(Figure 1) A boat owner pulls her boat into the dock shown, where there are six

Question

(Figure 1) A boat owner pulls her boat into the dock shown, where there are six capstans to which to tie the boat. She has three ropes. She can tie the boat from the boat's center (A) to any of the capstans (B through G) along the dotted arrows shown.
Suppose the owner has tied three ropes: one rope runs to A from B, another to A from D, and a final rope from A to F. The ropes are tied such that F(ab)=F(ad)

(Figure 1) http://session.masteringphysics.com/problemAsset/1010936/27/MFS_1l_7_a.jpg



What is the magnitude of the force provided by the third rope, in terms of theta?

A. F(ab)cos(theta)

B. 2F(ab)cos(theta)

C. 2F(ab)sin(theta)

D. F(ab)sin(theta)

Explanation / Answer

Take component of Fab , Fad in horizontal and vertical directin . vertical coponent s will get cancelled since they are of equal magnitude so Fab*cos(theta)+Fad*cos(theta) = Faf Faf = 2Fab*cos(theta) ANS : B

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