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Date November 2018 Marks available 1 Reference code 18N.3.SL.TZ0.1
Level Standard level Paper Paper 3 Time zone 0 - no time zone
Command term Draw Question number 1 Adapted from N/A

Question

In an investigation to measure the acceleration of free fall a rod is suspended horizontally by two vertical strings of equal length. The strings are a distance d apart.

When the rod is displaced by a small angle and then released, simple harmonic oscillations take place in a horizontal plane.

The theoretical prediction for the period of oscillation T is given by the following equation

T = c d g

where c is a known numerical constant.

In one experiment d was varied. The graph shows the plotted values of T against  1 d . Error bars are negligibly small.

State the unit of c.

[1]
a.

A student records the time for 20 oscillations of the rod. Explain how this procedure leads to a more precise measurement of the time for one oscillation T.

[2]
b.

Draw the line of best fit for these data.

[1]
c.i.

Suggest whether the data are consistent with the theoretical prediction.

[2]
c.ii.

The numerical value of the constant c in SI units is 1.67. Determine g, using the graph.

[4]
d.

Markscheme

m 3 2  ✔

 

Accept other power of tens multiples of  m 3 2 , eg:  c m 3 2 .

a.

measured uncertainties «for one oscillation and for 20 oscillations» are the same/similar/OWTTE

OR

% uncertainty is less for 20 oscillations than for one ✔

 

dividing «by 20» / finding mean reduces the random error ✔

b.

Straight line touching at least 3 points drawn across the range ✔

It is not required to extend the line to pass through the origin.

c.i.

theory predicts proportional relation « T 1 d , slope = Td  c g = constant » ✔

the graph is «straight» line through the origin

c.ii.

correctly determines gradient using points where ΔT≥1.5s

OR

correctly selects a single data point with T≥1.5s ✔

 

manipulation with formula, any new and correct expression to enable g to be determined ✔

Calculation of g ✔

With g in range 8.6 and 10.7 «m s−2» ✔

 

Allow range 0.51 to 0.57.

d.

Examiners report

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

Syllabus sections

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