Finding Tension and Forces in a Torque Diagram

In summary, the conversation is about a problem involving a beam attached to a wall with a hinge and supported by a wire. The task is to find the tension of the wire, the horizontal component of the force on the hinge, and the vertical component of the force on the hinge. The conversation discusses setting up equations for these values and using torque to solve the problem. There is also mention of placing a pivot point and using trigonometry to determine the angles and forces involved.
  • #1
Poutine
Hello all,
I'm having a problem with two of the problems I have to do, but I'm only going to put one here and the other one later if I can't figure
it out.

I made a quick diagram of the problem http://www.angelfire.com/nj4/angelus/prob.jpg [Broken]

The problem states:
In the figure one end of a uniform beam that weighs 214 N is attached to a wall with a hinge. The other end is supported by a wire.
a. find the tension of the wire
b. What is the horizontal component of the force on the hinge on the beam.
c. What is the vertical component of the force on the hinge on the beam.

Now from what my teacher told me I can place a pivot point at any place of my choosing than work with the torques with respect to that point. If I place the point at the hinge, then I find the sum of all torques which has to be equal to zero.

The problem is I'm not sure what numbers to use.

I was thinking about

0 = -(214 N) * (L * cos(40)/2) + something.

(where L is the length of the beam)
I'm not sure what to put there. I know that if it were a horizontal beam it would be (L * T * sin(angle to the horizontal) but with the beam at an angle I'm not sure what to put.

Also how would I find the horizontal and vertical forces?

sum of all forces = 0 = horizontal component of beam + what?
sum = 0 = vertical component of beam + what?

Any help would be appreciated.
 
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  • #2
Don't forget that to compute the torque, you have to multiply each force by its moment arm...

Horizontal and vertical forces are ... horizontal and vertical forces (or the horizontal and vertical components of forces) , regardless of the angle of the object.

You have to set up 3 equations, one for the torques summing to zero, one for the horizontal forces summing to zero, and one for the vertical forces summing to zero, and solve them simultaneously.

You can help yourself by showing the forces on your diagram by putting arrows that indicate the point where each force acts on the object, and the direction of each force. That will make it easier to figure out the angles and trig functions to use. For example, ask yourself: where does the tension act and in what direction? where does the weight of the beam act and in what direction?
 
  • #3
Thanks for the quick reply. :smile:

Okay so for the Horizontal then it would have to be
- T(cos 60) + Horizontal com. of force = 0

The vertical force I'm less sure about.
Would it be
- T(sin 60) + Vertical comp at hinge - 214N = 0 (?)

But the torque one is still throwing me.

That moment arm of the string is going to L(cos 40) I believe and the moment arm of the beam is L (cos(40)/2)

But what into the formula for the torque?

0 = -(214 N) * L (cos(40)/2) + T(sin 20) * L(cos 40) (?)
 
  • #4
The vertical force I'm less sure about.
Would it be
- T(sin 60) + Vertical comp at hinge - 214N = 0 (?)
Consider -- what is the significance of the + and - signs in that equation?

That moment arm of the string is going to L(cos 40) I believe and the moment arm of the beam is L (cos(40)/2)
The moment arm for the string is a line perpendicular to the string, going through the hinge. I don't see where 40 works into that. As for the torque equation, remember that torque is just the force times the length of the moment arm. Think about that some more.
 

1. What is a torque diagram problem?

A torque diagram problem is a physics problem that involves calculating the forces and torques acting on an object in order to determine its rotational equilibrium. This type of problem typically involves drawing a diagram to visualize the forces and applying equations such as Newton's second law and the torque equation.

2. How do I solve a torque diagram problem?

To solve a torque diagram problem, you first need to identify and draw all the forces acting on the object. Then, you can use equations such as Newton's second law and the torque equation to set up a system of equations and solve for the unknown variables. It is important to pay attention to the direction and sign of the forces, as well as the units being used.

3. What are some common mistakes when solving torque diagram problems?

Some common mistakes when solving torque diagram problems include forgetting to include all the forces acting on the object, using incorrect units, and not paying attention to the direction and sign of the forces. It is also important to take into account the point of rotation when calculating the torque.

4. Can you provide an example of a torque diagram problem?

Sure, here is a simple example: A seesaw with a length of 2 meters and a weight of 100 kg on one end is balanced by a weight of 50 kg on the other end. What is the distance of the 50 kg weight from the fulcrum? First, we draw a diagram and label the forces (weight of 100 kg, weight of 50 kg, and reaction force at fulcrum). Then, we can set up the equation: (100 kg)(2 m) = (50 kg)(x m). Solving for x, we get a distance of 4 meters from the fulcrum for the 50 kg weight.

5. What are some real-life applications of torque diagram problems?

Torque diagram problems have many real-life applications, such as designing structures and machines, analyzing the forces and torques on objects in motion (e.g. cars, airplanes), and understanding the balance of forces in the human body during activities such as lifting weights or throwing a ball. They are also important in fields such as engineering, physics, and biomechanics.

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