How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College
How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College.
Apr 02, 2015
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How do Sailboats Work? Vector Addition
Brandon Hoffman
General Physics
Houghton College
Outline
Background and Motivation
Theory
Experimental Procedure
Results
Conclusions
Outline
Why Sailboats?
Vector Addition
Sailcart Experiment
Outline
Why Sailboats?
Vector Addition
Sailcart Experiment
30°
AB
A + B
Outline
Why Sailboats?
30°
AB
A + B
Motivation
Practice using vectors as representations of forces.
Learn how vectors add together.
Improve trigonometry skills.
Vector Addition Applications
www.mit.eduwww. free-online-private-ground-school.com
www. Astronomyforbeginners.com
www. img.sparknotes.com
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
Forces on a Sailcart
30°
Fwind on cart
Ftrack on cart
Ftotal
Addition of Vectors
Fwind on cart Ftrack on cart
Ftotal
Ftotal = Fwind on cart + Ftrack on cart
= [Fwind on cart cos()] i
Procedure
• Angle between fan and sail kept constant at 30°
• Varied angle between sail and track.
• Measured acceleration of cart.
• Compared to theoretical prediction.
Apparatus
http://webapps.lsa.umich.edu
Apparatus
Apparatus
track
fan
sailcart
The Sailcart Experiment
30°
Angle between fan and sail held constant at 30
The Sailcart Experiment
30°
30°
30°30°
= 90°
30° = -30°
varied between -30 and 90
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.
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
Conclusion
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
Results
0
5
10
15
20
25
30
35
40
-30 -10 10 30 50 70 90
Results
Acceleration of Cart vs. Angle of Sail
0
5
10
15
20
25
30
35
40
-30 -10 10 30 50 70 90
Acceleration of Cart vs. Angle of Sail
0
5
10
15
20
25
30
35
40
-30 -10 10 30 50 70 90
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
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)
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().
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)
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.
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)
How do Sailboats Work? Vector Addition
Brandon Hoffman
General Physics
Houghton College
Outline
Why Sailboats?
30°
AB
A + B
Everybody Loves Sailing
Vector Addition Applications
www.mit.eduwww. free-online-private-ground-school.com
www. Astronomyforbeginners.com
www. img.sparknotes.com
Forces on a Sailcart
30°
Fwind on cart
Ftrack on cart
Ftotal
Addition of Vectors
Fwind on cart Ftrack on cart
Ftotal
Ftotal = Fwind on cart + Ftrack on cart
= [Fwind on cart cos()] i
Apparatus
sailcart
track
fan
The Sailcart Experiment
30°
The Sailcart Experiment
30°
30°
30°30°
= 90°
30° = -30°
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.
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)
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)
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