Physics Exemplars
AS90774 (Physics 3.1) Carry out a practical physics
investigation with guidance, that leads to a mathematical
relationship (version 2)
Level 3, 5 credits.
The following extracts from student work are intended to exemplify the boundaries
between Achievement, Merit and Excellence for this achievement standard. While a
particular grade would not be awarded on the basis of a single aspect of a student’s
work, these exemplars are designed to show features typical of work that level.
See also:
• 2008 National Moderator’s Report [http://www.nzqa.govt.nz/nqfdocs/ncearesource/reports/2008/nat-mod/physics.pdf]
• 2007 National Moderator’s Report [http://www.nzqa.govt.nz/nqfdocs/ncearesource/reports/2007/nat-mod/physics.pdf]
The explanatory notes (EN) of the standard give guidance about typical evidence that
contributes to a particular grade.
For Achievement, evidence will typically include (EN4):
• data relevant to the aim based on the manipulation of the independent variable
and the consideration of other variable(s) that could affect the results
• uncertainties in raw data appropriate to the measurement
• a linear graph, including an error line, based on the data and relevant to the
aim
• a conclusion that links to the aim and is drawn from information calculated
from the linear graph.
For Merit, evidence will typically include (EN5):
• accurate data relevant to the aim based on the manipulation of the independent
variable over a reasonable range and number of values
• a description of the control of other variable(s) that could significantly affect
the results
• the use of techniques to improve the accuracy of measurements
• appropriate uncertainties in raw and plotted data
• a linear graph with error bars and appropriate error line, based on sufficient
data, relevant to the aim
• a conclusion that is relevant to the aim, based on the data, and is drawn from
information calculated from the linear graph, including a processed
uncertainty
• a discussion that evaluates the quality of the results.
For Excellence, evidence will typically include, in addition (EN6):
•
•
•
uncertainties appropriately calculated in all processed data
information from the linear graph is correctly rounded
a discussion that shows critical thinking, evaluates and explains the validity of
the results, and considers relevant physics theory.
Conclusion
•
•
•
Achievement: a conclusion that links to the aim and is drawn from information
calculated from the linear graph.
Merit: a conclusion that is relevant to the aim, based on the data, and is drawn
from information calculated from the linear graph, including a processed
uncertainty
Excellence: information from the linear graph is correctly rounded
Student
1
Grade
Not
Achieved
Student Response
My results clearly show that
the greater the mass the longer
the period of oscillation
Moderator Commentary
The aim is to give a
mathematical relationship.
This is too general as it
does not refer to the nonlinear nature of the
relationship.
2
Not
Achieved /
Achieved
The relationship is y = m x2
If the student shows no
indication that they know
what y, m and x refer to,
this is not adequate.
However if elsewhere they
have identified y, x, and
have calculated a value for
m, this would be
acceptable.
3
Achieved
4
Merit
m = 24 (± 3.95) L2 + 12.33 (±
5.8)
The relationship given by
the equation is correct but
uncertainties are not
rounded appropriately,
which is required for
Excellence.
5
Excellence
m = 24 (± 4) L2 + 12 (± 6)
Uncertainties are rounded
appropriately.
m = 24 L2 + 12
The relationship given is
correct, but without
uncertainties.
Linear graph and error line
•
•
Achievement: a linear graph, including an error line, based on the data and
relevant to the aim
Merit/Excellence: a linear graph with error bars and appropriate error line,
based on sufficient data, relevant to the aim
Student
6
Grade
Not Achieved
Moderator Commentary
Students must have applied the appropriate
transformation to their raw data, to give a linear graph.
This graph of the raw data has a straight line drawn (i.e.
a linear relationship implied), but it does not show the
expected transformation (T2) so cannot be accepted.
7
Achieved
For Achieved, an attempted error line is needed, but
error bars are not.
8
Merit /
Excellence
Error bars and error line show the effect data
uncertainty has on the gradient. There is no distinction
between Merit and Excellence in the graph, so the final
grade would depend on other aspects of the report.
