Tension on two cables holding a weight

In summary, the problem involves an 18.0 kg spotlight suspended 2.40m below a horizontal pole by two 3.90m long cables that are angled upward at equal angles. The equation for tension is T=\mu*m*g/(cos\vartheta+\musin\vartheta), but since there is no static friction, a free body diagram must be used to find the sum of forces in the vertical and horizontal directions. The tension forces must also be separated into their horizontal and vertical components to fit into the equations.
  • #1
bran8015
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Homework Statement



A 18.0 kg spotlight is suspended 2.40m below a horizontal pole by two 3.90m long cables that angle upward at equal angles and reach from the top of the light to either end of the horizontal pole.


Homework Equations



The only equation I have for tension is T=[tex]\mu[/tex]*m*g/(cos[tex]\vartheta[/tex]+[tex]\mu[/tex]sin[tex]\vartheta[/tex])

The Attempt at a Solution


My problem is [tex]\mu[/tex] stands for the static friction, which there is none. Do I still need to use this equation or is there a different one I don't know about. Thanks!
 
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  • #2
Welcome to PF!
Tension is just the force that a string or cable pulls with. You need a "free body diagram" showing the 3 forces acting on the load, with angles. Then you write
"sum of the forces = 0" for the vertical direction (and perhaps for the horizontal direction separately). The tension forces must be separated into their horizontal and vertical components to fit into these equations.
 
  • #3
Thanks, I was making it way to difficult.
 

FAQ: Tension on two cables holding a weight

What is tension?

Tension is a force that is exerted on an object in opposite directions, typically along a rope, cable, or similar structure.

How is tension calculated on two cables holding a weight?

Tension on two cables holding a weight can be calculated by using the following formula: T = (W/2) + (W/2 * cosθ), where T is the tension, W is the weight being held, and θ is the angle between the two cables.

How does the angle between the two cables affect the tension?

The tension on the cables increases as the angle between the two cables decreases. This is because a smaller angle means a greater horizontal component of the weight, which requires a larger tension to counteract.

What happens to the tension if the weight changes?

If the weight being held changes, the tension on the two cables will also change. As the weight increases, the tension will increase, and vice versa.

Can tension on two cables ever be completely equal?

Yes, tension on two cables can be completely equal if the weight is perfectly centered between the two cables and the angle between them is 180 degrees. In this case, the tension on both cables will be equal to half of the weight.

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