Calculating Forces in a Static Equilibrium Bridge System

In summary, the picture depicts an impossible equilibrium where the leftmost end of the bridge would have to be overweighed by 4 kilograms in order to balance the weight of the bridge.
  • #1
akan
60
0
http://img150.imageshack.us/img150/5393/bridgeef8.png [Broken]
http://g.imageshack.us/img150/bridgeef8.png/1/ [Broken]

Sum(T_z) [pivot at L] = 2 F_r - 4 mg = 0
2 F_r = 4 mg
F_r = 2 mg
F_r = 2 * 120 * 10
F_r = 2400

Sum(F_y) = F_l + F_r - mg = 0
Sum(F_y) = F_l + 2400 - 1200 = 0
F_l = -1200

Answer: 1200 N downward. Is this right? This picture seems to portray an impossible equilibrium, so I'm confused. I think the right end should actually bring the whole thing down by overwheighing...
 
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  • #2
Hi akan! :smile:

I can't get your picture links to work. :cry:

Can you describe the bridge? :smile:
 
  • #3
Why can't you get it to work? It's on Image Shack. :S.
Anyway, my description will be weird, but so is the picture - so bear with me.

Problem statement:
A uniform bar of length 8.0 m and mass 120 kg is supported by two vertical posts spaced by 2.0 m, see the figure. Calculate the force on the leftmost support (magnitude and direction!).

Note: please use g = 10 m/s^2 for simplicity. Show all work.

Picture description:
There is a horizontal bridge, whose length is 8 meters. The leftmost end is supported by an upright post support. There is another post support 2 meters to the right from the left one. The force of gravity acts at the center of mass, so I understand it is 4 meters from the leftmost end (or, likewise, the rightmost one). There are no other supports besides these two, so I don't know how there is an equilibrium. But that's the whole problem, as it is stated. Thanks. :)
 
  • #4
akan said:
Sum(T_z) [pivot at L] = 2 F_r - 4 mg = 0
2 F_r = 4 mg
F_r = 2 mg
F_r = 2 * 120 * 10
F_r = 2400

Sum(F_y) = F_l + F_r - mg = 0
Sum(F_y) = F_l + 2400 - 1200 = 0
F_l = -1200

Answer: 1200 N downward. Is this right? This picture seems to portray an impossible equilibrium, so I'm confused. I think the right end should actually bring the whole thing down by overwheighing...
akan said:
Why can't you get it to work? It's on Image Shack. :S.
Anyway, my description will be weird, but so is the picture - so bear with me.

Hi akan! :smile:

hmm … picture works fine now … it shows up as part of the post … didn't yesterday … mystery :confused:

good description, anyway! :smile:


Yup … 1200N is correct …

though it would have been a lot quicker if you'd just taken moments about the right-hand post, wouldn't it? :wink:

I agree the question is badly worded … "support" begins with "sup", which is the same as "sub", from the Latin meaning "under". :mad:

The equilibrium is as expected … you have equal forces (1200N) at equal distances from the right-hand post, so the whole thing is balanced on that post! :smile:
 
  • #5
I'm trying to solve a similar problem using this example, but I'm confused as to where the 4 comes from in the first equation:

Sum(T_z) [pivot at L] = 2 F_r - 4 mg = 0
 
  • #6
Nevermind, it is the downward force due to gravity that is causing a torque force rotating about the axis denoted by L.

Just tired this afternoon... :)
 

What is bridge static equilibrium?

Bridge static equilibrium refers to the state in which a bridge is balanced and not experiencing any movement or deformation due to external forces. This is an important concept in bridge design and construction to ensure the safety and stability of the structure.

How is bridge static equilibrium achieved?

To achieve bridge static equilibrium, the forces acting on the bridge must be balanced. This means that the sum of all the horizontal and vertical forces must equal zero, and the sum of all the moments (torques) acting on the bridge must also equal zero. This can be achieved through proper design and construction, as well as regular maintenance and inspection.

What are the factors that affect bridge static equilibrium?

The factors that affect bridge static equilibrium include the design and materials used in construction, the weight of the bridge itself, the weight of any vehicles or objects on the bridge, and external forces such as wind or earthquakes. Changes in any of these factors can affect the balance of forces on the bridge and potentially lead to instability.

How is bridge static equilibrium different from dynamic equilibrium?

Bridge static equilibrium refers to a bridge that is balanced and not experiencing any movement or deformation. Dynamic equilibrium, on the other hand, refers to a bridge that is in motion but the forces acting on it are balanced, resulting in a constant speed and direction. Both types of equilibrium are important to consider in bridge design and maintenance.

Why is bridge static equilibrium important?

Bridge static equilibrium is important because it ensures the safety and stability of the bridge. If a bridge is not in static equilibrium, it may experience excessive movement or deformation, which can lead to structural failure or collapse. By understanding and maintaining bridge static equilibrium, engineers can ensure the longevity and safety of bridges for years to come.

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