Discussion
•
•
Merit: a discussion that evaluates the quality of the results.
Excellence: a discussion that shows critical thinking, evaluates and explains
the validity of the results, and considers relevant physics theory.
Student
9
Grade
Achieved
Student Response
The period of oscillation is
a T α √LB relationship, as
the graph drawn with the
transformation is a straight
line.
The range over which the
lengths were measured was
relatively small which
provided only a small range
of results. A large range
could be used in further
experiments.
The angle from which the
pendulum was released was
also inexact, as this had to
be estimated. In future
experiments a protractor
could be used to measure
this more accurately.
The lengths were hard to
measure as the metre ruler
was accurate to 1 mm but
the string could bend. Also
the centre of mass had to be
estimated. This could be
found accurately, and then
used. Air resistance would
have an effect on the
system, causing it to have a
different period.
The original equipment
changed L, but this would
also affect the period, so
the method was modified to
only change LB. There was
human error in the timing,
as the distances had to be
judged by sight.
Moderator Commentary
For Merit, students should have
a discussion that evaluates the
quality of the results. This
discussion does not evaluate the
quality of the results beyond
general comment on
experimental limitations.
10
Merit
I improved my accuracy in Discussion evaluates the quality
many ways. I timed the
of the results, giving reasons
period for each mass three
why they are reliable.
times and took the average,
and the range helped me
make a reasonable
uncertainty. By repeating
and taking averages I
reduced the human timing
error. I also times 10
oscillations and divided it
by 10 as it would have been
hard to time one oscillation,
especially with the smaller
masses where the period is
quite small. If I had timed a
single oscillation my
uncertainty would be
unreasonably high.
I controlled variables by
making sure they were all
the same for each test. I
made sure that I pulled the
end of the cantilever down
2 cm for each one, so the
distance of the oscillations
is the same. I also kept the
length of the cantilever the
same for each test and
made sure that when I
added masses, they were
stacked on top of each
other so the weight force
acted on the same part of
the cantilever for all tests.
11
Merit
The relationship between
the distance apart of the
ropes (D) and the period of
oscillation (T) is:
T = (0.74 ± 0.04)/D + (0.0
± 0.3)
When I substitute values of
g = 9.81, r = 1.01, L = 0.4
into the theory equation I
get:
This comparison of theory and
experiment assesses the validity
of the results (shows how they
fit with expected values), and
also considers relevant physics
theory. However this is not
enough for Excellence.
T = (0.75)/D
This fits with my
experimental relationship
as the value 0.75 is near the
middle of my gradient
range 0.74 ± 0.04, and the
intercept (0) is also in the
middle of my intercept
range (0 ± 0.3).
12
Excellence This experiment was
designed to model a person
jumping on a trampoline,
but there are some flaws:
The ruler is not the same
shape as a trampoline, and
it is not known whether the
ruler will deflect in the
same way as a trampoline
as it is loaded. However,
without a real trampoline,
this cannot be tested.
On a trampoline the mass
(person) bounces on top of
the mat, inputting their own
energy to the motion. Also
the force they exert will
change, increasing as they
land, and maybe
disappearing if they leave
the surface. In my
experiment the mass was
hung passively below the
ruler, a so it applied a
constant force to the ruler.
This would cause the ruler
to oscillate with damped
SHM, unlike the
trampoline, which would
not do SHM on account of
the irregular force being
applied by the person
jumping.
Critical thinking shown in the
comparison of model and reallife situation (ruler c.f.
trampoline).
A factor is identified, and its
effect is described (changing
force applied as person
bounces, causing non-SHM
motion).
Below are further examples of individual discussion statements. In most which
exemplify Excellence level “critical thinking”, the student identifies some factor
which could affect the results and explains the effect which that factor might have
had. The overall grade attained would, of course, depend on many other aspects of the
report.
