Sir Lost-a-Lot dons his armor and sets out from the castle on his trusty steed (

Question

Sir Lost-a-Lot dons his armor and sets out from the castle on his trusty steed (see figure below). Usually, the drawbridge is lowed to a horizontal position so that the end of the bridge rests on the stone ledge. Unfortunately Lost-a-Lot's squire didn't lower the drawbridge far enough and stopped it at ? = 20.0? above the horizontal. The knight and his horse stop when their combined center of mass is d = 1.00 m from the end of the bridge. The uniform bridge is ? = 6.50 m long and has a mass of 1 700 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 h = 12.0 m above the bridge. Lost-a-Lot's mass combined with his armor and steed is 1 050 kg.

(a) Determine the tension in the cable.


(b) Determine the horizontal force component acting on the bridge at the hinge.

(c) Determine the vertical force component acting on the bridge at the hinge.
magnitude

magnitude N direction ---Select--- to the left? to the right? Sir Lost-a-Lot dons his armor and sets out from the castle on his trusty steed (see figure below). Usually, the drawbridge is lowed to a horizontal position so that the end of the bridge rests on the stone ledge. Unfortunately Lost-a-Lot's squire didn't lower the drawbridge far enough and stopped it at ? = 20.0½ above the horizontal. The knight and his horse stop when their combined center of mass is d = 1.00 m from the end of the bridge. The uniform bridge is ? = 6.50 m long and has a mass of 1 700 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 h = 12.0 m above the bridge. Lost-a-Lot's mass combined with his armor and steed is 1 050 kg. (a) Determine the tension in the cable. (b) Determine the horizontal force component acting on the bridge at the hinge. magnitude N direction (c) Determine the vertical force component acting on the bridge at the hinge. magnitude magnitude N direction

Explanation / Answer

Let T = tension in the lift cable(s)

If we assume the wall is vertical and draw a horizontal line from the cable-to-bridge connection point to the wall, we can determine the angle ? of the cable with the horizontal.

tan? = (12 - 5sin20) / 5cos20
? = 65.46

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