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
Forces on a Sailcart 30° F wind on cart F track on cart F total
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
Procedure Angle between fan and sail kept constant at 30° Varied angle between sail and track. Measured acceleration of cart. Compared to theoretical prediction.
track fan sailcart
The Sailcart Experiment 30° Angle between fan and sail held constant at 30
The Sailcart Experiment 30° = 90° 30° = -30° varied between -30 and 90
The Sailcart Experiment 30° F fan on cart 30° F fan on cart Force of fan on cart always points forward.
Acceleration is directly proportional to cos( ).
Acceleration of Cart vs. Angle of Sail Acceleration is directly proportional to cos ( ).
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° F fan on cart F track on cart F total
How do Sailboats Work? Vector Addition Brandon Hoffman General Physics Houghton College