How Does Sir Lost-a-Lot's Quest Impact the Forces on the Drawbridge?

[eightbrown8]

Sir Lost-a-Lot dons his armor and sets out from the castle on his trusty steed in his quest to improve communication between damsels and dragons. Unfortunately his squire lowered the draw bridge too far and finally stopped it 20.0° below the horizontal. Lost-a-Lot and his horse stop when their combined center of mass is 1.00 m from the end of the bridge. The uniform bridge is 10.00 m long and has a mass of 1800 kg. The lift cable is attached to the bridge 5.00 m from the hinge at the castle end, and to a point on the castle wall 12.0 m above the bridge. Lost-a-Lot's mass combined with his armor and steed is 950 kg.

(a) Determine the tension in the cable.
kN

(b) Determine the horizontal force component acting on the bridge at the hinge.
magnitude
kN
direction
to the left
to the right


(c) Determine the vertical force component acting on the bridge at the hinge.
magnitude
kN
direction
downwards
upwards

 

[Astronuc]

This is a statics problem so that the sum of the forces in horizontal (x) and vertical (y) directions are zero. Furthermore, the net moment of the bridge is zero.

The center of mass (weight) of the knight and horse act downward at 9 m from the pivot. The mass of the bridge acts downard at it center of mass, midway along the bridge. The rope/cable acts at some angle with respect to horizontal and that angle must be determined. The cable is attached at the midpoint of the bridge. Unfortunately the triangle formed by bridge, wall and cable is not a right triangle, but rather the largest angle is 110°.

Please make an effort at solving the problem and show the work.