Calc Min Steel Wire Diameter for 323kg Load

In summary, using the given information and the formula for Young's modulus, the minimum diameter of a 17.2 m long steel wire that will stretch no more than 7.38 mm when a mass of 323 kg is hung on the lower end is approximately 0.007 m, or 6.85 mm, assuming a value of 9.80 for the acceleration due to gravity. However, this may vary depending on the number of significant figures used or the method of rounding.
  • #1
iamtrojan3
56
0

Homework Statement


Find the minimum diameter of an l = 17.2 m long steel wire that will stretch no more than 7.38 mm when a mass of 323 kg is hung on the lower end. (Hint: The Young's modulus of steel is 200.0 GPa.)


Homework Equations



Youngs = (Force / Area) / (change L / L)
= (mg / pi*r^2) / (change L / L)

The Attempt at a Solution


Simple enough... just plug and chug right?
just to clarify, 200.0GPa = 2x10^11 N/m^2 correct?
and 7.38mm = 0.00738m
If so,

Then after solving for r... i got .006853m, which is wrong. And i did multiply by 2 for the diameter. 0.0685 is also wrong, so is .685m

What am i doing wrong?? or am i just way off??

Thanks
 
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  • #2
What value of g did you use?
 
  • #3
I used the same formula as you did and I get 0.0069 m. Do you know the correct answer?
 
  • #4
Sorry for not replying earlier... fell asleep.
I used 9.81 as g, and idk what the right answer is... =(
 
  • #5
You have the right answer. Maybe you have the wrong number of significant figures, or are rounding incorrectly.

g=9.81 gives 6.86 mm, and g=9.80 gives 6.85 mm for the diameter.
 

What is the calculation method for determining the minimum steel wire diameter needed to support a load of 323kg?

The calculation method for determining the minimum steel wire diameter for a specific load involves using the formula F = (π*d^2*SWL)/4, where F is the force in Newtons, d is the wire diameter in meters, and SWL is the safe working load in kilograms. By rearranging the formula, we can solve for d, which will give us the minimum wire diameter needed for a load of 323kg.

What factors influence the minimum steel wire diameter needed for a 323kg load?

There are several factors that can influence the minimum steel wire diameter needed for a specific load, including the type and grade of steel wire being used, the angle of the wire from the vertical, and any environmental factors such as temperature or corrosion.

Why is it important to calculate the minimum steel wire diameter for a load of 323kg?

Calculating the minimum steel wire diameter is important because it ensures the safety and stability of the load being supported. Using a wire diameter that is too small can result in the wire breaking and causing damage or injury.

What are some common applications for using steel wire to support a 323kg load?

Steel wire is commonly used to support heavy loads in various industries such as construction, transportation, and manufacturing. It can be used for lifting and rigging purposes, as guy wires for towers and poles, and for securing cargo on trucks and ships.

Are there any alternative methods for supporting a 323kg load besides using steel wire?

Yes, there are alternative methods for supporting a 323kg load, such as using chains, ropes, or synthetic fibers. The choice of material will depend on the specific application and the required strength and durability needed for the load. It is important to carefully consider all factors before selecting the appropriate support method.

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