A sign hangs from a wall, as shown. The upper left corner is supported by a pin joint, firmly attached to the wall. The upper right corner is supported by a rope. The rope is at a 30° angle from the horizontal. The pin joint is at the same height as the point where the sign attaches to the rope. The sign has a mass of 20kg. It is 2m long and the center-of- mass is 1m from the wall. a) Consider torques about the pin joint. Draw the line-of-action and lever-arm for both the tension force and the weight force. 1m c) What is the tension in the rope? mg b) What is the magnitude of the torque produced by the weight force about the pin joint? d) What are the reaction (support) forces at the pin joint? Write your answer as a vector. Y₁ -X 30° 2m
A sign hangs from a wall, as shown. The upper left corner is supported by a pin joint, firmly attached to the wall. The upper right corner is supported by a rope. The rope is at a 30° angle from the horizontal. The pin joint is at the same height as the point where the sign attaches to the rope. The sign has a mass of 20kg. It is 2m long and the center-of- mass is 1m from the wall. a) Consider torques about the pin joint. Draw the line-of-action and lever-arm for both the tension force and the weight force. 1m c) What is the tension in the rope? mg b) What is the magnitude of the torque produced by the weight force about the pin joint? d) What are the reaction (support) forces at the pin joint? Write your answer as a vector. Y₁ -X 30° 2m
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Question
done a,b,c just need help with (D)
all work has been provided below
Transcribed Image Text:Mass of the sign, -20 kg
Length of sign, L-2m
Angle, 8-10
Find:
(a) Draw the line of action and lever arm for both the tension force and the weight force
(b) The magnitude of the torque produces by the weight force about the pin joint
(c) The tension in the rope
(a)
leverarm
of
a
1m
Tu-W:
73
Line of t
Ange
20x9.81x1
2
T
Tens 10
1™
-98.1 Na
(b)
The torque produced by the weight about the pin joint,
Trin 30
Line of action
of taon
A sign hangs from a wall, as shown. The upper left corner is
supported by a pin joint, firmly attached to the wall. The
upper right corner is supported by a rope. The rope is at a
30° angle from the horizontal. The pin joint is at the same
height as the point where the sign attaches to the rope.
The sign has a mass of 20kg. It is 2m long and the center-of-
mass is 1m from the wall.
a) Consider torques about the pin joint.
Draw the line-of-action and lever-arm for both the
tension force and the weight force.
c)
y
What is the tension in the rope?
1m
b) What is the magnitude of the torque produced by the weight force about the pin joint?
Img
d) What are the reaction (support) forces at the pin joint? Write your answer as a vector.
-X
30°
www.****
2m
Transcribed Image Text:(c)
The torque about hinge point is zero,
T₁-T₁=0
98.1-Tsin 30° (L)-T cos 30° (0)=0
98.1-7 sin 30°(2) = 0
T=98.1 N
(b) The magnitude of the torque produced by the weight force about the pin joint is 98.1 Nm.
(c) The tension in the rope is 98.1 N.
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