What’s In The Bag Adapted from Dr. Margaret Niess.

What’s In The Bag

Adapted from Dr. Margaret Niess

The Basic Idea

Add a certain volume of water to a container measure how much the height increases.

Task 1

Get data to graph Total Volume vs. Height for a bottle with a constant circumference

Get data to graph Total Volume vs. Height for a bottle with a changing circumference

Figure out what the slope of a Total Volume vs. Height graph means

What would be the graph for a beaker?

Total Volume vs Height of Fluid

0.00

5.00

10.00

15.00

20.00

25.00

0 100 200 300 400

Total Volume (mL)

He

igh

t o

f F

luid

(c

m)

What would be the graph for a flask?

Total Volume vs Height of Fluid

0.00

5.00

10.00

15.00

20.00

25.00

0 100 200 300 400

Total Volume (mL)

He

igh

t o

f F

luid

(c

m)

What Does The Slope Mean

The slope is the reciprocal of the area of the bottle

AV

hSlope

x

ySlope

1

And now for something completely different

See if you can estimate the shape of the bottle

Here’s the data collected from the bottle

mL of H2O Added Total Volume Height of Water Column (cm)

0 0 0.00

30 30 0.40

30 60 0.85

30 90 1.35

30 120 1.95

30 150 2.68

30 180 3.55

30 210 4.80

30 240 7.80

30 270 8.984981645

30 300 9.91538457

30 330 10.65970691

30 360 11.47846148

30 390 12.44608053

10 400 15

10 410 16

10 420 17

5 425 19

5 430 21

Task 2: See if you can eyeball the shape of the bottle

Total Volume vs Height of Fluid

0.00

5.00

10.00

15.00

20.00

25.00

0 100 200 300 400 500

Total Volume (mL)

He

igh

t o

f F

luid

(c

m)

Task 3: Graph the bottle

Given the data and the formula for area come up with a way to calculate the radius for each data point.

See if any unit conversions are needed

Come up with a graph of the Bottle’s Radius vs. Height

Given To Us

Some Collected Data We can assume that the bottle has a

circular circumference. Areacircle = r2

Volume = Areacircle *height

The DatamL of H2O Added Total Volume Height of Water Column (cm)

0 0 0.00

30 30 0.40

30 60 0.85

30 90 1.35

30 120 1.95

30 150 2.68

30 180 3.55

30 210 4.80

30 240 7.80

30 270 8.984981645

30 300 9.91538457

30 330 10.65970691

30 360 11.47846148

30 390 12.44608053

10 400 15

10 410 16

10 420 17

5 425 19

5 430 21

height

radiusarea

Volume

Here’s What I Did

h

Vr

h

Vr

hrV

AhV

2

2

Which volume to use?

Volume Added Total Added

Which height to use?

Volume Added Total Added

Which height to use?

Volume Added Total Added

Just how do you get h?

height fluid previous -height fluidcurrent height

height

Check unit conversions

11

1

1 3

cmmL

cmmLcm

Here’s What I Did

Height difference was calculated by subtracting the current liquid height from the previous one.

Height Difference (cm) Width of Glass

4.887264093

0.4 4.887264093

0.45 4.607756776

0.5 4.371301895

0.6 3.990434422

0.73 3.617715189

0.87 3.313875414

1.25 2.764654066

3 1.784576526

1.184981645 2.839487699

0.930402925 3.204499955

0.74432234 3.582739866

0.818754574 3.41600843

0.967619042 3.142270731

2.553919474 1.116687298

1 1.784576526

1 1.784576526

2 0.892288263

2 0.892288263

Here’s What I Did

mL of H2O Added Total VolumeHeight of Water

Column (cm)Height Difference

(cm) Width of Bottle

0 0 0.00 4.887264093

30 30 0.40 0.4 4.887264093

30 60 0.85 0.45 4.607756776

30 90 1.35 0.5 4.371301895

30 120 1.95 0.6 3.990434422

30 150 2.68 0.73 3.617715189

30 180 3.55 0.87 3.313875414

30 210 4.80 1.25 2.764654066

30 240 7.80 3 1.784576526

30 270 8.984981645 1.184981645 2.839487699

30 300 9.91538457 0.930402925 3.204499955

30 330 10.65970691 0.74432234 3.582739866

30 360 11.47846148 0.818754574 3.41600843

30 390 12.44608053 0.967619042 3.142270731

10 400 15 2.553919474 1.116687298

10 410 16 1 1.784576526

10 420 17 1 1.784576526

5 425 19 2 0.892288263

5 430 21 2 0.892288263

Height vs Width

0

1

2

3

4

5

6

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 22.00

Height of Fluid (cm)

Ra

diu

s o

f B

ott

le (

cm)

Height vs Width

0

1

2

3

4

5

6

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 22.00

Height of Fluid (cm)

Ra

diu

s o

f B

ott

le (

cm)