 %. In this experiment the charging current is maintained at 65 µA. The data from the experiment produces a straight-line graph for the variation of pd with time. This shows that the pd across the capacitor increases at a rate of 98 mV s–1.
Calculate the capacitance of the capacitor.
capacitance = ____________________µF
(2)
(g) Deduce whether the capacitor is within the manufacturer’s tolerance.
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(1)
(h) The student decides to confirm the value of the capacitance by first determining the time constant of the circuit when the capacitor discharges through a fixed resistor.
Describe an experiment to do this. Include in your answer:
• a circuit diagram
• an outline of a procedure
• an explanation of how you would use the data to determine the time constant.
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(4)
(Total 15 marks)
Q15.
Conductive paper, sometimes called Teledeltos paper, is produced by coating one surface of the paper with a thin layer of graphite paint. To investigate its electrical properties, pieces of the paper can be joined to a conventional wired circuit using copper electrodes and bulldog clips, as shown below.
It is known that the paper obeys Ohm’s Law providing the current through it does not exceed 200 mA. The company that manufactures it estimates that under typical laboratory conditions, the resistivity of the paint is between 1.0 × 10−5 Ωm and 5.0 × 10−5 Ωm.
Design an experiment that investigates some characteristic of the conductive paper.
You should consider the following in your answer.
• The variables you intend to measure and how to ensure that they are measured accurately.
• The factors you will need to control and how you will do this.
• The expected outcome of the experiment that you design.
• How any difficulties in performing the experiment could be overcome.
(Total 8 marks)
Q16.
(a) (i) Draw and label suitable apparatus required for measuring the Young modulus of a material in the form of a long wire.
(ii) List the measurements you would make when using the apparatus described in part (i).
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(iii) Describe briefly how the measurements listed in part (ii) would be carried out.
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(iv) Explain how you would calculate the Young modulus from your measurements.
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(13)
(b) A uniform heavy metal bar of weight 250 N is suspended by two vertical wires, supported at their upper ends from a horizontal surface, as shown.
One wire is made of brass and the other of steel. The cross-sectional area of each wire is 2.5 ×10–7 m2 and the unstretched length of each wire is 2.0 m.
the Young modulus for brass = 1.0 × 1011 Pa the Young modulus for steel = 2.0 × 1011 Pa
(i) If the tension, T, in each wire is 125 N, calculate the extension of the steel wire.
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(ii) Estimate how much lower the end A will be than the end B.
______________________________________________________________
______________________________________________________________
(3)
(Total 16 marks)
Q17.
Two students discuss how the intensity of the illumination provided by a spotlight varies with the distance along the axis of the lamp.
Student A argues that the lamp should be regarded as a point source so the intensity of illumination should vary as the inverse-square of the distance along the axis from the lamp. Student B disagrees, pointing out that the lamp incorporates a reflector that produces a narrow concentrated beam. Therefore, he reasons, the intensity must decrease exponentially with the distance along the axis from the lamp. Researching the problem, the students discover the calibration graph, shown below, that shows how the resistance of a light dependent resistor (LDR) varies with the intensity of the illumination falling on it.
Design an experiment that the students could perform to test their theories.
You should assume that a well-equipped physics laboratory is available to you.You are advised to draw a suitable diagram of the arrangement you intend to use as part of your answer.
You should also include the following in your answer:
• The quantities you intend to measure and how you will measure them.
• How you propose to use your measurements to settle the argument between the students.
• The factors you will need to control and how you will do this.
• How you could overcome any difficulties in obtaining reliable results.
(Total 8 marks)
Q18.
The decay of a radioactive substance can be represented by the equation
A = A0e–λt
where A = the activity of the sample at time t A0 = the initial activity at time t = 0 λ = the decay constant
The half life, T½ of the radioactive substance is given by
T½ =
An experiment was performed to determine the half-life of a radioactive substance which was a beta emitter. The radioactive source was placed close to a detector. The total count for exactly 5 minutes was recorded. This was repeated at 20 minute intervals. The results are shown in the table below.
time, t /minutes
total count, C,recorded in5 minutes
count rate, R /counts minute–1
corrected countrate, RC /counts minute–1
ln (RC / minute–1)
0
1016
203
183
5.21
20
892
178
158
5.06
40
774
155
135
4.90
60
665
133
113
4.73
80
608
122
102
4.62
100
546
109
89
4.49
(a) A correction has been made to the count rate, R, to give the corrected count rate, RC.Explain why this correction has been made and deduce its value from the table.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(2)
(b) Draw an appropriate straight line through the plotted points.
