A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of
ID: 1785929 • Letter: A
Question
A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mb = 6.7 kg and the sign has a mass of ms = 17.5 kg. The length of the beam is L = 2.86 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 = 34.9°.
1)
What is the tension in the wire?
N
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Saturday, October 21 at 3:37 PM
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2)
What is the net force the hinge exerts on the beam?
N
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3)
The maximum tension the wire can have without breaking is T = 818 N.
What is the maximum mass sign that can be hung from the beam?
kg
Explanation / Answer
mb = 6.7kg
ms = 17,5 kg
net torque about hinge is equal to zero
ms*g*L*costheta + mb*g*L/2*costheta - T*(2/3)*L*sintheta = 0
ms*g*costheta + mb*g*1/2*costheta - T*(2/3)*sintheta = 0
(17.5*9.8*cos34.9)+(6.7*9.8*1/2*cos34.9) - (T*2/3*sin34.9) = 0
T = 439.35 N
b)
T + Fx = 0
Fx = -T
Fy - (mb+ms)*g = 0
Fy = (mb+ms)*g = (6.7+17.5)9.8= 237.16N
F = sqrt(Fx^2+Fy^2)= squt((435.35)^2+ (237.16)^2) = 495.75 N
C) (ms*9.8*cos34.9)+(6.7*9.8*1/2*cos34.9) - (818*2/3*sin34.9) = 0
ms = 35.5 kg