The figure below shows a 25-foot sailboat. The mast is a uniform 123-kg pole tha

Question

The figure below shows a 25-foot sailboat. The mast is a uniform 123-kg pole that is supported on the deck and held fore and aft by wires as shown. The tension in the forestay (wire leading to the bow) is 830 N. Determine the tension in the backstay (wire leading aft) and the normal force that the deck exerts on the mast. (Assume that the frictional force the deck exerts on the mast to be negligible.) tension . N normal force . kN Draw an extended free-body diagram showing the forces acting on the mast. Because the mast is in equilibrium, you can apply the conditions for translational and rotational equilibrium to find the tension in the backstay and the normal force that the deck exerts on the mast

Explanation / Answer

E ngineering A pplication Figure 12-31 shows a 25-foot sailboat. The mast is a uniform 120-kg pole that issupported on the deck and held fore and aft by wires as shown. Thetension in the forestay (wire leading to the bow) is 1000N. Determine the tension in the backstay (wire leadingaft) and the normal force that the deck exerts on the mast. (Assumethat the frictional force the deck exerts on the mast to benegligible.)

1) First find (F) which is the angle of the forestay with the vertical.

(F) = tan-1 (2.74 /4.88) = 29.3degrees

2) Apply (torque) = 0

with pivot at bottom of the mast

2.74 * 100 * cos 29.3 = 4.88*T(backwire)*cos45T(backwire) = 692 N3)

Apply F = 0 to mast

F(D) = force exerted by the deck on the mast

F(Dy) = normal force = 692*cos45+1000*cos29.3 + 120g =2539 N

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