# Work Done By Stretching a Steel Wire

• ehralley
In summary, the conversation discusses the calculation of the amount a wire is stretched by a hanging fish, the work done by gravity during downward motion, and the work done by a force applied to the fish. The initial attempt at solving the problem resulted in an incorrect answer, which prompted the person to seek help from their professor. The professor recommended using Young's Modulus and the formula W=0.5kx^2, but the answer was still incorrect. The professor then suggested calculating a second value for the spring constant, which led to confusion and questioning of their expertise. The expert summarizer advises the person to try again and not rely solely on the professor's guidance.
ehralley

## Homework Statement

An angler hangs a 5.50 kg fish from a vertical steel wire 1.30 m long and 4.32×10^-3 cm in cross-sectional area. The upper end of the wire is securely fastened to a support.

Calculate the amount the wire is stretched by the hanging fish. (I found this to be 8.11x10-4 m)

The angler now applies a force F to the fish, pulling it very slowly downward by 0.569mm from its equilibrium position. For this downward motion, calculate the work done by gravity. (I found this to be 3.07x10^-2 J)

For this downward motion, calculate the work done by the force F.

## Homework Equations

E=FL_0/A_0ΔL
W=Fd
My prof reccomended using: k=EA_0/L_0 and W=0.5kx^2

## The Attempt at a Solution

Using Young's Modulus, F=EA_0ΔL/L_0
F=(2x10^11 N/m)(4.32x10^-7 m ^2)/(1.300811 m)
Solving for F=37.8 N

W=Fd
W=(37.8 N)(0.000569 m)
W=2.2x10^-2 J

Then I emailed my prof and he said to do it like this:

k=EA_0/L_0
k=(2x10^11 N/m)(4.32x10^-7 m^2)/(1.300811 m)
k=66420 N/m

W=0.5kx^2
W=(0.5)(66420 N/m)(0.000569 m)^2
W=1.08x10^-2 J

The stretch done by the freely hanging fish comes out to .00162 m. Your answer is off by a factor of two, and I'm wondering if you forgot to divide by .5 somewhere.

You correctly calculated the work done by gravity (during angler stretching).

Your prof then says to do this:
k=(2x10^11 N/m)(4.32x10^-7 m^2)/(1.300811 m)

At this point I must question if he/she is really a prof and really not just a T.A. What he or she has done is to ask you to calculate a SECOND value for k - for k, the spring CONSTANT! The same spring should not have two different values for k. When doing this problem, the distance used in calculating the potential energy should always be measured as the displacement from the wire's prestressed length of 1.30 m. Then you're going to need to subtract from this the work done by gravity calculated using the total displacement.

Give it another try and give up on the idea that the "prof" is always right.

## 1. What is work done by stretching a steel wire?

Work done by stretching a steel wire refers to the amount of energy required to stretch the wire from its original length to a new length. This work is typically measured in joules.

## 2. How is the work done by stretching a steel wire calculated?

The work done by stretching a steel wire can be calculated by multiplying the force applied to the wire by the distance the wire is stretched. This can be represented by the equation W = F * d, where W is the work done, F is the force, and d is the distance.

## 3. What factors can affect the work done by stretching a steel wire?

The work done by stretching a steel wire can be affected by several factors, including the initial length and thickness of the wire, the amount of force applied, and the type of material the wire is made of. Environmental factors such as temperature and humidity can also play a role.

## 4. Is the work done by stretching a steel wire reversible?

No, the work done by stretching a steel wire is not reversible. When a force is applied to stretch the wire, its molecular structure changes, making it difficult to return to its original length without permanently deforming the wire.

## 5. What are some real-world applications of work done by stretching a steel wire?

The concept of work done by stretching a steel wire is used in various fields, such as engineering, construction, and physics. It is often used in designing and testing structures such as bridges and buildings, as well as in the development of new materials and products. It is also a fundamental concept in understanding the behavior of springs and elastic materials.

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