Need help solving tension problem.

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In summary, to support the load shown with a tension not exceeding 870 N, the shortest length of cable that can be used is 5.22m. This is achieved by setting the tension in both portions AC and BC of cable ACB to be equal and using the force diagram at point C to solve for the angle and height needed.
  • #1
X8V
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Knowing that portions AC and BC of cable ACB must be equal, determine the shortest length of cable that can be used to support the load shown if the tension in the cable is not to exceed 870 N.

i attached the picture that came with the problem.

i am lost and not sure how to approach the problem.
 

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  • #2
Hi X8V,

X8V said:
Knowing that portions AC and BC of cable ACB must be equal, determine the shortest length of cable that can be used to support the load shown if the tension in the cable is not to exceed 870 N.

i attached the picture that came with the problem.

i am lost and not sure how to approach the problem.

Try drawing a force diagram for the point C. What does that give you?
 
  • #3
I think i figured it out. Here's what I did.

T'=1200 N
T=T

Fx = - Tcosθ + Tcosθ = 0
Fy = Tsinθ + Tsinθ - 1200N = 0

2Tsinθ = 1200N
2(870N)sinθ = 1200N
(1740N)sinθ = 1200N
sinθ = 1200N / 1740N
θ = 43.6 degrees

h = 1.8m / sin43.6
h = 2.61m

5.22m is the minimum length the cable can achieve when T=870N
 

Related to Need help solving tension problem.

1. What is tension and how is it defined?

Tension is a force that is applied to an object in a way that pulls the object apart. It is often described as the pulling force that occurs when two objects are connected by a string, rope, cable, or other similar object.

2. How do I solve a tension problem?

The first step in solving a tension problem is to identify all the forces acting on the object and their directions. Then, use Newton's Second Law of Motion (F=ma) to calculate the net force acting on the object. Finally, use the equation T=mg to find the tension in the string or rope.

3. What factors affect tension?

The tension in a string or rope is affected by several factors, including the mass of the object, the acceleration due to gravity, the angle of the string, and any external forces acting on the object.

4. Can tension be negative?

Yes, tension can be negative. This occurs when the force pulling on an object is greater than the force pushing on it, resulting in a net force that pulls the object in the opposite direction. In this case, the tension is considered to be negative.

5. Are there any real-life applications of tension problems?

Yes, tension problems are common in many real-life situations such as lifting objects with ropes and pulleys, calculating the stress on a bridge or cable, and determining the force needed to support an object hanging from a ceiling. Understanding tension is important in fields such as engineering, physics, and construction.

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