(1)
(c) Determine the gradient G of your graph.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(3)
(d) Use your graph to determine the half-life in minutes of the radioactive substance used in this experiment.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
half-life, T½ ______________________ minutes
(2)
(e) Due to the nature of a radioactive decay there will be an uncertainty in the total count recorded. What type of error is this called?
___________________________________________________________________
(1)
(f) (i) It can be shown that the error in the total count C, is given by
uncertainty in total count C = ± √C
Using data from the table, calculate the uncertainty in the smallest total count, C.
______________________________________________________________
______________________________________________________________
(1)
(ii) Hence calculate the percentage uncertainty in the smallest total count, C.
______________________________________________________________
______________________________________________________________
______________________________________________________________
(1)
(iii) Another student performed the same experiment with identical equipment but took total counts over a 1 minute period rather than a 5-minute period. The total count, C, at 140 minutes was equal to 84 counts. Estimate the percentage uncertainty in this total count, and hence explain the advantage of using a larger time.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(2)
(Total 13 marks)
Q19.
A student investigates the vertical oscillations of the mass–spring system shown in Figure 1.
The system is suspended from one end of a thread passing over a pulley.
The other end of the thread is tied to a weight.
The system is shown in Figure 1 with the mass at the equilibrium position.
The spring constant (stiffness) is the same for each spring.
(a) Explain why the position of the fiducial mark shown in Figure 1 is suitable for this experiment.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(1)
The table below shows the measurements recorded by the student.
Time for 20 oscillations of the mass-spring system/s
22.9
22.3
22.8
22.9
22.6
(b) (i) Determine the percentage uncertainty in these data.
percentage uncertainty = _________________________________________
(3)
(ii) Determine the natural frequency of the mass-spring system.
natural frequency = _________________________________________
(1)
(c) The student connects the thread to a mechanical oscillator. The oscillator is set in motion using a signal generator and this causes the mass–spring system to undergo forced oscillations.
A vertical ruler is set up alongside the mass–spring system as shown in Figure 2. The student measures values of A, the amplitude of the oscillations of the mass as f, the frequency of the forcing oscillations, is varied.
A graph for the student’s experiment is shown in Figure 3.
(i) Add a suitable scale to the frequency axis.
You should refer to your answer in part (b)(ii) and note that the scale starts at 0 Hz.
(1)
(ii) Deduce from Figure 3 the amplitude of the oscillations of X, the point where the mass–spring system is joined to the thread.
You should assume that the length of the thread is constant.
amplitude of X = _________________________________________
(1)
(d) (i) State and explain how the student was able to determine the accurate shape of the graph in the region where A is a maximum.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(2)
(ii) The student removes one of the springs and then repeats the experiment.
Add a new line to Figure 3 to show the graph the student obtains.
You may wish to use the equation .
(2)
(Total 11 marks)
Q20.
Two grids of parallel ruled lines can be used to produce Moiré fringe patterns, as shown below.
A student obtains two diffraction gratings thought to be identical with a line spacing of about 3 × 10–6 m. The student finds that when these are placed together and viewed against a white background a Moiré fringe pattern is observed when one grating is rotated slightly. For small angles, the distance between the Moiré interference fringes, D, is given by the approximate equation, D ≃ , where α is in degrees.By assuming that p = 3.0 × 10–6 m, the student uses this equation in a spreadsheet to find D for values of α up to 16°.
The student's results are shown below.
α / °
D / mm
2 4 6 810121416
0.08550.04280.02850.02140.01710.01430.01220.0107
The student intends to view the Moiré fringes through a microscope to check the spreadsheet results for D by measuring D using the microscope directly.The vernier scale on the microscope can measure to the nearest 0.01 mm.
(a) Explain using suitable calculations why this microscope is not suitable to check the results of the spreadsheet calculation.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(4)
(b) The equation for D can be rearranged to give p ≃ .
The student suggests that if a better microscope can be provided and α can be set to produce values of D greater than 0.10 mm, the value of p can be found experimentally. Discuss whether the student’s suggestion is sensible.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(2)
(c) The theoretical separation of the Moiré fringes when α = 2°, shows D = 0.0859 mm. Calculate the percentage difference between this value and the student's spreadsheet result for D when α = 2°.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(2)
(Total 8 marks)
Q21.
(a) The power P dissipated in a resistor of resistance R is measured for a range of values of the potential difference V across it. The results are shown in the table below.
V / V
V2 / V2
P / W
1.00
1.0
0.21
1.71
2.9
0.58
2.25
1.01
2.67
1.43
3.00
9.0
1.80
3.27
10.7
2.18
3.50
12.3
2.43
(i) Complete the table above.
