Sir Lost-a-Lot dons his armor and sets out from the castle on his trusty steed (
ID: 2261651 • Letter: S
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
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 degree 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 = 8.50 m long and has a mass of 1 900 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 900 kg Determine the tension in the cable. Determine the horizontal force component acting on the bridge at the hinge. Determine the vertical force component acting on the bridge at the hinge. magnitudeExplanation / Answer
This is a torque problem. The pivot point is at hinge.
Torque = Force * Perpendicular distance from the pivot point.
The weight of the bridge and the weight of the man and horse will produce clockwise torque. The vertical component of the tension will produce counter clockwise torque.
Weight of bridge = 1900 * 9.8 = 18620 N, Weight of man and horse = 900 * 9.8 = 8820 N
The weight vector for the bridge is located at the center of the bridge. This point is 3 meters from the hinge. The weight vector for the man and horse is located at the 1 meter from the end of the bridge.
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