Tension and Angles of Frame on Wall

In summary, the problem involves finding the angle at which a frame suspended by two wires will remain in equilibrium, with the tension in each wire being 0.75 times the weight of the frame. Using the condition for equilibrium, which states that the vertical forces must add to zero, the angle can be found by taking the arccosine of half the weight divided by 0.75 times the weight.
  • #1
Heat
273
0

Homework Statement


A frame hung against a wall is suspended by two wires attached to its upper corners.

If the two wires make the same angle with the vertical, what must this angle be if the tension in each wire is equal to 0.75 of the weight of the frame? (Neglect any friction between the wall and the picture frame.)

Homework Equations



F=ma
w=mg

The Attempt at a Solution



I think it looks something like this:

http://img405.imageshack.us/img405/6182/46664005mf5.jpg [Broken]

It says .75 weight of frame, so I did the following to convert to N.

w=.75(9.8) = 7.35N

That is 7.35 on each side, and this is the part that get's me "if the tension in each wire is equal to 0.75 of the weight of the frame?"

I am lost, here. but for angle I think it should be something like this arc cos (14.7/7.35)

well at least i tried :D
 
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  • #2
You are not given the weight of the frame so don't assume any particular value. Instead, just call that weight W.

You are given the tension in the wires in terms of that weight. The tension equals 0.75*weight, so T = 0.75*W.

Now apply the condition for equilibrium, namely that vertical forces acting on the frame must add to zero. (What are the vertical components of the wire tension?)
 
  • #3
so the tension on each wire is .75w, where w is unknown.

"condition for equilibrium, namely that vertical forces acting on the frame must add to zero."

vertical must add up to w, for them to cancel out, right?

if so where do I go from there.

the angle would not be:::: arc cosine (w/.75w)?
 
  • #4
Almost! Realize that there are two wires pulling up on the frame.
 
  • #5
so that means they are sharing the weight, so it should be half of w. ?
 
  • #6
Heat said:
so that means they are sharing the weight, so it should be half of w. ?
You can certainly think of it that way.
 
  • #7
so it would be arc cosine of .5w/.75w = arc cosine .66 = 48.19 ?
 
  • #8
Yep. Looks good.
 
  • #9
thank you :)
 

1. What is tension in a frame on a wall?

Tension in a frame on a wall refers to the amount of force that is pulling or stretching the frame in different directions. This force is created by the weight of the frame and any objects attached to it, as well as any external forces acting on it, such as wind or gravity.

2. How is tension calculated in a frame on a wall?

Tension can be calculated using the formula T = Fcosθ, where T is the tension force, F is the weight or force acting on the frame, and θ is the angle between the frame and the direction of the force. This formula takes into account both the weight of the frame and the angle at which it is attached to the wall.

3. What happens to tension when the angle of the frame changes?

The tension in a frame on a wall will increase as the angle of the frame increases. This is because as the angle increases, the force acting on the frame becomes more perpendicular to the wall, resulting in a greater component of force pulling the frame away from the wall.

4. How does the weight of objects attached to the frame affect tension?

The weight of objects attached to the frame will increase the overall tension in the frame. This is because the weight of these objects adds to the force acting on the frame, and the tension force is directly proportional to the force acting on the frame.

5. Why is it important to consider tension and angles in a frame on a wall?

It is important to consider tension and angles in a frame on a wall because these factors can greatly affect the stability and strength of the frame. If the tension is too high, the frame may become unstable and could potentially collapse. Additionally, understanding the angles at which the frame is attached to the wall can help determine the best placement and distribution of weight to ensure the frame can support its intended load without breaking or causing damage to the wall.

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