(1)
(ii) Complete the graph below by plotting the two remaining points and draw a best fit straight line.
(2)
(iii) Determine the gradient of the graph.
gradient = ____________________
(3)
(iv) Use the gradient of the graph to obtain a value for R.
R = ____________________
(1)
(b) The following questions are based on the data in the table above.
(i) Determine the value of R when V = 3.50 V.
R = ____________________ Ω
(1)
(ii) The uncertainty in V is ± 0.01 V. The uncertainty in P is ± 0.05 W.
Calculate the percentage uncertainty in the value of R calculated in part (1).
percentage uncertainty = ____________________ %
(3)
(iii) Hence calculate the uncertainty in the value of R.
uncertainty = ____________________
(1)
(iv) State and explain whether the value of R you calculated in part (1) is consistent with the value of R you determined from the gradient in part (a)(iv).
(2)
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(Total 14 marks)
Q22.
The voltage produced by a solar cell may be assumed to be proportional to the light intensity incident on it. A student uses a solar cell in an experiment to determine the half value thickness for glass i.e the thickness of glass that reduces the output voltage by half. The student uses a varying number N of microscope slides between a light source and the solar cell and measures the output voltage V for each value of N. The graph below was produced from the student’s data.
Assuming that the output voltage of the solar cell is directly proportional to the light intensity incident upon it, the student intends to determine the half-value thickness of glass, ie the thickness of glass that would reduce the output voltage by half.
(a) Use the information provided in the student’s graph to calculate N0.5, the value of N equivalent to the half-value thickness of the glass.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(3)
(b) To determine the half-value thickness of the glass in mm, the student needs to make one additional measurement.
(i) Identify the measurement the student needs to make and explain how this is used to determine the half-value thickness of the glass.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
The student uses a micrometer screw gauge to make the additional measurement.
(ii) Identify one procedure that can be used to reduce the effect of random errors when making the measurement.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(iii) Identify one procedure that can be used to detect, and hence correct, for possible systematic errors in the measurements made with the micrometer screw gauge.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(3)
The student uses a travelling microscope to learn more about the properties of the glass slides.
The eyepiece of the microscope is arranged to move vertically up or down above a scrap of newspaper showing a photograph.The photograph is composed of dots which are only clearly visible when viewed through the microscope. By adjusting the position of the microscope the student brings the dots into focus and then reads the position of the microscope, R0, using the vernier scale.The student then places a stack of 12 slides over the photograph and refocuses the microscope. She records the new reading, R1.Finally, she places the photograph on top of the slides, refocuses the microscope, and records the new reading R2.
The sequence of operations is illustrated below.
The readings made by the student are shown in the table below.
R0/mm
R1/mm
R2/mm
2.74
7.31
17.02
(c) Assuming that the slides have identical dimensions, use the readings to determine the thickness of one glass microscope slide.
___________________________________________________________________
___________________________________________________________________
(1)
(d) Determine n, the refractive index of the glass, given by n = .
___________________________________________________________________
___________________________________________________________________
(1)
(e) The uncertainty in each of the readings R0, R1 and R2, is 0.04 mm.
(i) State the uncertainty in R2 – R0.
______________________________________________________________
(ii) State the uncertainty in R2 – R1.
______________________________________________________________
(iii) Hence calculate the percentage uncertainty in n.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(3)
(Total 11 marks
Q23.
In an experiment, a set of light emitting diodes LEDs that emitted light of different colours was used. The minimum pd Vmin for light to be emitted by each diode was measured. The results are given in the table, together with the average wavelength λ of the light emitted by each diode and the corresponding frequencies f for some of the LEDs. Some points are plotted on the graph of Vmin against f.
colour
wavelengthλ/nm
frequencyf / 1014 Hz
minimum pdVmin /V
infrared
940
3.19
0.92
red
665
4.51
1.54
orange
625
4.80
1.54
yellow
595
5.04
1.78
green
565
1.87
blue
470
2.37
(a) Complete the table.
(1)
(b) Complete the graph by plotting the missing two points and drawing a straight line of best fit.
(2)
(c) (i) Determine the gradient of the graph.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(3)
Graph of minimum pd against frequency
(ii) Discuss the reliability of your value for the gradient.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(2)
(d) Theory predicts that the energy lost by the electron in passing through the LED is theenergy of the emitted photon. Hence
eVmin = hf,
where h is the Planck constant and e = 1.60 × 10−19 C.
(i) Find a value for h by using the general equation of a straight line, y = mx + c, and your answer to part (c)(i).
