How to find the Tension in a support cable?

In summary, a wrecking ball weighing 5910 N is supported by a boom weighing 2820 N. The support cable runs from the top of the boom to a tractor, with an angle of 32° between the cable and the horizontal and an angle of 48° between the boom and the horizontal. The tension in the support cable and the magnitude of the force exerted on the lower end of the boom by the hinge at point P can be found by balancing forces and moments. The tension formula T=mv²/L is not applicable in this case. The angle between the boom and the cable should be 16°, not 48-32=16.
  • #1
MKM
16
0
A wrecking ball (weight = 5910 N) is supported by a boom, which may be assumed to be uniform and has a weight of 2820 N. As the drawing shows, a support cable runs from the top of the boom to the tractor. The angle between the support cable and the horizontal is 32°, and the angle between the boom and the horizontal is 48°. Find (a) the tension in the support cable and (b) the magnitude of the force exerted on the lower end of the boom by the hinge at point P.
I have been having trouble trying to finf the tension, not sure how I originally thought to just do the sum of the torques but it's not coming out. I thougit was just T = 3/4 sin 90 ? very confused?
 

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  • Support cable.doc
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  • #2
You need to construct a FBD, then do,

ΣFv = 0
ΣFh = 0
ΣM = 0

where M is a moment, or torque.
 
  • #3
This is how I set up my equation Torque sum =
-2820N (L/2)sin 138
+ T(3/4)L sin 90
- 5910sin138 =0 and I get 6530 ?
What I realized later was that I think I'm supposed to use the 32 angle for the tension force in some way but I'm not sure. I hope m attachment isn;t pending for very long it's a good description
 
  • #4
I think I have an idea of what your attachment will look like.
Is it like mine ?

http://img476.imageshack.us/img476/4256/mkm10sa.jpg [Broken]

If so, then the FBD could be something like my 2nd attachment

http://img476.imageshack.us/img476/5760/mkm26qe.jpg [Broken]
 

Attachments

  • mkm1.jpg
    mkm1.jpg
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  • mkm2.jpg
    mkm2.jpg
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  • #5
wow It's exactly like your second attachment . I actually had the Tension facing outward perpendicular to the support cable but maybe I was wrong.
 
  • #6
MKM said:
wow It's exactly like your second attachment . I actually had the Tension facing outward perpendicular to the support cable but maybe I was wrong.

Tension is always in the direction of the cable (or whatever else is providing the tension).
 
  • #7
okay I have evrything set up but I dont; understnad how to aply the tension formula which I think is T= mv squared/ L. Also when I am looking for the sum of the torques should I just add the tension to the other forces and find Rx and Ry?
 
  • #8
MKM said:
okay I have evrything set up but I dont; understnad how to aply the tension formula which I think is T= mv squared/ L. Also when I am looking for the sum of the torques should I just add the tension to the other forces and find Rx and Ry?
I don't understand your tension formula. What is the v ? There is no velocity involved.

Do what I suggested in my first post. Do a balance of forces, both horizontal and vertical. Then do a balance of moments (or torques).

ΣFv = 0
ΣFh = 0
ΣM = 0

When doing the sum of torques, Pick a point, A say, and take the moments of every force about this point. All the forces are listed in Fig2. Remember that the tension T, in Fig2, should be ignored since it has been resolved into horizontal and vertical components, Tcos32 and Tsin32 respectively. And it is these two forces that should have their moments taken, not T.
 
  • #9
should the angle between the boom and the cable be 48-32=16?
 

1. What is tension?

Tension is a force that is exerted on an object by a stretched or compressed material. In the case of a support cable, tension is the force that is pulling on the cable and keeping it in place.

2. Why is it important to find the tension in a support cable?

Knowing the tension in a support cable is important for ensuring the stability and safety of the structure it is supporting. If the tension is too low, the cable may not be able to hold the weight of the structure, while if the tension is too high, it may cause unnecessary strain on the structure and the cable itself.

3. What factors affect the tension in a support cable?

The tension in a support cable is affected by the weight of the structure it is supporting, the angle at which the cable is attached to the structure, and the properties of the cable itself, such as its strength and elasticity.

4. How do you calculate the tension in a support cable?

The tension in a support cable can be calculated using the formula T = (W * L) / 2sinθ, where T is the tension, W is the weight of the supported structure, L is the length of the cable, and θ is the angle at which the cable is attached to the structure.

5. What tools or equipment are needed to find the tension in a support cable?

To find the tension in a support cable, you will need a measuring tape to measure the length of the cable, a scale to measure the weight of the structure, and a protractor to measure the angle at which the cable is attached to the structure. You may also need a calculator to perform the necessary calculations.

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