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How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College.

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Presentation on theme: "How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College."— Presentation transcript:

1 How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College

2 Outline  Background and Motivation  Theory  Experimental Procedure  Results  Conclusions

3 Outline  Why Sailboats?  Vector Addition  Sailcart Experiment

4 Outline  Why Sailboats?  Vector Addition  Sailcart Experiment  30° A B A + B

5 Outline  Why Sailboats?   30° A B A + B

6 Motivation  Practice using vectors as representations of forces.  Learn how vectors add together.  Improve trigonometry skills.

7 Vector Addition Applications www. free-online-private-ground-school.com www. Astronomyforbeginners.com www. img.sparknotes.com

8 Theory F total = F fan on cart + F track on cart = [(F fan on cart + F track on cart ) cos(  )] i + [(F fan on cart + F track on cart )sin (  )] j = [(F fan on cart + F track on cart ) cos(  )] i = [(F fan on cart ) cos(  )] i

9 Forces on a Sailcart  30° F wind on cart F track on cart F total

10 Addition of Vectors F wind on cart F track on cart F total  F total = F wind on cart + F track on cart = [F wind on cart cos(  )] i

11 Procedure Angle between fan and sail kept constant at 30° Varied angle between sail and track. Measured acceleration of cart. Compared to theoretical prediction.

12 Apparatus

13 Apparatus

14 track fan sailcart

15 The Sailcart Experiment  30° Angle between fan and sail held constant at 30 

16 The Sailcart Experiment 30°  = 90° 30°  = -30°  varied between -30  and 90 

17 The Sailcart Experiment 30° F fan on cart 30° F fan on cart Force of fan on cart always points forward.

18 Cart Mass (kg)Sail Angle (°)Cart Acceleration (cm/s 2 ) Results

19 Conclusion

20 Cart Mass (kg)Sail Angle (°)Cart Acceleration (cm/s 2 ) Results

21

22

23 Acceleration of Cart vs. Angle of Sail

24

25

26 Acceleration is directly proportional to cos(  ).

27 Acceleration of Cart vs. Angle of Sail Acceleration is directly proportional to cos (  ).

28 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.

29 Conclusions 1.Vector addition can be used to predict sailboat motion. 2.Acceleration of sailcart has cosine dependence.  30° F fan on cart F track on cart F total

30 How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College

31 Outline  Why Sailboats?   30° A B A + B

32 Everybody Loves Sailing

33 Vector Addition Applications www. free-online-private-ground-school.com www. Astronomyforbeginners.com www. img.sparknotes.com

34 Forces on a Sailcart  30° F wind on cart F track on cart F total

35 Addition of Vectors F wind on cart F track on cart F total  F total = F wind on cart + F track on cart = [F wind on cart cos(  )] i

36 Apparatus sailcart track fan

37 The Sailcart Experiment  30°

38 The Sailcart Experiment 30°  = 90° 30°  = -30°

39 The Sailcart Experiment 30° F fan on cart 30° F fan on cart Force of fan on cart always points forward.

40 Acceleration of Cart vs. Angle of Sail Acceleration is directly proportional to cos (  ).

41 Conclusions 1.Vector addition can be used to predict sailboat motion. 2.Acceleration of sailcart has cosine dependence.  30° F fan on cart F track on cart F total


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