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Lift Cable Correct Loadings This Time

12/30/2010 11:04 AM

A designer wishes to calculate the thickness of a steel cable for suspending a passenger lift. The total length of the cable supporting the lift when it is at the ground floor is 14 m.

The mass of the lift when full of passengers is 800 kg.

The designer has decided to incorporate a safety factor of 10 into the lift cable. So the cable must be able to withstand 10 times the load it will actually be exposed to in service before it fails.

The steel selected for the cable has a failure stress of 1050 MN m-2

Using this information, what is the required diameter of the cable.

Assuming that the cable is a single piece of steel, with a circular cross section.

Ignore any effects of the cable weight.

F= m x g

F= down force on the cable.

m= mass expressed in kg

g = 10 ms-2

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Guru
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#1

Re: lift cable correct loadings this time

12/30/2010 11:40 AM

Okay, you've admitted this is homework. So let me ask you some questions.

1. What is the density of the steel used for the cable?

2. What is the formula for finding the mass of a cylinder, given the length, diameter and density?

3. What would be the total mass of the lift plus the cable itself?

4. What is the minimum force needed at the top of the cable to lift this mass?

Also -- can you answer these questions? If not, why not?

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Guru
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#2
In reply to #1

Re: lift cable correct loadings this time

12/30/2010 11:51 AM

I missed this in my earlier read-through:

Ignore any effects of the cable weight.

It makes the problem even easier if you can ignore the weight of the cable.

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#3

Re: Lift Cable Correct Loadings This Time

12/30/2010 1:23 PM

This is about the weirdest gedankenexperiment I've ever seen. Who would ever use a single-strand cable?

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#4

Re: Lift Cable Correct Loadings This Time

12/30/2010 1:49 PM

"the cable is a single piece of steel, with a circular cross section."

That's NOT cable! It's rod stock. Anyway, we're ignoring it, except to size it?????????

I'd think you would want to get close to reality, but what do I know?

This makes no sense. Totally unrealistic, and tell the teach I said so.

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#5

Re: Lift Cable Correct Loadings This Time

12/30/2010 2:12 PM

Please forward your completed design to the Sugar Loaf Ski Resort in Maine as they are in dire need of a new Design.

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Guru
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#6

Re: Lift Cable Correct Loadings This Time

12/30/2010 3:11 PM

(Pi/4)*d2*(1,050,000,000) = 800*10*10. (The first 10 is for the artificial g; the second is the safety factor.) Solve for d.

Meters are strange units for measuring cable diameters, unless maybe the Golden Gate Bridge.

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Guru
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#7
In reply to #6

Re: Lift Cable Correct Loadings This Time

12/30/2010 4:12 PM

We were often told to measure everything in meters as it is the standard unit, yes it made it all a whole lot more confusing but you get used to writing 2.3x10^-3 for example

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