A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of
ID: 2297082 • Letter: A
Question
A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mb = 6.2 kg and the sign has a mass of ms = 17.5 kg. The length of the beam is L = 2.59 m. The sign is attached at the very end of the beam, but the horizontal wire holding up the beam is attached 2/3 of the way to the end of the beam. The angle the wire makes with the beam is ? = 34.7 A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mb = 6.2 kg and the sign has a mass of ms = 17.5 kg. The length of the beam is L = 2.59 m. The sign is attached at the very end of the beam, but the horizontal wire holding up the beam is attached 2/3 of the way to the end of the beam. The angle the wire makes with the beam is ? = 34.7Explanation / Answer
1) along vertical
T*sin34.7 + Fy = (ms + mb)*g
T*cos34.7 + Fx = 0
along horizontal
T*cos34.7 = -Fx
net torque = 0
T*sin34.7* (2/3)*L = ms*g*L + mb*g*(L/2)
T*sin34.7*(2/3) = (17.5*9.8) + (6.2*9.8*0.5)
T = 531.936 N
2) Fx = -T*cos34.7 = -437.328 N
Fy = ?70.56 N
F = sqrt(Fx^2 +Fy^2) = 442.984 N
3) T*sin34.7* (2/3)*L = ms*g*L + mb*g*(L/2)
876*sin34.7*(2/3) = (ms*9.8) + (6.2*9.8*0.5)
ms = 30.824 kg
keeping the wire attached at the same location on the beam, make the wire perpendicular to the beam