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Date November 2019 Marks available 3 Reference code 19N.3.SL.TZ0.1
Level Standard level Paper Paper 3 Time zone 0 - no time zone
Command term Determine Question number 1 Adapted from N/A

Question

A student investigates how the period T of a simple pendulum varies with the maximum speed v of the pendulum’s bob by releasing the pendulum from rest from different initial angles. A graph of the variation of T with v is plotted.

Suggest, by reference to the graph, why it is unlikely that the relationship between T and v is linear.

[1]
a.

Determine the fractional uncertainty in v when T = 2.115 s, correct to one significant figure.

[2]
b.

The student hypothesizes that the relationship between T and v is T = a + bv2, where a and b are constants. To verify this hypothesis a graph showing the variation of T with v2 is plotted. The graph shows the data and the line of best fit.

Determine b, giving an appropriate unit for b.

[3]
c.

The lines of the minimum and maximum gradient are shown.

Estimate the absolute uncertainty in a.

[2]
d.

Markscheme

a straight line cannot be drawn through all error bars
OR
the graph/line of best fit is /curved/not straight/parabolic etc.
OR
graph has increasing/variable gradient ✔

NOTE: Do not allow “a line cannot be drawn through all error bars” without specifying “straight”.

a.

v=1.15«ms-1»  AND  v=0.05«ms-1»

«0.051.15=»0.04 

NOTE: Accept 4 %

b.

use of 2 correct points on the line with Δv> 2 ✔

b in range 0.012 to 0.013 ✔

sm–2 

c.

amax=2.101 «s» ±0.001 «s» AND amin=2.095«s» ±0.001 «s» ✔

«2.101-2.0952=» 0.003 «s» ✔

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.

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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