Object Lifted By Cord (Stress/Tension Problem)

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SUMMARY

The discussion centers on calculating the height at which a 25kg object will be lifted by a nylon cord with a diameter of 1.10mm, strung over two 3.50m high poles spaced 4.8m apart. Participants explore the equations of tension and forces acting on the object, specifically using F=EA and F=ma to analyze the problem. The key challenge identified is the need to account for the height and weight of the cord, which complicates the calculations. The use of trigonometric functions to determine angles and tensions is emphasized, with specific references to the geometry of the setup.

PREREQUISITES
  • Understanding of basic physics concepts such as tension and forces (F=ma).
  • Familiarity with trigonometric functions (sin, cos, tan) and their application in physics.
  • Knowledge of material properties, specifically Young's modulus (E) for the nylon cord.
  • Ability to interpret and analyze free-body diagrams in mechanics.
NEXT STEPS
  • Study the application of Young's modulus in calculating material tension.
  • Learn how to derive and solve equations involving multiple unknowns in physics problems.
  • Explore the use of free-body diagrams to visualize forces in static equilibrium.
  • Investigate the relationship between geometry and trigonometry in physics applications.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and tension problems, as well as educators seeking to enhance their teaching strategies in these areas.

kritzy
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Homework Statement


A 25kg object is being lifted by pulling on the ends of a 1.10mm diameter nylon cord that goes over two 3.50m high poles that are 4.8 m apart. How high above the floor will the object be when the cord breaks?

Homework Equations


F=EA
F=ma

The Attempt at a Solution


I thought that by using this equation, I could find the tension in the cord.
F=(500 x 10^6)(pi)(.00055)^2=475

X-dir force
Tcos θ + Tcos θ = 2Tcos θ=0

Y-dir force
Tsin θ + Tsin θ -mg=0
2Tsin θ=mg

I think my equations are incorrect. I didn't know how to account for the height and weight of the cord. Help would be much appreciated.
 
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kritzy said:
A 25kg object is being lifted by pulling on the ends of a 1.10mm diameter nylon cord that goes over two 3.50m high poles that are 4.8 m apart. How high above the floor will the object be when the cord breaks?

I didn't know how to account for the height and weight of the cord.

Hi kritzy! :smile:

(what does the weight have to do with it? :confused:)

Use the triangle whose length is 3.5 - h and whose width is 2.4 to find cosθ and sinθ :wink:
 
tiny-tim said:
Hi kritzy! :smile:

(what does the weight have to do with it? :confused:)

Use the triangle whose length is 3.5 - h and whose width is 2.4 to find cosθ and sinθ :wink:


I tried to solve for sinθ and cosθ but I end up with to many unknowns.
T=tension
cosθ=2.4/T
sinθ=(3.5-h)/T
I tried to substitute for T. I got
tanθ=(3.5-h)/2.4
I still have two unknowns and only one equation.
Can you give me another hint?
I attached a file which shows the diagram. Maybe it will help
 

Attachments

kritzy said:
I tried to substitute for T.

I'm confused … isn't T the breaking strength, which I assume is given in the question? :confused:

and I'm off to bed now :zzz: …
 

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