Data-Based Questions (Paper 1B) (DP IB Physics: HL): Exam Questions

A group of students investigate the Beaufort scale for describing wind intensity. On this scale, the average wind speed increases with the Beaufort scale value B, according to the relationship:

where and are constants.

Explain why a graph of  against  should give a straight line.

The table shows the data recorded by the students for values of  and corresponding values of .

(i) Plot a graph of  against  on the grid below.

Use the columns provided to show any processed data.

[5]

(ii) Use your graph to determine the values of and .

[3]

A student investigates the behaviour of a thermistor using the circuit shown in the diagram.

The student heated the thermistor to 100°C and measured the potential difference across it. They decreased the temperature and recorded further measurements of  and until the temperature reached 10°C.

Suggest a suitable method for varying the temperature of the thermistor.

The reading of when the thermistor was at room temperature is shown on the voltmeter in the diagram below.

Calculate the percentage uncertainty in the measured value of .

The student plotted a graph of the measurements of and θ.

Estimate the value of for a temperature of 0°C.

The student proposes the hypothesis that is inversely proportional to the absolute temperature in Kelvin.

Deduce, using two suitable data points from the graph, whether the student's hypothesis is supported.

A group of students investigate how the period of oscillation of a mass-spring system varies with the number of vertical springs.

The students attach a mass to a vertical spring which is fixed at its upper end. The mass is displaced by a small vertical distance and then released. The time for one oscillation is measured for identical springs attached in parallel.

The table shows some of the data collected by the students.

(i) is provided by two identical slotted masses, each of known mass, with an uncertainty of 0.001 kg.

State the uncertainty in the total mass .

[1]

(ii) is measured with an electronic stopwatch that measures to the nearest 0.1 s.

Describe how an uncertainty in of less than 0.1 s can be achieved using this stopwatch.

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The graph shows the variation of with . The uncertainty in is negligibly small.

(i) Outline why it is unlikely that the relationship between and is linear.

[1]

(ii) Calculate the largest fractional uncertainty in for these data.

[2]

The students suggest the following theoretical relationship between and :

where is a constant.

To verify the relationship, the variation of with is plotted.

(i) Determine by drawing the line of best fit.

[3]

(ii) State the units of .

[1]

(iii) The theoretical relationship assumes that the springs behave as ideal springs following Hooke's law.

Suggest why, in order to test the relationship, the amplitude of oscillation should be kept small compared to the natural length of the springs.

[2]

A student is analysing a sample of sunflower oil. To determine its density, the student measures the volume with a measuring cylinder and the mass with an electronic balance.

Identify one way to ensure that the volume is read accurately.

The following data are collected:

• Volume = (15.0 ± 0.2) cm³

• Mass = (13.77 ± 0.01) g

(i) Calculate the density of the sample and its absolute uncertainty.

[2]

(ii) State your answers in kg m^-3 and with correct precision.

[1]

When the density was measured, the sample was at 25 °C. The student has a graph that shows the variation with temperature of the density of pure sunflower oil.

Suggest whether the oil sample can be considered pure.

A student determines the density of a solid metal cylinder.

The student makes the following measurements:

Length of the cylinder = (27.3 ± 0.2) mm

Readings for the diameter of the cylinder:

Mass of the cylinder = 29.8 g ± 1.5 %

Outline why the measurements of were made at different places along the cylinder.

Suggest suitable instruments for the measurement of

(i)

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(ii)

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(i) Show that the mean diameter of the cylinder is about 12.5 mm.

[2]

(ii) Calculate the fractional uncertainty in the diameter of the cylinder.

[2]

(iii) Calculate the fractional uncertainty in the length of the cylinder.

[1]

The density of the cylinder is given by

where is the cross-sectional area of the cylinder.

Calculate the value of and its absolute uncertainty. State your answers to an appropriate number of significant figures.

A student investigates the electromotive force (emf) and internal resistance of a cell.

They do this by measuring the terminal potential difference and current in the circuit shown.

A graph of the variation of with is plotted. The uncertainty in is negligible.

Draw, on the graph, the lines of maximum and minimum gradient.

(i) Determine, using the graph, the emf of the cell, including its absolute uncertainty. Give your answers to an appropriate number of significant figures.

[3]

(ii) Outline how the internal resistance can be determined from this graph.

[2]

The student adds a second identical cell in series with the first cell and repeats the experiment.

Describe the key features of the graph for this second experiment compared to the first.

In an experiment to measure the specific latent heat of vaporisation of water, a student uses an electric heater to boil water. When the water is boiling steadily, they use an electronic balance to measure the mass of water that vaporises in time = 240 s.

The theoretical relationship is given by

where is the potential difference across the heater and is the current in it.

(i) is provided by two identical power supplies connected in series. The potential difference of each of the power supplies is known with an uncertainty of 0.2 V.

State the uncertainty in the potential difference .

[1]

(ii) Draw a suitable circuit diagram that would enable to be determined. The symbol for a heater is shown.

[2]

The student repeated the experiment for different powers supplied to the heater. They plot a graph of the power of the heater against the mass of water vaporised in 240 seconds.

(i) Outline how the student obtained different values of .

[2]

(ii) The percentage uncertainty in is ±5 %.

Calculate the absolute uncertainty in when = 100 W and draw the uncertainty bar for this data point on the graph.

[2]

(i) Determine by drawing the line of best fit.

[4]

(ii) State the units of .

[1]

Outline one source of systematic error in the experiment and its effect on the calculated value of the specific latent heat of vaporisation of water.

A student uses Young’s double-slit apparatus to determine the wavelength of monochromatic light using the relation

where is the separation of the fringes, is the separation of the slits, and is the distance from the slits to the screen.

is measured using a ruler with a smallest scale division of 1 mm.

Describe how an uncertainty in of less than 1 mm can be achieved using this ruler.

Discuss the effect on the fractional uncertainty in when using a larger value of .

(i) To determine , the student plots a graph with on the vertical axis.

State the variable that must be plotted on the horizontal axis to obtain a line of best fit that is straight.

[1]

(ii) The calculator value obtained from the graph gives = 630.102 nm with a percentage uncertainty of ±8 %.

Deduce how this value of should be recorded in a conclusion, including the absolute uncertainty, to the appropriate number of significant digits.

[2]

A student conducts an experiment to determine the speed of sound in air using standing waves in a tube.

The student holds a tuning fork of known frequency at the open end of the plastic tube, which is partially submerged in a measuring cylinder of water. The student slowly lowers the tube into the water and measures the length of the air column when the first loud sound is heard.

The experiment is repeated several times for the same tuning fork. The student obtains the following repeated readings of .

(i) Calculate the mean value of and its percentage uncertainty.

[3]

(ii) Suggest one reason for the variation in the measured value of .

[1]

The procedure is repeated using tuning forks of different values of frequency .

The student plots a graph of the variation of with . They add an uncertainty bar for for the first data point and draw the best-fit line.

(i) Suggest why the student has not drawn uncertainty bars for .

[1]

(ii) For the value of calculated in (a)(i), draw the uncertainty bar on the graph for this data point only.

[2]

(i) Determine the gradient of the student's best-fit line.

[2]

(ii) Draw on the student's graph the line of maximum gradient.

[1]

(iii) Determine the value of the speed of sound with its absolute uncertainty.

[2]