How Many Steel Strands Are Needed to Safely Lower a Lift into a Mine?

In summary, a lift is used to lower miners 4000m into a mine, supported by high strength steel strands of 3mm diameter. The ultimate stress for the steel strands is 1200MPa and the allowable stress is 600MPa. The empty lift weighs 15kN and has a capacity of 20 persons, with each person weighing 800N. To calculate the number of strands required, you need to find the force and stress in each strand under the given loads and ensure that the stress does not exceed 600MPa. This can be done by including the weight of the cable itself, which can be calculated using its density and cross-sectional area. The maximum depth to which the lift can be lowered
  • #1
pvpkillerx
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A lift is used to lower miners 4000m into a mine. The lift is supported by many high strength steel strands of 3mm diameter each. The ultimate stress for the steel strands is 1200MPa and the allowable stress is 600MPa. The empty lift weighs 15kN. It has a capacity of 20 persons. The density of steel is 77kN/m3 and each person weighs 800N.
1)Calculate the number of strands required.
2)What is the maximum depth to which the lift can be lowered before the cable snaps?
I am assuming we have to use [itex]\epsilon = \sigma/E[/itex]
I am not sure how to start this question. The biggest problem I have is that I don't know how to use that equation (what each variable stands for), (and for this course we have no textbook, so I can't find any sample problems). Any help is appreciated.
 
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  • #2
The equation you have noted is for the stress-strain relationship. That is not needed for this problem.. What you need to find out is the force (P) and stress (P/A) in each strand under the given loads to be sure that there are a sufficient number of strands such that the stress does not exceed 600 MPa. You must include the weight of the cable itself, based on the given density and calculated volume... you have enough information given to calculate it's weight, and it's cross section area. You need a basic understanding of P/A axial stress.
 

Related to How Many Steel Strands Are Needed to Safely Lower a Lift into a Mine?

1. What is Hooke's Law?

Hooke's Law is a fundamental principle in physics that states the relationship between the force applied to an elastic material and the resulting deformation or change in length. It states that the force applied is directly proportional to the extension or compression of the material, as long as the elastic limit is not exceeded.

2. Who discovered Hooke's Law?

Hooke's Law was first discovered and stated by the English scientist, Robert Hooke, in 1676. He observed the behavior of springs and elastic materials and found that the force applied to them was directly proportional to the displacement or change in length of the material.

3. What is the equation for Hooke's Law?

The equation for Hooke's Law is F = -kx, where F is the force applied, k is the spring constant or stiffness of the material, and x is the displacement or change in length of the material. This equation shows the direct relationship between force and displacement in an elastic material.

4. What is the difference between elasticity and plasticity?

Elasticity is the property of a material to return to its original shape and size after being deformed under stress. Hooke's Law applies to elastic materials, which can only be deformed up to a certain limit without causing permanent damage. Plasticity, on the other hand, refers to the permanent deformation of a material under stress. Plastic materials do not follow Hooke's Law and do not return to their original shape after being deformed.

5. How is Hooke's Law used in real life?

Hooke's Law is used in various real-life applications, such as in the design of springs, shock absorbers, and elastic bands. It is also used in engineering and construction to determine the amount of force needed to stretch or compress materials without causing permanent damage. Hooke's Law is also used in the medical field, for example, in orthodontics, to determine the amount of force needed to move teeth into their desired position.

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