What are the forces acting on a hinge?

  • Thread starter Thread starter drkidd22
  • Start date Start date
  • Tags Tags
    Forces Hinge
Click For Summary
SUMMARY

The discussion focuses on calculating the hinge force acting on a 3.4-meter-long beam with a mass of 100 kg. Participants emphasize the importance of using Newton's first law to resolve the forces acting on the beam, specifically the tension force (T) and its components in both the x and y directions. The correct approach involves drawing a free body diagram and applying the equations of equilibrium to find the resultant hinge force. Key calculations include determining T and resolving it into its components, leading to the conclusion that the hinge force can be derived from these components.

PREREQUISITES
  • Understanding of Newton's first law of motion
  • Ability to draw and interpret free body diagrams
  • Knowledge of trigonometric functions (sine and cosine)
  • Familiarity with the equations of equilibrium for static systems
NEXT STEPS
  • Learn how to draw and analyze free body diagrams for static equilibrium problems
  • Study the application of Newton's laws in two-dimensional force systems
  • Explore the concept of torque and its role in static equilibrium
  • Practice solving similar problems involving tension and hinge forces in beams
USEFUL FOR

Physics students, engineering students, and anyone studying mechanics, particularly those focusing on static equilibrium and force analysis in structures.

drkidd22
Messages
59
Reaction score
0

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.
 

Attachments

  • ch9f3.gif
    ch9f3.gif
    1.7 KB · Views: 2,244
Physics news on Phys.org
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.
 

Attachments

  • physics.PNG
    physics.PNG
    2.1 KB · Views: 718
  • #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.
 

Similar threads

Flag pole finding horizontal force component at hinge.
  • · Replies 1 ·
Replies
1
Views
3K
Force Acting on Hinge: 2744 N Torque on Beam Homework: Find Force on Hinge
  • · Replies 6 ·
Replies
6
Views
2K
What mistake did I make in finding the reaction at hinge A?
  • · Replies 3 ·
Replies
3
Views
2K
Torque on Rod Due to Normal Force at a Hinge
  • · Replies 14 ·
Replies
14
Views
4K
What is the force exerted by each hinge on the door?
  • · Replies 3 ·
Replies
3
Views
13K
Hinged Water Storage Tank -- Calculate the force on one side
  • · Replies 15 ·
Replies
15
Views
3K
Rotational Torque/Force Problem (rod around hinge)
  • · Replies 15 ·
Replies
15
Views
3K
What is the third force acting on a plank attached to a wall by a hinge?
  • · Replies 5 ·
Replies
5
Views
2K
Finding Acceleration and Reaction Forces in Rotating Thin Rod on a Hinge
  • · Replies 2 ·
Replies
2
Views
3K
Find Hinge Force of Rod Undergoing Circular Motion
  • · Replies 65 ·
3
Replies
65
Views
12K