Maximum load that a 2mm steel cable can hold.

In summary, the platform will sink 5cm if a mass of 50kg is placed on it, and the wires on the platform can only hold a maximum load of 10 327.04N before they break.
  • #1
TheSodesa
224
7

Homework Statement



A platform (m = 5,0kg) is suspended from 4 steel cables whose length is 3,0m and diameter 2mm.

a) How much further will the platform sink if a mass of 50kg is placed on the platform?

b) What is the maximum load that the wires can hold before breaking?

Homework Equations



[tex]\dfrac{\Delta F}{A} = E\dfrac{\Delta L}{L}[/tex]

The Attempt at a Solution



Part A was easy enough; simply assume that the wires remain in the elastic zone of deformation and that A doesn't change much and plug in the values. However part B baffles me, and I'm not sure where to start.

Surely the cross sectional area A doesn't go to zero as the cable breaks(division by zero)? Am I supposed to use calculus to figure out when E changes(doesn't really make sense since E is a constant for elastic situations)? How would I even do that? Does steel have documented values for when a wire of certain L and A starts deforming plastically? I couldn't find any.

I don't have the right answers for this problem, so I can't just try one of the above methods to find out if it was the correct one, not that any of them make any sense to me. If someone could point me in the right direction, that would be great.
 
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  • #2
Just as you must be given E to solve part a, you must be given the ultimate breaking stress of the cable to solve part b. The ultimate breaking stress usually assumes no change in area.
 
  • #3
PhanthomJay said:
Just as you must be given E to solve part a, you must be given the ultimate breaking stress of the cable to solve part b. The ultimate breaking stress usually assumes no change in area.

Alright, so I used Wolfram alpha to find out the ultimate breaking stress of steel and calculated the maximum force the 4 wires could take using [tex]F = pA[/tex] This gave me a value of 10 327.04N and a maximum mass of [tex]m = \dfrac{F}{g} = 1.053\cdot 10^3 kg[/tex] Seems realistic enough, but I can't be sure until Thursday when I have to turn these problems in.
 

1. What is the maximum load that a 2mm steel cable can hold?

The maximum load that a 2mm steel cable can hold depends on a variety of factors such as the type of steel, the quality of the cable, and the environmental conditions. However, on average, a 2mm steel cable can hold a maximum load of approximately 180 kilograms.

2. How is the maximum load of a 2mm steel cable determined?

The maximum load of a 2mm steel cable is determined by conducting load tests in a controlled environment. This involves gradually increasing the weight placed on the cable until it reaches its breaking point. The weight at which the cable breaks is considered the maximum load it can hold.

3. Can a 2mm steel cable hold more weight if it is thicker?

Generally, a thicker steel cable will be able to hold more weight than a thinner one. However, the maximum load also depends on other factors such as the type of steel and the quality of the cable. It is important to consult with a professional to determine the appropriate cable size for a specific load requirement.

4. What is the safety factor for a 2mm steel cable?

The safety factor for a 2mm steel cable refers to the ratio between the maximum load it can hold and the actual load being applied. The higher the safety factor, the more weight the cable can safely hold. For a 2mm steel cable, the safety factor is typically around 5:1, meaning it can hold up to 5 times its maximum load.

5. How can I ensure that a 2mm steel cable is safe for use?

To ensure the safety of a 2mm steel cable, it is important to follow the manufacturer's recommendations for maximum load and safety factor. Regular inspections should also be conducted to check for any signs of wear or damage. It is also recommended to consult with a professional to determine the appropriate cable size for a specific application.

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