how do sailboats work? vector addition brandon hoffman general physics houghton college
TRANSCRIPT
![Page 1: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/1.jpg)
How do Sailboats Work? Vector Addition
Brandon Hoffman
General Physics
Houghton College
![Page 2: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/2.jpg)
Outline
Background and Motivation
Theory
Experimental Procedure
Results
Conclusions
![Page 3: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/3.jpg)
Outline
Why Sailboats?
Vector Addition
Sailcart Experiment
![Page 4: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/4.jpg)
Outline
Why Sailboats?
Vector Addition
Sailcart Experiment
30°
AB
A + B
![Page 5: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/5.jpg)
Outline
Why Sailboats?
30°
AB
A + B
![Page 6: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/6.jpg)
Motivation
Practice using vectors as representations of forces.
Learn how vectors add together.
Improve trigonometry skills.
![Page 7: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/7.jpg)
Vector Addition Applications
www.mit.eduwww. free-online-private-ground-school.com
www. Astronomyforbeginners.com
www. img.sparknotes.com
![Page 8: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/8.jpg)
Theory
Ftotal = Ffan on cart + Ftrack on cart
= [(Ffan on cart + Ftrack on cart) cos()] i
+ [(Ffan on cart + Ftrack on cart)sin ()] j
= [(Ffan on cart + Ftrack on cart) cos()] i
= [(Ffan on cart) cos()] i
![Page 9: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/9.jpg)
Forces on a Sailcart
30°
Fwind on cart
Ftrack on cart
Ftotal
![Page 10: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/10.jpg)
Addition of Vectors
Fwind on cart Ftrack on cart
Ftotal
Ftotal = Fwind on cart + Ftrack on cart
= [Fwind on cart cos()] i
![Page 11: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/11.jpg)
Procedure
• Angle between fan and sail kept constant at 30°
• Varied angle between sail and track.
• Measured acceleration of cart.
• Compared to theoretical prediction.
![Page 12: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/12.jpg)
Apparatus
http://webapps.lsa.umich.edu
![Page 13: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/13.jpg)
Apparatus
![Page 14: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/14.jpg)
Apparatus
track
fan
sailcart
![Page 15: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/15.jpg)
The Sailcart Experiment
30°
Angle between fan and sail held constant at 30
![Page 16: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/16.jpg)
The Sailcart Experiment
30°
30°
30°30°
= 90°
30° = -30°
varied between -30 and 90
![Page 17: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/17.jpg)
The Sailcart Experiment
30°
30°
30°30° 30
°
Ffan on cartF fan on cart
F fan
on ca
rt
30°
Ffan on cart
F fan
on c
art
Ffan on cart
Force of fan on cart always points forward.
![Page 18: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/18.jpg)
Cart Mass (kg) Sail Angle (°) Cart Acceleration (cm/s2)
0.30 -30 34.6
0.30 0 40.0
0.30 30 34.6
0.30 60 20.0
0.30 75 10.4
0.30 90 0
0.60 -30 17.3
0.60 0 20.0
0.60 30 17.3
0.60 60 10.0
0.60 75 5.2
0.60 90 0
0.90 -30 11.5
0.90 0 13.3
0.90 30 11.5
0.90 60 6.7
0.90 75 3.5
0.90 90 0
Results
![Page 19: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/19.jpg)
Conclusion
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Cart Mass (kg) Sail Angle (°) Cart Acceleration (cm/s2)
0.30 -30 34.6
0.30 0 40.0
0.30 30 34.6
0.30 60 20.0
0.30 75 10.4
0.30 90 0
0.60 -30 17.3
0.60 0 20.0
0.60 30 17.3
0.60 60 10.0
0.60 75 5.2
0.60 90 0
0.90 -30 11.5
0.90 0 13.3
0.90 30 11.5
0.90 60 6.7
0.90 75 3.5
0.90 90 0
Results
![Page 21: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/21.jpg)
Results
0
5
10
15
20
25
30
35
40
-30 -10 10 30 50 70 90
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Results
Acceleration of Cart vs. Angle of Sail
0
5
10
15
20
25
30
35
40
-30 -10 10 30 50 70 90
![Page 23: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/23.jpg)
Acceleration of Cart vs. Angle of Sail
0
5
10
15
20
25
30
35
40
-30 -10 10 30 50 70 90
![Page 24: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/24.jpg)
Acceleration of Cart vs. Angle of Sail
0
5
10
15
20
25
30
35
40
-30 -10 10 30 50 70 90
Angle of Sail
Acc
eler
atio
n o
f C
art
![Page 25: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/25.jpg)
Acceleration of Cart vs. Angle of Sail
0
5
10
15
20
25
30
35
40
-30 -10 10 30 50 70 90
Angle of Sail (degrees)
Acc
eler
atio
n o
f C
art
(cm
/s2)
![Page 26: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/26.jpg)
0
5
10
15
20
25
30
35
40
-30 -10 10 30 50 70 90
Angle of Sail (degrees)
Acc
eler
atio
n o
f C
art
(cm
/s2)
Acceleration of Cart vs. Angle of Sail
Acceleration is directly proportional to cos().
