Question 1a

Marks: 3

A student uses a stopwatch to measure the time taken for a pendulum to complete one swing.

The display on the stopwatch after the pendulum completes 10 swings is shown on the diagram.

1-2-q1a-question-stem-easy-sq-sl-phy

(a)

For this reading, determine:

(i)

The absolute uncertainty

[1]

(ii)

The fractional uncertainty

[1]

(iii)

The percentage uncertainty

[1]

Key Concepts

Uncertainties

Question 1b

Marks: 4

(b)

Calculate the mean time for one complete swing with its absolute uncertainty and a percentage uncertainty.

Give your answer to an appropriate number of significant figures.

[4]

Key Concepts

Uncertainties

Question 1c

Marks: 2

(c)

Draw lines between the three types of error to show if the error affects the precision or accuracy of a result.

1-2-q1c-question-stem-easy-sq-sl-phy

[2]

Key Concepts

Random & Systematic Errors

Question 1d

Marks: 4

In order to reduce errors, a different student collected measurements of time over 20 cycles instead of 10.

(d)

Complete the following sentences by circling the correct word and placing a tick (✓) next to the correct explanation

Repeated measurements reduce systematic / random errors because...

	using a larger sample to calculate the mean value reduces the uncertainty in the final value
	these cause values to be different by the same amount each time, hence they are not influenced by repetition

Repeated measurements have no effect on systematic / random errors because...

	using a larger sample to calculate the mean value reduces the uncertainty in the final value
	these cause values to be different by the same amount each time, hence they are not influenced by repetition

[4]

Key Concepts

Random & Systematic Errors

Question 2a

Marks: 2

(a)

Outline the difference between precise and accurate measurements.

[2]

Key Concepts

Random & Systematic Errors

Question 2b

Marks: 3

A student investigates the relationship between the height that a small metal sphere is dropped from and the time it takes to fall. The ball is dropped from rest through a distance of 543 ± 2 mm.

1-2-q2b-question-stem-easy-sq-sl-phy

The student predicts the expected time the sphere should take to fall this distance is 0.323 s, using the following equation:

acceleration due to gravity = $\frac{2 \times d i s t a n c e f a l l e n b y c e n t r e o f m a s s o f s p h e r e}{{(m e a s u r e d t i m e t o f a l l)}^{2}}$

The time taken for the sphere to fall from the point of release to a trapdoor is measured. This measurement is repeated a number of times.

Time, t₁ / s	Time, t₂ / s	Time, t₃ / s	Time, t₄ / s	Time, t₅ / s	Time, t₆ / s
0.423	0.422	0.424	0.421	0.423	0.424

(b)

For the student's results:

(i)

Calculate the mean value

[1]

(ii)

Explain why the results are precise but not accurate

[2]

Key Concepts

Random & Systematic Errors

Question 2c

Marks: 2

The student repeats the experiment and obtains the following data:

Measured time to fall	0.322 ± 0.002 s
Distance between the point of release and the trapdoor	543 ± 1 mm
Diameter of the metal sphere	10.0 ± 0.1 mm

(c)

For this data, calculate:

(i)

The total distance fallen by the centre of mass of the sphere

[1]

(ii)

The absolute uncertainty in this distance

[1]

Key Concepts

Propagating Uncertainties

Question 2d

Marks: 5

(d)

Calculate the acceleration due to gravity, including an estimate of the absolute uncertainty in your answer.

You may use the following rules for propagating uncertainties:

Operation	Example	Propagation Rule
Addition & Subtraction	$y = a \pm b$	$Δ y = Δ a + Δ b$ The sum of the absolute uncertainties
Multiplication & Division	$y = a \times b$ or $y = \frac{a}{b}$	$\frac{Δ y}{y} = \frac{Δ a}{a} + \frac{Δ b}{b}$ The sum of the fractional uncertainties
Power	$y = a^{\pm n}$	$\frac{Δ y}{y} = n (\frac{Δ a}{a})$ The magnitude of n times the fractional uncertainty

[5]

Key Concepts

Propagating Uncertainties

Question 3a

Marks: 4

(a)

List the following currents from largest to smallest percentage uncertainty:

4.1 ± 0.2 A

5 ± 1 mA

7.30 ± 0.23 A

0.5 ± 0.05 mA

[4]

Key Concepts

Uncertainties

Question 3b

Marks: 4

A circuit is set up to measure the resistance, R, of a resistor. The potential difference (p.d), V, across the resistor and the current, I, are related by the equation:

$V = I R$

The readings for the p.d, V, and the corresponding current, I, are obtained and plotted on a graph with a line of best fit drawn.

