How Is the Vertical Force Calculated at the Hinge in a Beam and Sign System?

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In summary: To get the most accurate answer, forget the results for earlier parts of the problem. Using those introduces rounding errors.Take moments about the point of attachment of the wire.
  • #1
Anonymous123451234
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A shop sign weighing 215 N hangs from the end of a uniform 155-N beam.

Tension in supporting wire= 642 N
Horizontal force exerted by the hinge= 526N


Find the vertical force exerted by the hinge on the beam at the wall

upload_2017-11-13_22-1-52.png


Fy= Fhy + Ft * sin() - mg - Mg =0

My attempt:
Fhy= -(Ft *sin() - mg - Mg)
=-(642*sin(35) - 155 - 215)
= 1.76 N

My answer is incorrect, but I don't know what I'm doing wrong.
 

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  • #2
Anonymous123451234 said:
A shop sign weighing 215 N hangs from the end of a uniform 155-N beam.

Tension in supporting wire= 642 N
Horizontal force exerted by the hinge= 526N


Find the vertical force exerted by the hinge on the beam at the wall

View attachment 215006


Fy= Fhy + Ft * sin() - mg - Mg =0

My attempt:
Fhy= -(Ft *sin() - mg - Mg)
=-(642*sin(35) - 155 - 215)
= 1.7 N

My answer is incorrect, but I don't know what I'm doing wrong.
How did you get that tension? I get rather less.
 
  • #3
haruspex said:
How did you get that tension? I get rather less.
I used the formula Ft= (mg length/2 + Mglength) / (length*sin(35))
 
  • #4
Anonymous123451234 said:
I used the formula Ft= (mg length/2 + Mglength) / (length*sin(35))
The cable is not attached to the end of the rod.
 
  • #5
haruspex said:
The cable is not attached to the end of the rod.

It doesn't matter where on the rod it's attached to in this scenario. It goofed me up at first because I thought it did matter when it actually did not. This is the correct tension.
 
  • #6
Anonymous123451234 said:
It doesn't matter where on the rod it's attached to in this scenario. It goofed me up at first because I thought it did matter when it actually did not. This is the correct tension.
For the torque, it matters.
However, you are right that the tension is 642N, I made a mistake.
 
  • #7
So, now I wonder whether your 1.7 is not quite accurate enough. I get exactly 5/3N. (There's a lot of cancellation, and angle turns out not to matter.)
 
  • #8
haruspex said:
So, now I wonder whether your 1.7 is not quite accurate enough. I get exactly 5/3N. (There's a lot of cancellation, and angle turns out not to matter.)
I get exactly 1.7639278626, rounded to 3 sig figs is 1.76 N which is incorrect.
 
  • #9
Anonymous123451234 said:
I get exactly 1.7639278626, rounded to 3 sig figs is 1.76 N which is incorrect.
To get the most accurate answer, forget the results for earlier parts of the problem. Using those introduces rounding errors.
Take moments about the point of attachment of the wire.
 

Related to How Is the Vertical Force Calculated at the Hinge in a Beam and Sign System?

1. What causes a sign to hang at an angle?

There are several factors that can cause a sign to hang at an angle. It could be due to uneven mounting hardware, an unlevel surface, or strong winds pushing against the sign.

2. How can I fix a sign that is hanging at an angle?

If the sign is hanging at an angle due to uneven mounting hardware, you can try adjusting the screws or bolts to make sure they are evenly tightened. If the surface is unlevel, you may need to adjust the placement of the sign or use shims to level it out. For windy conditions, try using stronger or additional mounting hardware to secure the sign.

3. Can a sign hanging at an angle affect its visibility?

Yes, a sign that is hanging at an angle may be more difficult to see and read, especially from certain angles. It is important to make sure your sign is level and properly mounted to ensure maximum visibility.

4. Is it safe to hang a sign at an angle?

It depends on the type and size of the sign, as well as the mounting hardware used. In general, it is best to have a sign mounted securely and level to avoid any potential safety hazards.

5. How can I prevent a sign from hanging at an angle in the future?

To prevent a sign from hanging at an angle, make sure to use proper mounting hardware and secure it to a level surface. Regularly check and adjust the sign as needed to ensure it stays level over time.

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