Student
13
Student Response
Moderator Commentary
It was extremely hard to get all A possible factor, but no explanation of its
of the string lengths exactly the effect on the results: Not Excellence.
same.
14
To determine the accuracy of
my results and their validity I
decided to use my
mathematical relationship to
interpolate a temperature value
for an arbitrary current, and
then compare this to a
theoretical value…
Evaluating the quality of the results:
Merit level, so far.
15
The experimental gradient is
steeper than the theory
predicted. This could be
because the theory doesn’t take
into account friction in the
real-life scenario.
Explanation too vague to be of use: Not
Excellence.
16
The bridge wouldn’t be
uniform along its length like a
ruler. That would obscure the
results.
A possible factor, but no specific effect
suggested: Not Excellence.
17
In the real life situation there
were people standing on the
swing-bridge. This would
affect the position of the centre
of mass, moving it towards the
end where the people were.
Identifies the factor of people standing on
the bridge, and describes it in terms of
relevant physics (COM), but does not
specify its effect on the results: Not
Excellence
18
I noticed that the wood was
made up of several layers. This
means its stiffness factor may
have varied depending on the
degree to which the wood was
bent. As it bent, the upper
layers would be stretched
more, so could become stiffer.
Similarly the lower layers
would be compressed,
changing their stiffness.
Possible factors described in some detail,
though their actual effect on the results
obtained is not stated: A weak Excellence.
19
With my graph there is an
intercept at T = -0.2 s,
implying that the period is
negative, which cannot happen.
A possible reason for this is the
way I timed the pendulum. I
judged the end of the 10
oscillations by eye, but if I
anticipated the end point too
early, my times would be too
short, and the periods would be
shorter than they should be,
causing the negative intercept.
Attempts to give a reason for the negative
intercept. A weak Excellence at best. (It
is unlikely, where the time for ten swings
has been measured, that the period would
be out by 0.2 s.)
20
The formula would not apply
in real life as the suspensions
would be steel cables, not
cotton thread. Because the steel
cable has more mass, it would
have greater rotational inertia
about the axis. This would
make the bridge more reluctant
to move, making its period
longer.
Identifies an aspect of physics, that
heavier cables mean greater inertia, and
how this might affect the period:
Excellence.
21
The horizontal length of the
ruler varied when it sagged.
This sagging meant that the
mass was significantly closer
to the bench than if the ruler
remained horizontal. At larger
masses (greater sags), the
effective length would
therefore be smaller, so the
period would be smaller than
expected.
Explains why the applied mass will affect
the period differently from expectation:
Excellence.
22
The mass of the rod itself was
not taken into account. This
resulted in the intercept being
far from zero. When the square
root of the mass was found the
effect of the non-zero mass of
the rod would be more
significant for smaller masses.
Explains why the rod’s mass will affect
the gradient of the graph: Excellence.
23
According to the formula the
period for no mass should be
zero. If my line passed through
Uses physics theory to evaluate student’s
results, and account for differences
between actual and expected results:
that point (0, 0), the gradient
would be steeper, so the
stiffness factor would be lower
and closer to the theoretical
value.
Excellence.
24
For one of the masses (0.075
kg) the times were all the same
so there was no range of data
to estimate uncertainty from.
There must be some
uncertainty, given human
reaction time, so a nominal
uncertainty of 0.05 s was
assigned to it.
Evaluates and explains the validity of the
results: Excellence.
25
The range of masses used is
nowhere near the mass of the
object it is designed to model.
Even though my data fits the
graph well, I cannot be sure
that the trend would continue
like this for the much larger
real-life mass, so the
conclusion might not apply in
reality.
Evaluates and explains the validity of the
results: Excellence.
26
As the mass swung back and
forth it also spun. The spinning
caused the string to untwist,
increasing the length of L. The
increased length would cause
the time period to be greater,
increasing the value of the
intercept.
A factor identified, and its effect
described: Excellence.