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Date May 2019 Marks available 2 Reference code 19M.3.SL.TZ1.2
Level Standard level Paper Paper 3 Time zone 1
Command term Suggest Question number 2 Adapted from N/A

Question

In an investigation a student folds paper into cylinders of the same diameter D but different heights. Beginning with the shortest cylinder they applied the same fixed load to each of the cylinders one by one. They recorded the height H of the first cylinder to collapse.

They then repeat this process with cylinders of different diameters.

The graph shows the data plotted by the student and the line of best fit.

Theory predicts that H = c D 2 3 where c is a constant.

Suggest why the student’s data supports the theoretical prediction.

[2]
a.

Determine c. State an appropriate unit for c.

[3]
b.

Determine c. State an appropriate unit for c.

[3]
b.

Identify one factor that determines the value of c.

[1]
c.

Markscheme

theory « H = c D ( 2 3 ) » predicts that H3D

graph «of H3 vs D2 » is a straight line through the origin/graph of proportionality ✔

Allow H = c D ( 2 3 ) gives H3 = c3D2 for MP1.

Do not award MP2 for “the graph is linear” without mention of origin.

a.

evidence of gradient calculation to give gradient = 3.0 ✔

c3 = 3.0 ⇒ c = 1.4 ✔

m 1 3

b.

evidence of gradient calculation to give gradient = 3.0 ✔

c3 = 3.0 ⇒ c = 1.4 ✔

m 1 3

b.

the load/the thickness of paper/the type of paper/ the number of times the paper is rolled to form a cylinder ✔

c.

Examiners report

Load on a cylinder. The question was successful for candidates well prepared to write conclusions in their lab reports. Theory in the stem of the question predicts a directly proportional relationship between H and D2/3, which graphed are H3 and D2. Well prepared candidates were able to identify, that the theory predicts that H3 should be directly proportional to D2 and that this proportionality can be seen from the graph. Many candidates were able to mention that the relationship was linear and passed through the origin (as an alternative to proportional). However, a common response mentioned only linear or linear regression which is not sufficient to fully demonstrate proportionality.

a.

Part b) was the most difficult part of section A, but still accessible. Many candidates only calculated the slope of the graph and did not realise that the third root of the slope is the constant c. Some students who were able to achieve the numerical value of c=1.4 struggled to establish the correct unit - perhaps lacking confidence or familiarity with the notion that a unit could be raised to a fractional index.

b.

Part b) was the most difficult part of section A, but still accessible. Many candidates only calculated the slope of the graph and did not realise that the third root of the slope is the constant c. Some students who were able to achieve the numerical value of c=1.4 struggled to establish the correct unit - perhaps lacking confidence or familiarity with the notion that a unit could be raised to a fractional index.

b.

In c) most of the candidates well identified the load or the type of the paper as possible controlled variables. A common mistake here was answer discussing the height or the diameter of the cylinders.

c.

Syllabus sections

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