Sir Lost-a-Lot dons his armor and sets out from the castle on his trusty steed (
ID: 1491639 • 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° 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 = 6.00 m long and has a mass of 1 800 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 850 kg. (a) Determine the tension in the cable. (b) Determine the horizontal force component acting on the bridge at the hinge. magnitude (c) Determine the vertical force component acting on the bridge at the hinge. magnitude
Explanation / Answer
here
the angle between the bridge and the wall is ( 90 - 20 ) = 70deg
by using the law of cosines
c^2 = 5^2 + 12^2 - 2 * 5 * 12 * cos(70deg)
c = 11.3 m
the length of cable is 11.3 m
the angle between the bridge and cable is
sin(theta) / 12 = sin(70deg) / 11.3
theta = 85.46 deg
then sum all moments about the hinge point to zero
(9.8 * (1800 * (6 * cos20/2) + 850 * (5 * cos20)) - T * sin85.46 * 5 = 0
solve for T
T = 17829.3 N
b)
angle between cable and wall
theta = 180 - 70 - 85.46 = 24.54 deg
horizontal force is
Fx = T* sin(24.54deg)
Fx = 17829.3 * sin(24.54deg)
Fx = 7405 N
c)
Fy = 9.8 * ( 1800 + 850) - 17829.3 * cos(24.54deg) = 9751 N