How Much Does a Steel Wire Stretch When Supporting Moving Masses?

In summary, a 1.80-m long round steel wire with a cross-sectional diameter of 0.80 mm is connected to a 23.0-kg mass and a 14.0-kg mass through a light frictionless pulley. The wire stretches by approximately 340163 N/m^2 when the masses are in motion. This stress value can be used in the equation S=Ye, where Y is Young's modulus for steel, to further analyze the wire's behavior.
  • #1
kopinator
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A 1.80-m long round steel wire with a cross-sectional diameter of 0.80 mm is placed over a light frictionless pulley, with one end of the wire connected to a 23.0-kg mass and the other end connected to a 14.0-kg mass. By how much does the wire stretch when the masses are in motion? S= F/A
e= ΔL/L°
S= Ye (where Y is Young's modulus for steel= 210 GN/m^2)

I figured the F i needed in the first equation would be the tension in the wire. I got 171N for that answer and then I applied it to S= F/A. I found my S to be about 340163 N/m^2. I don't know whether to use that S for S=Ye or not. Where do I go from here?
 
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  • #2
I haven't check your numbers, but yes, the tensile stress is the tension force divided by the cross-sectional area, and this is the stress that goes into your equation involving young's modulus.
 

FAQ: How Much Does a Steel Wire Stretch When Supporting Moving Masses?

1. What is stress and strain in the context of steel wire?

Stress and strain refer to the amount of force and deformation that a steel wire undergoes when subjected to a load. This can be measured in terms of the force per unit area (stress) and the resulting change in length or shape of the wire (strain).

2. How is stress and strain calculated for steel wire?

Stress and strain are calculated using the formula: stress = force/area and strain = change in length/original length. These values can be measured experimentally or determined using mathematical models.

3. What factors can affect the stress and strain of steel wire?

The stress and strain of steel wire can be affected by various factors such as the type and quality of the steel, the diameter and length of the wire, the temperature, and the amount and direction of the applied load.

4. How does stress and strain impact the strength and durability of steel wire?

Excessive stress and strain can weaken the steel wire, making it more prone to breaking. However, a certain level of stress and strain can also improve the strength and durability of the wire by increasing its resistance to deformation and failure.

5. What are some common applications of studying stress and strain in steel wire?

Studying stress and strain in steel wire is important for various industries such as construction, engineering, and manufacturing. It helps engineers and designers determine the appropriate size and type of wire to use for different applications, ensuring the safety and efficiency of structures and products.

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