What are the forces acting on a hinge?

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Homework Help Overview

The discussion revolves around analyzing the forces acting on a hinge connected to a bar that is 3.4 meters long and has a mass of 100 kg. Participants are attempting to determine the magnitude of the hinge force while considering the tension in a supporting wire and the weight of the bar.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculation of tension and its relation to the hinge force, with some suggesting the use of free body diagrams to visualize the forces involved. There are questions about the correctness of the tension calculation and its implications for the hinge force.

Discussion Status

There is an ongoing exploration of the relationships between the forces acting on the bar, with participants providing insights into the components of the hinge force. Some participants express confusion and seek clarification on specific calculations, while others suggest methods for breaking down the forces into components.

Contextual Notes

Participants mention the need to consider equilibrium equations and moments, indicating that the problem may involve multiple interpretations of the forces at play. There is also a reference to discrepancies between calculated tension values and those provided in a textbook, which raises questions about the assumptions made in the calculations.

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Homework Statement



In the figure below, the bar is 3.4 meters long and has a mass of 100 kg.
what is the magnitude of the hinge force?

The Attempt at a Solution



cosβ=2/sqrt(2^2+3.4^2)
cosβ=0.51
0.51T=mg/2
T= 100*9.8/(2*0.51)=960.8

I'm not 100% sure if I did this right.
Any assistance will be appreciated.
 

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drkidd22 said:

Homework Statement



In the figure below, the bar is 3.4 meters long and has a mass of 100 kg.
what is the magnitude of the hinge force?


The Attempt at a Solution



cosβ=2/sqrt(2^2+3.4^2)
cosβ=0.51
0.51T=mg/2
T= 100*9.8/(2*0.51)=960.8

I'm not 100% sure if I did this right.
Any assistance will be appreciated.
Looks like you took a short cut (not a good idea) to correctly solve for T, the cable tension force. But the problem wants the hinge force; try Newton 1 to solve for the x and y components of the force at the hinge.
 
drkidd22 said:

Homework Statement



In the figure below, the bar is 3.4 meters long and has a mass of 100 kg.
what is the magnitude of the hinge force?


The Attempt at a Solution



cosβ=2/sqrt(2^2+3.4^2)
cosβ=0.51
0.51T=mg/2
T= 100*9.8/(2*0.51)=960.8

I'm not 100% sure if I did this right.
Any assistance will be appreciated.

I think you got the tension right. Draw a free body diagram of the beam, label all the forces on the bar. The hinge applies a force on the beam in the x and y directions.
 
well yeah, you are both right, but that's were I'm stuck.
 
drkidd22 said:
well yeah, you are both right, but that's were I'm stuck.

The beam has three forces acting on it. The tension force of the wire, the weight force of the beam and the force of the hinge which can be thought of as a sum of two forces, a force acting in the vertical direction on the beam and a force acting to the right on the beam.
 
Last edited:
so Fhx=Tsinβ= 489.95N?
 
drkidd22 said:
so Fhx=Tsinβ= 489.95N?
If cos B =0.51, then sin B =?
 
drkidd22 said:
so Fhx=Tsinβ= 489.95N?

Draw a picture roughly to scale. Fhx is considerably more then half T.

More like T*sin(60degrees)
 
I'm completely lost. I give up. Will try again tomorrow
 
  • #10
PhanthomJay said:
If cos B =0.51, then sin B =?

= 59.34 degrees
sinB = 0.86
 
  • #11
drkidd22 said:
= 59.34 degrees
sinB = 0.86
Yes, that is correct. So if Fhx = T sinB, as you correctly noted, then Fhx =? Now you still need to calculate Fhy.
 
  • #12
PhanthomJay said:
Yes, that is correct. So if Fhx = T sinB, as you correctly noted, then Fhx =? Now you still need to calculate Fhy.

Fhx = 826.3N
 
  • #13
drkidd22 said:
Fhx = 826.3N
Yes, in which direction? And Fhy =??, and in which direction?? Once you get both components of the hinge force, the magnitude of the resultant hinge force is what the problem is asking.
 
  • #14
I think there is something wrong with the Tension. I still don't think I got it right.
 
  • #15
drkidd22 said:
I think there is something wrong with the Tension. I still don't think I got it right.
Except for some round off/sig figure errors, why do you think the tension is wrong? Your initial calculation for it is correct, although I question how you arrived at that formula.
 
  • #16
PhanthomJay said:
Except for some round off/sig figure errors, why do you think the tension is wrong? Your initial calculation for it is correct, although I question how you arrived at that formula.

Well I think there is something wrong with the tension I found because I'm working on a similar problem with just a different length for the Bar and I use the same formula the results is not right. I get 1485N as the wire tension, but the book says the tension is 1095.
 

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  • #17
drkidd22 said:
Well I think there is something wrong with the tension I found because I'm working on a similar problem with just a different length for the Bar and I use the same formula the results is not right. I get 1485N as the wire tension, but the book says the tension is 1095.
Don't believe everything you read, your answer is correct. But you should be summing moments and forces = 0 to calculate these values, do not blindly use formulas.
 
  • #19
Are you familiar with the 3 basic equations of equilibrium (for objects at rest) which comes from Newton's 1st law:
Sum of all forces acting in the x direction = 0
Sum of all forces acting in the y direction = 0
Sum of all moments (torques) of forces about any point =0?
Break up the unknown force F (let's call it P instead of F, to avoid confusion of letter designations) into 2 components, P_x and P_y, where P_x = P cos30 and P_y = P sin30 (don't forget the direction of those force components). Now sum moments about the hinge end to solve for P_y; note that there is no moment from P_x, or from the wall forces, when you choose the hinge as your point of reference for determining moments. So for moments, you have the moment from P_y and the moment from the board weight (the board weight force acts at the center of the board). Add them up, set them equal to zero, and solve for P_y. Then you can get P_x and P from trig.
 

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