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(3)
(ii) The accepted value for h = 6.63 × 10−34 J s. Calculate the percentage difference between the value calculated in part (d)(i) and the accepted value.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(1)
(iii) The precision of the voltmeter was ± 0.01V. Calculate the percentage uncertainty this produces in the value of Vmin for the infrared radiation.
______________________________________________________________
______________________________________________________________
______________________________________________________________
(1)
(iv) A student assumes that the percentage difference calculated in part (d)(ii) is due only to the uncertainty in Vmin, as determined in part (d)(iii), and the uncertainty in the frequency. Using this assumption calculate the uncertainty in the value of the infrared frequency quoted in the table.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(3)
(Total 16 marks)
Q24.
A stream of water flowing from a tap at a constant rate accelerates due to gravity. The stream becomes narrower the further it falls, before eventually breaking up into droplets.
An experiment is carried out to find out how d, the diameter of the stream of water, depends on s, the vertical distance the water has fallen. To avoid problems due to the effects of the tap outlet, s is measured from a reference level below the outlet.
The arrangement used for the experiment is shown in Figure 1
(a) The distance s is measured to the nearest mm using a vertical ruler.
The diameter d is measured to the nearest 0.1 mm using a travelling microscope.
Suggest why a travelling microscope was chosen to measure d rather than vernier callipers.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(1)
(b) The data from the experiment suggest that s = kdn where k is a constant and n is an integer.
These data are used to plot the graph in Figure 2.
(i) Determine n using Figure 2.
n _________________________________________
(2)
(ii) Explain how the numerical value of k can be obtained from Figure 2.
______________________________________________________________
______________________________________________________________
______________________________________________________________
(1)
(iii) Deduce the unit of k.
unit of k = _________________________________________
(1)
(Total 5 marks)
Q25.
This question is about the determination of the Young modulus of the metal of a wire.
In an experiment, two vertical wires P and Q are suspended from a fixed support. The fixed part of a vernier scale is attached to P and the moving part of the scale is attached to Q. The divisions on the fixed part of the scale are in mm.
An empty mass hanger is attached to Q and the scale is set to zero. A load is added to the mass hanger so that the extension of Q can be measured as shown in Figure 1.
Figure 1
(a) The reading on the vernier scale can be used to determine ∆l, the extension of Q.
Determine ∆l using Figure 1.
∆l = ____________________ mm
(1)
(b) Figure 2 shows how ∆l varies with m, the mass added to the hanger.
Determine the mass added to the hanger shown in Figure 1.
Figure 2
mass = ____________________ kg
(1)
(c) A student uses digital vernier callipers to measure the diameter of Q. She places Q between the jaws of the callipers and records the reading indicated. Without pressing the zero button she removes Q and closes the jaws.
Views of the callipers before and after she closes the jaws are shown in Figure 3.
Figure 3
Calculate the true diameter of Q.
diameter = ____________________ mm
(1)
(d) The original length of Q was 1.82 m.
Determine the Young modulus of the metal in Q.
Young modulus = ____________________ Pa
(4)
(e) The student repeats her experiment using a wire of the same original length and metal but with a smaller diameter.
Discuss two ways this change might affect the percentage uncertainty in her result for the Young modulus.
1. _________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
2. _________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(4)
(Total 11 marks)
Q26.
A student investigates how the height h of water flowing out of a burette varies with time t. A burette is used by chemists to measure a volume of liquid.
The apparatus the student used is shown in Figure 1.
h0 is the height of the water level above the tap in the burette at time t = 0.
As the tap was opened the student started a stopclock and recorded the height h every 10.0 s as the water drained into the beaker.
Values of h and h0 were measured using a metre ruler.
The student repeated this procedure twice more. The results are shown in the table below.
t/s
Height above the tap/mm
In (h/mm)
h1
h2
h3
mean height h
0
665
665
665
665
6.500
10.0
571
569
576
572
6.349
20.0
517
512
509
513
6.240
30.0
434
429
421
428
6.059
40.0
380
384
379
50.0
340
338
331
60.0
291
287
295
291
5.673
(a) Complete the table above.
(1)
(b) Plot the two missing points on the graph in Figure 2 and draw a best fit straight line.
(2)
(c) Determine the gradient of your line.
gradient = _________________________________________
(3)
(d) Theory predicts that the relationship between h and t is given by the equation
where H and λ are constants.
State values for H and λ with their units.
H = _______________________ unit = _______
λ = _______________________ unit = _______
(3)
(e) Suggest a possible source of systematic error in the burette experiment.
Explain whether this would have affected the value you found for λ.
Source _____________________________________________________________
___________________________________________________________________
Explanation _________________________________________________________
___________________________________________________________________
(3)
(f) Suggest a possible source of random error in the burette experiment.
