Displaying data and calculations
How many trials
have been
performed?
Were there
enough to
satisfy the IB
Internal
Assessment
criteria?
FYI: IB wants a minimum of FIVE
data points, which will produce a
FUNCTIONAL RELATIONSHIP
(like a line or a curve).
Displaying data and calculations
STEP 1: The heading of each data and
calculation column should contain...
The data point's spelled out name.
The data point's variable symbol, a
Resistance
R / k
R =  5%
slash, and the data point's unit.
1.7
The data point's uncertainty.
1.8
Be
sure to include a note below the
data table explaining why you gave
it this uncertainty.
STEP 2:
Enter the data below...
2.0
2.2
2.5
The data should be lined up.
The data should have the
correct number of significant
figures. Be sure to include
a note justifying the number
of significant figures.
FYI: IB wants a minimum of FIVE
data points, which will produce a
FUNCTIONAL RELATIONSHIP
(like a line or a curve).
Gathering data
FYI: IB moderators want a minimum of FIVE data points, which will
produce a FUNCTIONAL RELATIONSHIP (like a line or a curve).
STEP 1: Gather at least 5 data points...
Your data should produce a function or relationship
that can be revealed through graphing.
Design your experiment so that this can happen.
STEP 2: There should be at least three trials for
each data point.
The average of the three trials becomes your data
point.
The uncertainty in the average can be the range
divided by 2.
A sample experiment
A student is asked to "Investigate a physical
property of a bouncing ball."
She decides on the following design:
The effect of surface on rebound height of a ball.
FYI: The title should reflect a very focused line of research.
"The aim of this investigation is to determine the
effect of changing the surface on to which a ball is
dropped on the rebound height of the ball. The
experiment is limited to increasing the number of
sheets of paper on to which the ball is dropped.
The ball is always dropped from the same height and
the number of sheets of paper is increased from 0 to
16 in steps of 2. The sheets are attached to the
hard floor surface."
FYI: The aim is a clear statement of the experiment so that the reader
has a good idea of what to expect upon further reading.
A sample experiment
A student is asked to "Investigate a physical
property of a bouncing ball."
The effect of surface on rebound height of a ball.
The apparatus for this investigation is
 electronic balance
 rubber ball
 a meter stick
 sticky tape
 A4-size paper
 butcher's paper
 marking pen
A sample experiment
A student is asked to "Investigate a physical
property of a bouncing ball."
ruler
butcher's paper
The effect of surface on rebound height of a ball.
Method
1 Set up the equipment as shown in
the sketch.
2 Release the ball in a straight
ball
line from a height of 70.0 cm.
3 Mark the highest point of the top
of the ball of the first bounce on
the butcher's paper.
4 Repeat this three times, numbering
the lines on the butcher's paper.
5 Place 2 sheets of A4 paper on the
floor where the ball will bounce.
6 Repeat steps 2 through 5 until
A4 paper
data has been gathered for 16
sheets of paper.
floor
FYI: This will yield 9 data points, three trials each.
A sample experiment
Experimental Data and Calculations
Sheets
n / no units
n = 0
Rebound Height
hi / cm
hi = 0.2 cm
Average Rebound
Height
h / cm
h = 2.0 cm
Trial 1
Trial 2
Trial 3
0
54.8
55.1
54.6
55
2
53.4
52.5
49.6
52
4
50.7
48.7
48.6
49
6
49.0
47.1
48.5
48
8
45.9
45.0
44.6
45
10
39.5
41.4
42.4
41
12
35.8
34.0
35.1
35
14
31.1
33.5
33.0
33
16
29.7
27.2
29.3
29
FYI: The explanation accompanying the presentation of the data
should justify all of the uncertainties.
A sample experiment
The average rebound height h was calculated from
each of the three trials. For the first row of data
h was calculated like this:
h1 + h2 + h3
h =
= 54.8 + 55.1 + 54.6 = 54.8
3
3
I have rejected and not recorded some measurements
because the ball did not bounce along the vertical.
When this happened I just repeated the drop. When
the ball moves off at a noticeable angle some of the
kinetic energy of the rebound is consumed in the
horizontal component of motion, detracting from the
rebound height.
Counting the sheets of paper has no uncertainty.
The rebound height is measured on the fly. I
estimate the uncertainty to be about 0.2 cm.
The uncertainty in the height was taken to be half
the largest range in the trial data, corresponding
to the row for 2 sheets of paper:
53.4 - 49.6 = 2
2
FYI: The explanation accompanying the presentation of the data
should justify all of the uncertainties.
A sample experiment
The graph shows the plot of average rebound height
against the number of sheets of paper.
Bounce Height
60
50
h / cm
40
30
y = -1.6333x + 56.067
20
10
0
0
5
10
number of sheets
15
20
FYI: Don't forget to find the uncertainty in the slope of your data:
A sample experiment
The graph shows the minimum and maximum slopes.
60
50
40
y = -1.375x + 53
30
m =
m =
20
mmax - mmin
2
-1.375
y = -1.875x + 57
2
-1.875
m = 0.25
10
m = -1.6 0.3
0
0
5
10
15
20
A sample experiment
The slope of the graph is -1.6 0.3 cm sheet-1 which
translates to "the ball loses 1.6 cm of rebound
height for each sheet of paper added.
Conclusion
The best line fit barely fits within the error bars
- perhaps because the rebound height was so
difficult to gauge. Perhaps data for 6 sheets and 8
sheets should have been retaken. These data points
are just on the extremes of the error bars. I think
we may conclude that for every sheet of paper added,
the ball will lose 1.6 cm of rebound.
Evaluation
Observing that the trend line only just fits within
the error bars we might ask if our data really is a
linear fit. The three main problems with the lab
were
•accurately recording the rebound height
•ensuring that the ball falls and rebounds
vertically
•ensuring successive sheets of paper do not trap
air
A sample experiment
Suggested improvements
The first two points can be addressed by taking many
more trials for each number of sheets of paper, or
by recording each drop with a video camera.
The third point can be addressed by ironing the
paper stack before each drop.
A sample experiment
60
50
40
30
y = -0.0373x 2 - 1.0359x + 54.673
FYI: If you use Excel or some other graphing software,
don't forget that you can experiment with fits. For
example, an x2 fit actually looks better than a linear one.
The student still made perfect marks on her lab.
20
10
0
0
5
10
15
20