# Log hanging from 2 steel wires. stress/strain youngs modulus

• J-dizzal
In summary, a 128 kg uniform log hangs by two steel wires, A and B, initially with wire A 2.00 mm shorter than wire B and both with a radius of 1.15 mm. With a Young's modulus of 2.00 × 1011 N/m2 for steel, the log is now horizontal. The magnitudes of the forces on it from wire A and wire B are 924 N and 330.4 N respectively. The ratio of dA/dB can be found by solving the moment equation -FAdA+FBdB=0, which can be done in a minute or so.
J-dizzal

## Homework Statement

In the figure, a 128 kg uniform log hangs by two steel wires, A and B, both of radius 1.15 mm. Initially, wire A was 2.80 m long and 2.00 mm shorter than wire B. The log is now horizontal. Young's modulus for steel is 2.00 × 1011 N/m2.

What are the magnitudes of the forces on it from (a) wire A and (b) wire B? (c) What is the ratio dA/dB?

## Homework Equations

$$Force/Area = E (ΔL/L)$$
E=2.00x1011N/m2
L is length of wire

## The Attempt at a Solution

edit. i managed to get the forces, working on da/db

Last edited:
does this look ok for FA?
$$W/2 + dAE/2L$$
W is weight of log
d is .002m
A is area of wire
E young's modulus
L length of wire.

J-dizzal said:
does this look ok for FA?
$$W/2 + dAE/2L$$
W is weight of log
d is .002m
A is area of wire
E young's modulus
L length of wire.
Only if you assume that the wires have the weight of the log evenly distributed between them, which doesn't seem to be the case, given the problem statement.

Go back to first principles here. Write the equations of static equilibrium which govern the log.

Pay careful attention to what the problem is telling you about the lengths of the wires:

a. Wire A is 2.80 m long and was 2 mm shorter than wire B initially, which I take to mean before the log was attached.

b. After the log has been attached, the shorter wire A and the longer wire B are now both the same length, which is why the log is horizontal. This suggests that wire A has stretched more than wire B, which also implies that the force acting in wire A is greater than the force acting in wire B, after the log is attached.

c. If you figure out the ratio of the forces in wires A and B which make them the same length, then you can also figure out the location of the wires relative to the c.o.m. of the log, because you have written the equations of static equilibrium for the log and the wires.

SteamKing said:
c. If you figure out the ratio of the forces in wires A and B which make them the same length, then you can also figure out the location of the wires relative to the c.o.m. of the log, because you have written the equations of static equilibrium for the log and the wires.

Im not sure how the forces are related to distance outside of finding the moment. M=Fd.
FA/FB ≠ dA/dB

this is what i have so far;
$$-FAdA+FBdB=0$$

i still need another question though

Last edited:
Looks like you assumed that wire A will stretch 2 mm. But wire B is also going to stretch some. So wire A will need to stretch more than 2 mm in order for the final length of A to equal the final length of B.

[Edit: I now see that you mentioned that you have found the forces. I think you have the right idea that you will need to consider moments in order to get the ratio of the distances.]

TSny said:
Looks like you assumed that wire A will stretch 2 mm. But wire B is also going to stretch some. So wire A will need to stretch more than 2 mm in order for the final length of A to equal the final length of B.
Yea i happen to assumed correctly based on a sample problem in the book. I am stuck on the last part its asking for dA/dB

FA=924N
FB=330.4N

J-dizzal said:
Im not sure how the forces are related to distance outside of finding the moment. M=Fd.
FA/FB ≠ dA/dB

this is what i have so far;
$$-FAdA+FBdB=0$$

Can you solve this for the ratio of d's?

J-dizzal
J-dizzal said:
Im not sure how the forces are related to distance outside of finding the moment. M=Fd.
FA/FB ≠ dA/dB

this is what i have so far;
$$-FAdA+FBdB=0$$

i still need another question though
It's not clear what you mean by needing "another question".

You won't be able to see how the ratio of the forces is related to the location of the c.o.m. relative to the wires unless you write the equations of statics, especially the moment equation.

It's not complicated. You can do it in a minute or so.

SteamKing said:
It's not clear what you mean by needing "another question".

You won't be able to see how the ratio of the forces is related to the location of the c.o.m. relative to the wires unless you write the equations of statics, especially the moment equation.

It's not complicated. You can do it in a minute or so.

I only needed one equation which is the moment equation, yes it had two unknowns but they are solved as a ratio. I didnt realize this at first but know i do. thank you.

## 1. What is the purpose of hanging a log from 2 steel wires?

The purpose of hanging a log from 2 steel wires is to measure the stress and strain on the wires when a force is applied to the log, in order to determine the Young's modulus of the wires.

## 2. How is stress defined in this experiment?

In this experiment, stress is defined as the force applied to the wires divided by the cross-sectional area of the wires. It is measured in units of force per unit area, such as N/m2 or Pa.

## 3. What is the relationship between stress and strain in this experiment?

The relationship between stress and strain in this experiment is linear, as long as the wires are in the elastic deformation region. This means that as the stress increases, the strain (change in length of the wires) also increases in a proportional manner.

## 4. How is Young's modulus calculated in this experiment?

Young's modulus is calculated by dividing the stress by the strain. This gives a measure of the stiffness of the wires, or how much they resist deformation under a given stress.

## 5. How can the results of this experiment be used?

The results of this experiment can be used to determine the strength and elasticity of the wires, which can be useful in engineering and construction applications. They can also be used to compare different types of wires and their suitability for specific purposes.

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