DP Physics (last assessment 2024)

Question 20N.3.SL.TZ0.1

Date	November 2020	Marks available	[Maximum mark: 9]	Reference code	20N.3.SL.TZ0.1
Level	SL	Paper	3	Time zone	TZ0
Command term	Comment, Identify, Show that, Sketch, State, Suggest	Question number	1	Adapted from	N/A

[Maximum mark: 9]

20N.3.SL.TZ0.1

A spherical soap bubble is made of a thin film of soapy water. The bubble has an internal air pressure $P_{i}$ and is formed in air of constant pressure $P_{o}$ . The theoretical prediction for the variation of $(P_{i} - P_{o})$ is given by the equation

$(P_{i} - P_{o}) = \frac{4 g}{R}$

where $γ$ is a constant for the thin film and $R$ is the radius of the bubble.

Data for $(P_{i} - P_{o})$ and $R$ were collected under controlled conditions and plotted as a graph showing the variation of $(P_{i} - P_{o})$ with $\frac{1}{R}$ .

(a)

Suggest whether the data are consistent with the theoretical prediction.

[2]

Markscheme

«theory suggests» $P_{i} - P_{o}$ is proportional to $\frac{1}{R}$ ✓

graph/line of best fit is straight/linear «so yes»
OR
graph/line of best fit passes through the origin «so yes» ✓

MP1: Accept ‘linear’

MP2 do not award if there is any contradiction
eg: graph not proportional, does not pass through origin.

Examiners report

Many students obtained full marks here although a significant number did not acknowledge that the graph was through the origin and lost a mark.

(b(i))

Show that the value of $γ$ is about 0.03.

[2]

Markscheme

gradient $=$ « $4 γ$ » $= 0.10$
OR
use of equation with coordinates of a point ✓

$γ = 0.025$ ✓

MP1 allow gradients in range $0.098$ to $0.102$

MP2 allow a range $0.024$ to $0.026$ for $γ$

Examiners report

Very well answered either by obtaining the gradient or replacing with the coordinates of a point.

(b(ii))

Identify the fundamental units of $γ$ .

[1]

Markscheme

$kg s^{- 2}$ ✓

Accept $\frac{kg}{s^{2}}$

Examiners report

Although the question was specifically about the fundamental units, several candidates lost the mark by answering Pa m.

(b(iii))

In order to find the uncertainty for $γ$ , a maximum gradient line would be drawn. On the graph, sketch the maximum gradient line for the data.

[1]

Markscheme

straight line, gradient greater than line of best fit, and within the error bars ✓

Examiners report

Almost all candidates were able to draw the correct maximum gradient line.

(b(iv))

The percentage uncertainty for $γ$ is $15 %$ . State $γ$ , with its absolute uncertainty.

[2]

Markscheme

« $15 %$ of $0.025$ » = $0.00375$
OR
« $15 %$ of $0.030$ » = $0.0045$ ✓

rounds uncertainty to 1sf
$\pm 0.004$
OR
$\pm 0.005$ ✓

Allow ECF from (b)(i)
Award [2] marks for a bald correct answer

Examiners report

Well answered. A significant number did not round the uncertainty to match the value of gamma.

(b(v))

The expected value of $γ$ is $0.027$ . Comment on your result.

[1]

Markscheme

Experimental value matches this/correct, as expected value within the range ✓
OR
experimental value does not match/incorrect, as it is not within range ✓

Syllabus sections

Core

Core » Topic 1: Measurements and uncertainties » 1.1 – Measurements in physics

Core » Topic 1: Measurements and uncertainties

Core » Topic 1: Measurements and uncertainties » 1.2 – Uncertainties and errors

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