Find the tension in the horizontal cable that supports the boom

In summary: The net torque will be zero, so the torque due to the weight of the boom and the marble slab must be balanced by the tension in the horizontal cable. Using the equation for torque, we can set up an equation and solve for the tension. In summary, to find the tension in the horizontal cable supporting the boom in the marble quarry, we must consider the net torque as zero and set up an equation using the torque due to the weight of the boom and the marble slab.
  • #1
k31453
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Homework Statement



A crane in a marble quarry is mounted on the rock walls of the quarry and is supporting a 2000 kg slab of marble as shown in the figure. The center of mass of the 900 kg boom is located one-third of the way from the pivot end of its 15-m length, as shown.



Given diagram: http://i38.tinypic.com/oqaltx.jpg

Homework Equations



a)Find the tension in the horizontal cable that supports the boom.

The Attempt at a Solution




net torque will be = 0,

at CM the torque will be 1/3 of length X 830 * 9.8 X cos50 ..

but i can't organize it for tension T
 
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  • #2
k31453 said:

Homework Statement



A crane in a marble quarry is mounted on the rock walls of the quarry and is supporting a 2000 kg slab of marble as shown in the figure. The center of mass of the 900 kg boom is located one-third of the way from the pivot end of its 15-m length, as shown.



Given diagram: http://i38.tinypic.com/oqaltx.jpg

Homework Equations



a)Find the tension in the horizontal cable that supports the boom.

The Attempt at a Solution




net torque will be = 0,

at CM the torque will be 1/3 of length X 830 * 9.8 X cos50 ..

but i can't organize it for tension T

It will be easier to solve this problem by considering the torque about the pivot point of the crane -- at the crane's base.

attachment.php?attachmentid=64235&stc=1&d=1385269638.jpg
 

Attachments

  • oqaltx.jpg
    oqaltx.jpg
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1. What is the purpose of finding the tension in the horizontal cable that supports the boom?

The tension in the horizontal cable is crucial in determining the stability and strength of the boom. It ensures that the weight of the boom and any attached objects is evenly distributed and supported, preventing any potential accidents or damages.

2. How is the tension in the horizontal cable calculated?

The tension in the horizontal cable can be calculated using the formula T = W/cosθ, where T is the tension, W is the weight of the boom and any attached objects, and θ is the angle between the cable and the horizontal. This formula takes into account the forces acting on the cable and provides an accurate estimation of the tension.

3. What factors can affect the tension in the horizontal cable?

The tension in the horizontal cable can be affected by various factors such as the weight of the boom and any attached objects, the angle of the cable, the material and strength of the cable, and external forces such as wind or movement of the boom.

4. How does the tension in the horizontal cable impact the stability of the boom?

The tension in the horizontal cable directly affects the stability of the boom. If the tension is too low, the boom may not be able to support its weight and could collapse. On the other hand, if the tension is too high, it could cause strain on the cable and potentially lead to breakage or damage. Therefore, finding the appropriate tension is crucial for the stability and safety of the boom.

5. Can the tension in the horizontal cable change over time?

Yes, the tension in the horizontal cable can change over time due to various factors such as wear and tear on the cable, changes in the weight or position of the boom and attached objects, and external forces such as wind or temperature. It is important to regularly monitor and adjust the tension to ensure the safety and stability of the boom.

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