# How Does Acceleration Impact Stress and Extension in a Steel Rope?

• sirhubert
In summary, the conversation was about solving a physics problem involving a winding engine lowering a 5 tonne load at a rate of 1.4m/s2 for a distance of 10m. The participants discussed using equations such as stress=force/area and strain=extension/original length to calculate the stress and extension in a steel rope, assuming that the load was suspended from it. One participant had some confusion about where the acceleration of 1.4m/s2 came into the solution and another clarified that it was the net acceleration acting on the object. They also discussed using Newton's second law to find the tension force in the rope, which was necessary due to the object's acceleration
sirhubert

## Homework Statement

A winding engine lowers a load of 5 tonne at the rate of 1.4m/s2 for a distance of 10m. Assuming that the load is suspended from a steel rope 12mm in diameter calculate the stress and the extension in the rope after traveling this distance. Assume Esteel=200 GN/m2 and g=10m/s2

## Homework Equations

I've used the following equations to base my answer around:-
Stress=Force/Area
Strain=extension/original length
E=Stress/Strain

## The Attempt at a Solution

My attempt to answer this is as follows:
A=3.142 * (6)^2
= 113.1mm2
= 113.1*10^-6 m2

F=5*1000*g where g=10m/s2
= 5*10^4

S=F/A = (5*10^4)/(113.1*10^-6)
Stress=442 MN/m2

using:- E=stress/strain
E= 200 GN/m2
strain=(442*10^6)/(200*10^9)
strain= 2.21*10^-3

My main query is where on Earth does the 1.4m/s2 come into the answer and am I anywhere near the correct solution? This has been bugging me for quite some time now so any help would be much appreciated

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sirhubert said:
My main query is where on Earth does the 1.4m/s2 come into the answer and am I anywhere near the correct solution?
Remember that 1.4m.s-2 is an acceleration.

Thank you for the advice what a complete idiot to miss out something so basic :-)

So I need to use Force=mass x acceleration to determine the actual 'downward pull', for want of a better word, of the load.

In that case if I have (5*10^4) * 1.4 the force would be 7 *10 ^4.

Would the rest of my calculations be correct if I plugged this value in?

Cheers

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sirhubert said:

So I need to use Force=mass x acceleration to determine the actual 'downward pull', for want of a better word, of the load.

In that case if I have (5*10^4) * 1.4 the force would be 7 *10 ^4.

Would the rest of my calculations be correct if I plugged this value in?

Cheers
Careful! There are two forces acting on the mass, tension acting upwards and weight acting downwards, causing the net acceleration. Therefore;

$$mg - T =ma$$

Where the tension is the force acting on the steel cable. Does that make sense?

Also note that one tonne = 1x103kg

I do apologise for being such a numpty it's been far too many years since I last attempted anything like this so you'll have to bear with me.

Right, I presume what you're saying is mass x gravity - T = mass x acceleration
In that case, 5000x10 - T = 5000x8.6
T = 7000

That's presuming an upward acceleration of 8.6 m/s2 opposing gravity at 10m/s2 (net acceleration 1.4m/s2).

w.r.t conversion of tonnes I was trying to change the weight into Newtons, hence 1x10^4 and I think by doing so have completely confused myself. Sorry!

sirhubert said:
I do apologise for being such a numpty it's been far too many years since I last attempted anything like this so you'll have to bear with me.
No problem, that's why we're here
sirhubert said:
Right, I presume what you're saying is mass x gravity - T = mass x acceleration
Good
sirhubert said:
In that case, 5000x10 - T = 5000x8.6
T = 7000

That's presuming an upward acceleration of 8.6 m/s2 opposing gravity at 10m/s2 (net acceleration 1.4m/s2).
Your almost there, but the acceleration in the equation, is the net acceleration i.e 1.4m/s2. Do you understand why?

Hmmmm not sure! I may be on completely the wrong track here but these are my thoughts... if the object was accelerating at 10m/s2 then it would have no force against it so tension in the cable would be zero. However, if the object was stationary it would be working against the full gravitational pull so tension would be m*g. As our object is accelerating at 1.4m/s it has m*1.4 less amount of force needed to hold it (if that makes any sense) so the actual Tension would need to take that into account => mg - ma = Tension ?

So, you are proposing that the acceleration is the difference between the acceleration due to gravity and the actual acceleration? (just making sure I've read your post correctly)

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Yes, I think :-) And your explanation is a hell of a lot simpler!

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why are you taking the acceleration to be 8.6 m/s^2.
Why is that so? That is wrong.

Using Newtons second law.
f=ma. f=net force acting on the body
the two forces acting on the object are its weight and tension in the rope.
so f=mg-T

hence, mg-T=ma
the net acceration given is 1.4 m?s^2

The tension force is there in the rope because the object is accelerating otherwise there would be no tension in the rope. i.e if a=0 m/s^2

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## 1. What is stress and extension?

Stress and extension is a scientific concept that refers to the relationship between the force applied to an object and the resulting deformation or change in length of the object. It is a measure of the internal forces within a material.

## 2. What causes stress and extension?

Stress and extension can be caused by a variety of factors, such as physical forces, temperature changes, and chemical reactions. It is a natural response of materials to external stimuli.

## 3. How is stress and extension measured?

Stress is typically measured in units of force per unit area, such as pounds per square inch (psi) or newtons per square meter (N/m^2). Extension is measured in units of length, such as meters (m) or inches (in). The relationship between stress and extension is represented by a stress-strain curve.

## 4. What are the practical applications of understanding stress and extension?

Understanding stress and extension is crucial in various industries, such as engineering, construction, and materials science. It allows for the design and testing of materials to ensure their safety and durability under different conditions.

## 5. How can stress and extension be managed or controlled?

Stress and extension can be managed or controlled through various methods, such as using stronger or more flexible materials, implementing structural reinforcements, and controlling external factors that may affect the material's behavior. Proper maintenance and monitoring are also essential in managing stress and extension in structures or materials.

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