My boat is tethered to a rope that can withstand a maximum of 8000 pounds of tension. The wind will exert, at maximum, 3000 pounds of force on the boat. How do I calculate the tension on the rope based on the angles that the rope is at? does it make a difference if the boat remains stationary while the wind blows, or if the wind causes it to move a bit? Thanks for the help (:
Ty = Tsin(theta)
Tx = Tcos(theta)
T = m*a ?
I also found this equation: F = (mv^2) / r for tension caused by a moving object, I'm not sure if that applies though....
The wind only acts in the x-direction, and in the y-direction the force from the water will balance any other y-forces out.
The Attempt at a Solution
It seems to me like the tension on the rope will be 3000lbf no matter what the angle. The angle would change the amount of force exerted in either direction, x or y, but the NET force would remain the same. HOWEVER, http://www.engineeringtoolbox.com/rope-angle-tension-increase-d_1507.html describes an increase in tension as the angle increases, with the least tension being when the side of the boat and the rope are perpendicular. If this is true, what causes this? why? what equations give the numbers of tension increase they've described? Thanks! (: