Tension and Hinge Force Problem

In summary, the problem involves a uniform beam pinned to the ground with a cable attached to its center to support wooden blocks suspended on it. The blocks are placed at two-fifths and three-fifths of the way up the beam, creating angles of 12° and 20° respectively. The task is to find the tension of the cable and the force exerted by the hinge at the bottom of the beam. To solve this, equations of equilibrium for the beam's horizontal and vertical components of forces and torque must be written. The letters used in the equations represent the tension, hinge force, length of the beam, and gravity.
  • #1
Art_Vandelay
33
0

Homework Statement



The 135-N uniform beam from which 14-N wooden blocks are suspended is pinned to the ground. The beam is then supported by a cable (attached at the center of the beam) to allow the blocks to hang freely.

If the blocks are attached two-fifths and three-fifths of the way up the beam, θc=12° and θb=20°, what tension must the cable supply?
What is the hinge force at the bottom of the beam?

The image can be seen here: http://i.imgur.com/tVm7RMS.jpg


Homework Equations



τ = rmgsinθ
Fx = 0
Fy = 0


The Attempt at a Solution



I'm not even sure where to begin tackling this problem. The two angles given are throwing me off, so I can't decide when or how to use either and if I should find the hinge forces first or the wire tension. Any help to point me in the right direction would be greatly appreciated!
 
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  • #2
Draw all force vectors. Find their horizontal and vertical components and write up the equations of equilibrium for the beam. Two for the x and y components of the forces and one for the torque. ehild
 
  • #3
ehild said:
Draw all force vectors. Find their horizontal and vertical components and write up the equations of equilibrium for the beam. Two for the x and y components of the forces and one for the torque. ehild
Does this seem correct? It's the closest thing I could think of. Also, would I substitute 1 for L, since the blocks are given as fractions along the beam?
Fx: Tension*cos12 - HingeForce*cos20 = 0
Fy: Tension*sin12 + HingeForce*sin20 - 135 N - 14 N = 0
τorque = (-gravity*.5Length*cos20) + (-gravity*(2/5+3/5)Length*cos20) + (Tension*.5Length*cos12) + (HingeForce*cos20)
 
Last edited:
  • #4
But nobody knows what are the meanings of the letters.

ehild
 
  • #5
ehild said:
But nobody knows what are the meanings of the letters.

ehild
Oops... :p

Just corrected it.
 
  • #6
A hinge can exert force to any direction, not only in the direction parallel to the beam.
What do you mean on "gravity" in the equation for the torque?
If you wrote the torque with respect to the hinge, what is the torque of the hinge force?

ehild
 

1. What is tension and hinge force problem?

The tension and hinge force problem is a common concept in physics and engineering, where the forces acting on a system of objects connected by strings or rods are analyzed to determine their motion and equilibrium.

2. How do you calculate the tension in a string or rod?

The tension in a string or rod can be calculated using the equations of Newton's Second Law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In the case of a tension and hinge force problem, the forces acting on each object must be balanced for equilibrium, so the tension can be calculated by setting the net force equal to zero and solving for the tension.

3. What is the difference between tension and hinge force?

Tension is the force that is transmitted through a string or rod, while hinge force is the force that acts on a hinge or pivot point in a system. In a tension and hinge force problem, both types of forces need to be taken into account in order to determine the equilibrium of the system.

4. How does the direction of tension and hinge force affect the system?

The direction of tension and hinge force can greatly affect the motion and equilibrium of a system. If the forces are in the same direction, they will add together to create a greater overall tension or hinge force. However, if they are in opposite directions, they will subtract from each other, potentially resulting in a lower overall tension or hinge force.

5. What are some real-life applications of tension and hinge force problems?

Tension and hinge force problems are commonly seen in structures such as bridges, cranes, and other types of mechanical systems. They are also used in everyday objects such as doors, drawers, and pulley systems. Understanding how these forces interact is crucial in designing and maintaining safe and stable structures and systems.

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