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... Resistance

R / kR = 5%

1.7

1.8

2.0

2.2

2.5

The data point's spelled out name.

The data point's variable symbol, a slash, and the data point's unit.

The data point's uncertainty. Be sure to include a note below the data table explaining why you gave it this uncertainty.

The data should be lined up.

STEP 2: Enter the data below...

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

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.

The average of the three trials becomes your data point.

STEP 2: There should be at least three trials for each data point.

The uncertainty in the average can be the range divided by 2.

FYI: IB moderators want a minimum of FIVE data points, which will produce a FUNCTIONAL RELATIONSHIP (like a line or a curve).

A sample experimentA 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.

"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.

FYI: The title should reflect a very focused line of research.

A sample experimentA 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 experimentA student is asked to "Investigate a physical property of a bouncing ball."

The effect of surface on rebound height of a ball.Method1 Set up the equipment as shown in the sketch.2 Release the ball in a straight 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 data has been gathered for 16 sheets of paper.

butc

her's

pap

er

A4 paper

rule

r

ball

floor

FYI: This will yield 9 data points, three trials each.

A sample experiment

Experimental Data and CalculationsSheets

n / no units

n = 0

Rebound Height

hi / cm

hi = 0.2 cm

Average Rebound Height

h / cm

h = 2.0 cm

0 5554.8 55.1 54.6

Trial 1 Trial 2 Trial 3

2 5253.4 52.5 49.6

4 4950.7 48.7 48.6

6 4849.0 47.1 48.5

8 4545.9 45.0 44.6

10 4139.5 41.4 42.4

12 3535.8 34.0 35.1

14 3331.1 33.5 33.0

16 2929.7 27.2 29.3

A sample experimentThe average rebound height h was calculated from each of the three trials. For the first row of data h was calculated like this:

FYI: The explanation accompanying the presentation of the data should justify all of the uncertainties.

h = h1 + h2 + h3

3= 54.8 + 55.1 + 54.6

3= 54.8

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 - 49.62

= 2

A sample experiment

FYI: The explanation accompanying the presentation of the data should justify all of the uncertainties.

Bounce Height

y = -1.6333x + 56.067

0

10

20

30

40

50

60

0 5 10 15 20

number of sheets

h /

cm

The graph shows the plot of average rebound height against the number of sheets of paper.

A sample experiment

FYI: Don't forget to find the uncertainty in the slope of your data:

The graph shows the minimum and maximum slopes.

y = -1.375x + 53

y = -1.875x + 57

0

10

20

30

40

50

60

0 5 10 15 20

m = mmax - mmin

2

m = -1.375 - -1.875

2

m = 0.25

m = -1.6 0.3

A sample experimentThe 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.ConclusionThe 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.EvaluationObserving 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 improvementsThe 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

y = -0.0373x2 - 1.0359x + 54.673

0

10

20

30

40

50

60

0 5 10 15 20

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.