![Page 27: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/27.jpg)
Acceleration of Cart vs. Angle of Sail
Acceleration is directly proportional to cos ().
0
5
10
15
20
25
30
35
40
0 0.2 0.4 0.6 0.8 1
Cosine of Angle of Sail
Acc
eler
atio
n o
f C
art
(cm
/s2)
![Page 28: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/28.jpg)
Conclusions
1. By adding the vectors representing the various forces together in head-to-tail fashion, we can calculate the total force on the sailcart. Because this force is proportional to the acceleration of the sailcart, the motion can be determined.
2. The acceleration of sailcart is directly proportional to the cosine of the angle between the sail and the direction of motion of the cart, assuming the angle between the fan and the sail is kept constant.
![Page 29: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/29.jpg)
Conclusions
1. Vector addition can be used to predict sailboat motion.
2. Acceleration of sailcart has cosine dependence.
30°
Ffan on cart
Ftrack on cart
Ftotal
Acceleration of Cart vs. Angle of Sail
0
5
10
15
20
25
30
35
40
0 0.2 0.4 0.6 0.8 1
Cosine of Angle of Sail
Acc
eler
atio
n o
f C
art
(cm
/s2)
![Page 30: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/30.jpg)
How do Sailboats Work? Vector Addition
Brandon Hoffman
General Physics
Houghton College
![Page 31: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/31.jpg)
Outline
Why Sailboats?
30°
AB
A + B
![Page 32: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/32.jpg)
Everybody Loves Sailing
![Page 33: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/33.jpg)
Vector Addition Applications
www.mit.eduwww. free-online-private-ground-school.com
www. Astronomyforbeginners.com
www. img.sparknotes.com
![Page 34: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/34.jpg)
Forces on a Sailcart
30°
Fwind on cart
Ftrack on cart
Ftotal
![Page 35: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/35.jpg)
Addition of Vectors
Fwind on cart Ftrack on cart
Ftotal
Ftotal = Fwind on cart + Ftrack on cart
= [Fwind on cart cos()] i
![Page 36: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/36.jpg)
Apparatus
sailcart
track
fan
![Page 37: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/37.jpg)
The Sailcart Experiment
30°
![Page 38: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/38.jpg)
The Sailcart Experiment
30°
30°
30°30°
= 90°
30° = -30°
![Page 39: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/39.jpg)
The Sailcart Experiment
30°
30°
30°30° 30
°
Ffan on cartF fan on cart
F fan
on ca
rt
30°
Ffan on cart
F fan
on c
art
Ffan on cart
Force of fan on cart always points forward.
![Page 40: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/40.jpg)
Acceleration of Cart vs. Angle of Sail
Acceleration is directly proportional to cos ().
0
5
10
15
20
25
30
35
40
0 0.2 0.4 0.6 0.8 1
Cosine of Angle of Sail
Acc
eler
atio
n o
f C
art
(cm
/s2)
![Page 41: How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College](https://reader035.vdocuments.mx/reader035/viewer/2022062511/551c4d3f5503469d6a8b4a32/html5/thumbnails/41.jpg)
Conclusions
1. Vector addition can be used to predict sailboat motion.
2. Acceleration of sailcart has cosine dependence.
30°
Ffan on cart
Ftrack on cart
Ftotal
Acceleration of Cart vs. Angle of Sail
0
5
10
15
20
25
30
35
40
0 0.2 0.4 0.6 0.8 1
Cosine of Angle of Sail
Acc
eler
atio
n o
f C
art
(cm
/s2)