Solve Equilibrium Problem: Two Uniform Beams, Hinge & Chain

  • Thread starter cheater1
  • Start date
  • Tags
    Equilibrium
In summary, the problem involves two uniform beams connected by a hinge and a chain of negligible mass. The system stands upright on a frictionless surface. The tension in the chain and the forces on the hinge and ground can be determined as functions of the length of the chain using the sum of forces and torque equations. The resulting equation for tension is T = Fx - W.
  • #1
cheater1
34
0

Homework Statement


[PLAIN]http://img820.imageshack.us/img820/3505/23625990.jpg

Two uniform beams, each of mass M and length L, are connected by a hinge at the top and by a chain of negligible mass attached between their centers. The system will stand upright on a frictionless surface as shown in the figure. Determine (a) the tension in the chain, (b) the force on the hinge by each plank, (c) the force of the ground on each plank, as a function of the length of the chain, l.

Homework Equations



My force diagram.

[PLAIN]http://img440.imageshack.us/img440/2272/98244983.jpg

Sum of F = 0
Sum of Torque = 0

Torque = (-T sinθ L ) + (-W cos θ L) + (Fx sin θ L) = 0

FxsinθL - WsinθL / sin θL = Tension is this right?

if this is right I will attempt part b.

The Attempt at a Solution

Homework Statement


Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution

 
Last edited by a moderator:
Physics news on Phys.org
  • #2
FxsinθL - WcosθL / sin θL = Tension

edit: FxsinθL - WsinθL / sin θL = Tension

then it will simplfy as ,

T = Fx-W = Tension... now it doesn't even seem right
 

1. How do you solve an equilibrium problem with two uniform beams, hinge, and chain?

To solve this type of problem, you first need to draw a free body diagram of the system, showing all the forces acting on the beams, hinge, and chain. Then, you can use the equations of equilibrium (sum of forces in x and y direction equals zero) to solve for the unknown forces and reactions. It is important to consider the direction and magnitude of each force and use the correct sign convention.

2. What is the purpose of a hinge and chain in an equilibrium problem with two uniform beams?

The hinge and chain act as supports for the beams, providing reactions at their points of connection. These reactions help maintain the beams in equilibrium by balancing out the external forces acting on the system. The hinge also allows for rotation of the beams, which is necessary for solving the equilibrium equations.

3. What are some common mistakes to avoid when solving an equilibrium problem with two uniform beams, hinge, and chain?

Some common mistakes include forgetting to include all the forces in the free body diagram, using incorrect sign conventions, and not considering the rotational equilibrium of the system. It is also important to double check the units and make sure they are consistent throughout the calculations.

4. Can you provide an example of a real-life situation where an equilibrium problem with two uniform beams, hinge, and chain may arise?

An example of this type of problem could be a construction scenario where two beams are connected by a hinge and supported by a chain. The beams may be used to support a platform or a bridge, and the hinge and chain provide stability and allow for rotation of the beams under different loads.

5. Are there any additional factors to consider when solving an equilibrium problem with two uniform beams, hinge, and chain?

Aside from the forces acting on the beams, hinge, and chain, it is important to consider the weight and dimensions of the beams and the angle of the chain. These factors can affect the magnitude and direction of the reactions and must be taken into account when solving the equilibrium equations.

Similar threads

An equilibrium problem -- Spinning a hinged rod and a ball
    • Introductory Physics Homework Help
Replies
21
Views
2K
Torque and rotational equilibrium question
    • Introductory Physics Homework Help
Replies
6
Views
2K
What is the force exerted by each hinge on the door?
    • Introductory Physics Homework Help
Replies
3
Views
11K
Flag pole finding horizontal force component at hinge.
    • Introductory Physics Homework Help
Replies
1
Views
3K
Force Acting on Hinge: 2744 N Torque on Beam Homework: Find Force on Hinge
    • Introductory Physics Homework Help
Replies
6
Views
1K
Lifting a Beam with a uniform weight distribution
    • Introductory Physics Homework Help
Replies
5
Views
4K
Equilibrium Problem - Balancing Torques
    • Introductory Physics Homework Help
Replies
4
Views
2K
Rotational Equilibrium Question
    • Introductory Physics Homework Help
Replies
2
Views
2K
Given a uniform chain on an incline, find the work done by friction
    • Introductory Physics Homework Help
Replies
8
Views
2K
Tension and net torque in a cable
    • Introductory Physics Homework Help
Replies
10
Views
4K

Hot Threads

Recent Insights

Back
Top