Explain whether this would have affected the value you found for λ.
Source _____________________________________________________________
___________________________________________________________________
Explanation _________________________________________________________
___________________________________________________________________
(2)
(Total 14 marks)
Q27.
A student uses a travelling microscope to investigate the perforation holes in a block of postage stamps.
The student positions the microscope to observe the line of perforation holes along the line XY shown in Figure 1.
Figure 2 shows the positions of the cross-wires of the microscope when the student makes readings R1, R2 and R3.
The student’s readings are shown in the table below.
reading
position / mm
R 1
25.51
R 2
29.80
R 3
31.82
(a) Determine the average separation s between the centres of adjacent perforation holes along line XY.
average separation s = ______________________________________ mm
(1)
(b) State the precision of the microscope readings.
precision = ______________________________________ mm
(1)
(c) Determine the percentage uncertainty in your result for s.
percentage uncertainty = ______________________________________ %
(2)
(d) Determine the diameter d of a perforation hole.
diameter d = ______________________________________ mm
(2)
(Total 6 marks)
Q28.
The first section of a full-size stroboscopic photograph of a marble released from rest and in free fall is shown below. Every time the strobe light flashes an image of the marble is recorded. The time interval between successive flashes of the strobe light was 0.0435 s.
(a) This photograph can be used to find a value for the acceleration due to gravity g.
(i) Take measurements from the diagram below that can be used to find an accurate value for g.
(2)
(ii) Calculate a value for g using your measurements from (a)(i).
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(2)
(b) Suggest why the duration of the flash of the strobe should be as short as possible.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(1)
(Total 5 marks)
Q29.
A student performs an experiment to find the acceleration due to gravity. The student measures the time t for a spherical object to fall freely through measured vertical distances s. The time is measured electronically. The results are shown in the table below.
s/m
t1/s
t2/s
t3/s
mean timetm/s
tm2/s 2
0.300
0.245
0.246
0.244
0.245
0.0600
0.400
0.285
0.286
0.286
0.286
0.0818
0.500
0.319
0.321
0.318
0.319
0.102
0.600
0.349
0.351
0.348
0.349
0.122
0.700
0.378
0.380
0.378
0.379
0.144
0.800
0.403
0.406
0.404
0.900
0.428
0.428
0.430
(a) Complete the table by entering the missing values for tm and tm2
(1)
(b) Complete the graph below by plotting the remaining two points and draw a line of best fit.
(2)
(c) Determine the gradient of the graph.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(3)
(d) Theory suggests that the equation for the line is where g is the acceleration due to gravity.
Calculate a value for g using the above equation and the gradient of your graph above.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(1)
(e) Calculate the percentage difference between your value for g and the accepted value of 9.81 m s –2.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(1)
(f) Calculate the uncertainty in the smallest value of tm.
___________________________________________________________________
___________________________________________________________________
(1)
(g) Calculate the value of g which would be given from the smallest value of tm and the corresponding value of s.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(3)
(h) The uncertainty in each value of s is ± 0.001 m.
Calculate the uncertainty in the value of g you calculated in part (g).
You will need to use the uncertainty for tm you calculated in part (f).
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(3)
(i) A student wishes to investigate the effect of changing the mass of the spherical object on the acceleration of free fall.
Explain how you would modify the experiment seen at the start of this question.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(3)
(Total 18 marks)
Q30.
In an experiment an unknown load, of weight, W, was supported by two strings kept in tension by equal masses, m, hung from their free ends, with each string passing over a frictionless pulley. The arrangement was symmetrical and is shown in Figure 1.
Figure 1
The distance x was kept constant throughout the experiment. The length y was measured for different values of m.
The distance between the strings at the pulleys, x = 0.500m
(a) Figure 2 shows the three forces acting through the point at which the strings are attached to the load. The weight of the load is W and the tension in each string is mg, where g is gravitational field strength.
Figure 2
(i) By resolving the forces vertically show that
where φ is the angle between each string and the vertical.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(1)
(ii) Draw the line of best fit through the points plotted on the graph.
(1)
(b) (i) Determine the gradient of your graph.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(3)
(ii) The equation for the straight line is
Given that g = 9.81Nkg–1, determine a value for W.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(2)
(c) When m was 0.300 kg, y was 0.400 m.
Calculate the percentage uncertainty in for m = 0.300 kg.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(3)
(d) (i) Explain the term systematic error.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
(1)
(ii) In practice, there may be a systematic error in this experiment because of friction in the pulleys.When the measurements were taken, increasing values of m were used. State and explain how friction in the pulleys would have affected the measured values of y.
______________________________________________________________
______________________________________________________________
___________________________________________________________