1-2-q3b-question-stem-easy-sq-sl-phy

(b)

Complete the following sentences by circling the correct words:

Current and potential difference have a directly / inversely proportional relationship.

This means when one quantity is zero, the other will be zero / non-zero.

On the graph, the y-intercept is zero / non-zero, hence, this shows the readings have / have not been affected by systematic / random uncertainties.

The points on the graph are close to / scattered around the line of best fit, hence, this shows the readings have / have not been affected by systematic / random uncertainties.

[4]

Key Concepts

Random & Systematic Errors

Question 3c

Marks: 6

The student plots error bars on the graph along with lines of maximum and minimum gradient.

1-2-q3c-question-stem-easy-sq-sl-phy

(c)

(i)

Determine the percentage uncertainty in the gradient using the following equations of the lines:

Best line	$I = 0.045 V + 0.05$
Maximum line	$I = 0.052 V + 0.03$
Minimum line	$I = 0.036 V + 0.07$

[3]

(ii)

The student suggests the analogue ammeter used to measure the current may have introduced a positive zero error. State what is meant by a zero error.

[1]

(iii)

Outline one way a zero error could affect the results and suggest how this type of error can be fixed.

[2]

Key Concepts

Determining Uncertainties from Graphs
Random & Systematic Errors

Question 3d

Marks: 5

In another student's experiment, the resistance of the resistor, R, is determined using the following data:

Current, I	0.74 ± 0.01 A
Potential difference, V	6.5 ± 0.2 V

(d)

Calculate the value of R, together with its percentage uncertainty. Give your answer to an appropriate number of significant figures.

[5]

Key Concepts

Propagating Uncertainties

Question 4a

Marks: 2

A vernier calliper has a positive zero error of 0.10 mm.

A student uses the vernier calliper to measure the length of a wire under various loads and records the data in a table.

Load / N	Length / mm	Corrected Length / mm
1.00	3.00
1.50	3.54
2.00	4.02
2.50	4.61
3.00	4.99

(a)

Correct the readings of the length of wire in mm for each load.

[2]

Key Concepts

Uncertainties

Question 4b

Marks: 2

The student wants to determine the extension of the wire after each load is applied. Part of the results table is shown below.

Load / N	Length / mm
1.00	3.00
1.50	3.54

The vernier calliper scales have an uncertainty of ± 0.01 mm

(b)

Using the data, calculate the extension of the wire and its absolute uncertainty.

[2]

Key Concepts

Uncertainties

Question 4c

Marks: 3

Another student decides to use a ruler to measure the length of the wire for each load and records the data in a table.

Load / N	Length / mm
1.00	3.00
1.50	4.00
2.00	4.00
2.50	5.00
3.00	5.00

The ruler has an uncertainty of ± 1.00 mm.

(c)

Calculate the fractional uncertainty in the length of the wire using a ruler when a load of 2.50 N is applied. Quote the final value with its fractional uncertainty.

[3]

Key Concepts

Uncertainties

Question 4d

Marks: 4

The student using the vernier calliper to measure the length of the wire obtained a length of 4.61 ± 0.01 mm when a load of 2.50 N was applied.

They quoted the percentage uncertainty in this length as 0.22 %.

(d)

State and explain whether or not the student has:

(i)

Calculated the percentage uncertainty correctly

[2]

(ii)

Quoted the percentage uncertainty correctly

[2]

Key Concepts

Uncertainties

DP IB Physics: HL

Topic Questions

1.2 Uncertainties & Errors

Question 1a

Key Concepts

Question 1b

Key Concepts

Question 1c

Key Concepts

Question 1d

Key Concepts

Question 2a

Key Concepts

Question 2b

Key Concepts

Question 2c

Key Concepts

Question 2d

Key Concepts

Question 3a

Key Concepts

Question 3b

Key Concepts

Question 3c

Key Concepts

Question 3d

Key Concepts

Question 4a

Key Concepts

Question 4b

Key Concepts

Question 4c

Key Concepts

Question 4d

Key Concepts

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