(13%) Problem 5: A shop sign weighing msg hangs from one end of a uniform beam weighing mpg. A hinge attaches the other end of the beam to a wall. The beam has a length of l1. A cable is attached to the beam a distance l2 from the hinge to help support the beam. The cable makes an angle 0 with the beam as shown. Paul's Auto Repain I A 13% Part (a) On the following free body diagram, draw all of the forces acting on the beam, representing the forces as vectors. Use a coordinate syster with the x-axis on the horizontal (along the length of the beam) and the y-axis vertical (perpendicular to the beam). Use "wb" for the weight of the beam, "ws" for the weight of the sign, "FT" for the force of tension, and "H" for the force on the hinge. Finally, since we don't know the angle that the force on the hinge will act based on the diagram alone, let it be acting at an angle be denoted "o" from the positive y-axis. I A 13% Part (b) Using the free body diagram from part (a), write an equation for the sum of forces in the x direction, Fx - A 13% Part (c) Once again using the free body diagram from part (a), write an equation for the sum of forces in the y direction, Fy - A 13% Part (d) Once again using the free body diagram from part (a), write an equation for the net torque taking the hinge as the axis of rotation, 7í P A 13% Part (e) If the sign weighs 210 N, the beam weighs 160 N, the length of the beam is 1.70 m, the cable is attached 1.35 m from the hinge, the tension in the cable is 730.4 N, and the cable makes a 30° angle with the beam, solve for the horizontal force exerted by the hinge on the beam.
(13%) Problem 5: A shop sign weighing msg hangs from one end of a uniform beam weighing mpg. A hinge attaches the other end of the beam to a wall. The beam has a length of l1. A cable is attached to the beam a distance l2 from the hinge to help support the beam. The cable makes an angle 0 with the beam as shown. Paul's Auto Repain I A 13% Part (a) On the following free body diagram, draw all of the forces acting on the beam, representing the forces as vectors. Use a coordinate syster with the x-axis on the horizontal (along the length of the beam) and the y-axis vertical (perpendicular to the beam). Use "wb" for the weight of the beam, "ws" for the weight of the sign, "FT" for the force of tension, and "H" for the force on the hinge. Finally, since we don't know the angle that the force on the hinge will act based on the diagram alone, let it be acting at an angle be denoted "o" from the positive y-axis. I A 13% Part (b) Using the free body diagram from part (a), write an equation for the sum of forces in the x direction, Fx - A 13% Part (c) Once again using the free body diagram from part (a), write an equation for the sum of forces in the y direction, Fy - A 13% Part (d) Once again using the free body diagram from part (a), write an equation for the net torque taking the hinge as the axis of rotation, 7í P A 13% Part (e) If the sign weighs 210 N, the beam weighs 160 N, the length of the beam is 1.70 m, the cable is attached 1.35 m from the hinge, the tension in the cable is 730.4 N, and the cable makes a 30° angle with the beam, solve for the horizontal force exerted by the hinge on the beam.
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter1: Tension, Compression, And Shear
Section: Chapter Questions
Problem 1.9.9P: A lifeboat hangs from two ship's davits. as shown in the figure. A pin of diameter d = 0.80 in....
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Transcribed Image Text:(13%) Problem 5: A shop sign weighing m;g hangs from one end of a uniform beam weighing mpg. A hinge attaches the
other end of the beam to a wall. The beam has a length of l1. A cable is attached to the beam a distance l2 from the hinge to
help support the beam. The cable makes an angle 0 with the beam as shown.
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4
Paul's
o o.
Auto Repair
E A 13% Part (a) On the following free body diagram, draw all of the forces acting on the beam, representing the forces as vectors. Use a coordinate systen
with the x-axis on the horizontal (along the length of the beam) and the y-axis vertical (perpendicular to the beam). Use "wb" for the weight of the beam, "ws"
for the weight of the sign, "FT" for the force of tension, and "H" for the force on the hinge. Finally, since we don't know the angle that the force on the hinge
will act based on the diagram alone, let it be acting at an angle be denoted "o" from the positive y-axis.
I A 13% Part (b) Using the free body diagram from part (a), write an equation for the sum of forces in the x direction, Fx
I A 13% Part (c) Once again using the free body diagram from part (a), write an equation for the sum of forces in the y direction, Fy
- A 13% Part (d) Once again using the free body diagram from part (a), write an equation for the net torque taking the hinge as the axis of rotation, TH
P A 13% Part (e) If the sign weighs 210 N, the beam weighs 160 N, the length of the beam is 1.70 m, the cable is attached 1.35 m from the hinge, the
tension in the cable is 730.4 N, and the cable makes a 30° angle with the beam, solve for the horizontal force exerted by the hinge on the beam.
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