Sag in wire due to a weight (given the Young's modulus)

In summary, the wire sags due to the weight being suspended from it and the change in length is due to the tension in the wire.
  • #1
ezioauditore
1
0

Homework Statement


A mild steel wire of length 1 m and cross-sectional area 0.5*10^-2 cm^2 is stretched within elastic limit horizontally between two pillars.A mass of 100 g is suspended from mid-point.Depression at mid-point?

Homework Equations



Sag in metal rod is=WL^3/(4BD^3Y) where W=weight, l=length,b=breadth,d=depth,Y=Young's modulus.But here its a wire.

The Attempt at a Solution


I tried to calculate the k of the wire since its stretched within its elasticity limit and found out the increase in length of the wire.But could not relate the sag to increase in length.
 
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  • #2
ezioauditore said:

Homework Statement


A mild steel wire of length 1 m and cross-sectional area 0.5*10^-2 cm^2 is stretched within elastic limit horizontally between two pillars.A mass of 100 g is suspended from mid-point.Depression at mid-point?

Homework Equations



Sag in metal rod is=WL^3/(4BD^3Y) where W=weight, l=length,b=breadth,d=depth,Y=Young's modulus.But here its a wire.

The Attempt at a Solution


I tried to calculate the k of the wire since its stretched within its elasticity limit and found out the increase in length of the wire.But could not relate the sag to increase in length.
Your sag formula for the metal rod appears to be developed for a rod with a rectangular or square cross section, which is not the cross section of a typical steel wire.
The wire is not going to be in bending; it supports the load by remaining in tension.

You should analyze this problem from first principles by drawing a free body diagram showing the weight suspended between two supporting points. Without getting into catenaries and stuff, you can assume each part of the wire suspending the weight is straight. You want the tensile stress in each part of the wire to be less than the elastic limit, whatever that number is.
 
  • #3
Show your attempt with all your working.
I think it's fair to assume the wire has zero stiffness, treat it as a string not a beam (or rod).
Draw a free body diagram of the weight and show how tension varies with angle (note how tension goes to infinity as theta goes to zero). Extension/sag depends on tension and tension depends on sag...
 
  • #4
+1

I would make TWO drawings..

1) A free body diagram showing the forces acting on the weight. This should lead you to equations - hint it's a statics problem.
2) A diagram showing the wire straight and deflected by the weight. Some geometry will give you an equation for the change in length of the wire(s).

Eventually you will have enough equations to solve it all.
 

Related to Sag in wire due to a weight (given the Young's modulus)

What is sag in wire?

Sag in wire is the amount of vertical displacement or deflection that occurs when a weight is applied to the wire. It can also refer to the curvature or drooping of the wire.

How is sag in wire affected by a weight?

The amount of sag in wire is directly proportional to the weight applied to it. As the weight increases, the sag in the wire also increases.

What is Young's modulus?

Young's modulus, also known as the modulus of elasticity, is a measure of the stiffness or rigidity of a material. It is the ratio of stress to strain and is a constant value for a given material.

How does Young's modulus affect sag in wire?

The sag in wire is inversely proportional to the Young's modulus of the material. A higher Young's modulus means the material is stiffer and will experience less sag when a weight is applied.

Are there any other factors that can affect sag in wire?

Yes, there are other factors that can affect sag in wire such as the diameter and length of the wire, the type of material, and the temperature. These factors can also impact the Young's modulus of the material and therefore influence the amount of sag in the wire.

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