Determine the smallest diameter rope that can safely support

In summary, to determine the smallest diameter rope that can safely support an expensive sculpture hanging from two ropes, you will need to find the tension in each rope and then use the strength rating of the rope to calculate the necessary cross-sectional area and diameter. This can be done by using the given equations and information, such as the angle at which the ropes will hang and the weight of the sculpture.
  • #1
StephenDoty
265
0
An artist friend of yours needs help hanging a sculpture from the ceiling. For artistic reasons, she wants to use just two ropes. One will be from vertical, the other . She needs you to determine the smallest diameter rope that can safely support this expensive piece of art. On a visit to the hardware store you find that rope is sold in increments of diameter and that the safety rating is pounds per square inch of cross section. What size (diameter) rope should you buy?
Give your answer to the nearest 1/8 inch.

Fx= T2sin60 - T1sin(30)= 0
Fy= (T1cos30 + T2cos60) -mg = 0

T1= (T2sin60)/ sin30

mg= ((T2sin60)/ sin30) cos30 + T2cos60

mg = 1.5 T2 + .5T2
mg = 2T2
T2= mg/2 where T2 is the 60 degree
T1= T2sin60/sin30

If you change g=9.8 to 32
T2= 500 * 32/2= 8000

So pi(n/16)^2 * 4000 > or equal to T2
so pi(n/16)^2 * 4000 > or equal to 8000
pi(n/16)^2 > or equal to 2


What do I do now to find the needed diameter?
PLEASE HELP! I have to complete this by Tomorrow

Stephen
 
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  • #2
Realize that you left out essential information when you presented the problem. For example, what's the strength rating of the rope?

Once you find the tension in each rope, you just need to find the minimum (I presume) diameter of rope that would survive such tension. If the rope is rated at X lbs/in^2, find the cross-sectional area of rope needed. Then convert that area to a diameter: [itex]A = \pi r^2 = \pi (d/2)^2[/itex].
 
  • #3
, to find the needed diameter, we can use the formula for the area of a circle, which is A = πr^2. In this case, we already know that the safety rating is 4000 pounds per square inch, so we can set up the equation like this:
4000 = πr^2
Next, we can solve for r by dividing both sides by π and then taking the square root:
r = √(4000/π)
This gives us a radius of approximately 35.64 inches. However, since we are looking for the diameter, we can simply double this value to get a diameter of approximately 71.28 inches.
Since the rope is sold in increments of 1/8 inch, we should round up to the nearest 1/8 inch, giving us a final diameter of 71.375 inches. Therefore, you should buy a rope with a diameter of 71 3/8 inches to safely support the sculpture.
 

Related to Determine the smallest diameter rope that can safely support

1. What factors determine the smallest diameter rope that can safely support a weight?

The smallest diameter rope that can safely support a weight is determined by several factors including the type of rope, the material it is made of, the weight being supported, and the intended use of the rope. Other factors such as the condition of the rope and the method of attachment also play a role.

2. How do I calculate the minimum safe diameter for a rope?

To calculate the minimum safe diameter for a rope, you will need to consider the weight being supported and the type of rope being used. Generally, a thicker diameter rope will be able to support more weight. You can also consult with a rope manufacturer or use online calculators to determine the minimum safe diameter for your specific needs.

3. Can a thinner rope be used if it is made of a stronger material?

In some cases, a thinner rope made of a stronger material may be able to support the same weight as a thicker rope. However, it is important to always follow the manufacturer's recommendations and not exceed the weight limit for the rope. Using a thinner rope than recommended could compromise its strength and safety.

4. What safety precautions should be taken when using a rope with a smaller diameter?

When using a rope with a smaller diameter, it is important to regularly inspect the rope for signs of wear and tear. Additionally, make sure to properly secure the rope and never exceed the weight limit recommended by the manufacturer. It is also recommended to have a backup or support system in place in case the rope fails.

5. Are there industry standards for determining the smallest diameter rope that can safely support a weight?

Yes, there are industry standards for determining the smallest diameter rope that can safely support a weight. These standards often vary depending on the intended use of the rope, such as in rock climbing or industrial applications. It is important to follow these standards and consult with experts to ensure the safety of using a rope for any specific purpose.

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