Chapter 7, Problem 52PCE

Predict/Calculate Beating to Windward A sailboat can be propelled into the wind by a maneuver called beating to windward. Beating requires the sailboat to travel in a zigzag pattern at an angle to the wind that is greater than the no-go zone, which is shaded red in Figure 7-23. When a sailboat is just outside the no-go zone (boats B in the figure) the wind exerts a force $\stackrel{\to }{F}$ on the sail that has a component in the direction of motion $\stackrel{\to }{v}$ Similar comments apply to boats C. The work done by the wind on the sail is W = Fdcosθ, and because v = d/t, the propulsion power P = W/t delivered to the sailboat is Fucasθ, where θ is the angle between the sail face and the direction of motion. (a) Assuming that F and u have the same magnitudes for each sailboat, will the propulsion power delivered to sailboats B be greater than, less than, or the same as the propulsion power delivered to sailboats C? Explain (b) If

F = 870 N

and

v = 11 m/s,

what propulsion power is delivered to sailboats B, for which

θ = 79°

? (c) What propulsion power is delivered to sailboats C for which

θ = 56°

?