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