Calculate Young's Modulus and Change in Diameter of Nylon Rope

In summary, a mountaineer's nylon rope extends by 1.5 m when carrying an 80 kg load. The total length of the rope is 50 m and its diameter is 10 mm. The problem is determining the Young's modulus of the material and the change in diameter due to stress with a Poisson's ratio of 0.1. However, this question should be posted in the appropriate subforum for homework problems and show effort before seeking help.
  • #1
hcchong
3
0
A piece of nylon rope used by a mountaineer extended by 1.5 m when carrying the load of the 80 kg mountaineer. If the total length of the rope is 50 m and its diameter is 10 mm, determine the Young’s of this material. If the Poisson’s ratio of nylon is 0.1, determine the change in the diameter of the rope due to this stress.
 
Physics news on Phys.org
  • #2
1. This is a homework/textbook problem. Please post it in the appropriate subforum; it does not belong here, in solid state physics.

2. We do not respond to such questions unless they conform to the posting guidelines for coursework problems. Specifically, we can not help you unless you show your effort first.
 
  • #3


To calculate Young's Modulus, we can use the equation E = (F/A) / (ΔL/L), where E is Young's Modulus, F is the applied force, A is the cross-sectional area of the material, ΔL is the change in length, and L is the original length. In this case, the force applied to the nylon rope is the weight of the mountaineer, which is 80 kg multiplied by the acceleration due to gravity, 9.8 m/s^2, which gives us a force of 784 N. The cross-sectional area of the rope can be calculated as πr^2, where r is the radius of the rope. In this case, the radius is half of the diameter, so it is 5 mm or 0.005 m. The original length of the rope is 50 m, and the change in length is 1.5 m. Plugging these values into the equation, we get E = (784 N) / (π(0.005 m)^2) / (1.5 m / 50 m) = 156.8 N/m^2.

To determine the change in diameter of the rope due to this stress, we can use the equation ΔD/D = -ν(ΔL/L), where ΔD is the change in diameter, D is the original diameter, ν is the Poisson's ratio, ΔL is the change in length, and L is the original length. In this case, ν is given as 0.1, ΔL is 1.5 m, and L is 50 m. Plugging these values into the equation, we get ΔD/D = -(0.1)(1.5 m / 50 m) = -0.003, or a decrease of 0.3%. This means that the diameter of the nylon rope would decrease by 0.03 mm under the stress of the mountaineer's weight.

In conclusion, the Young's Modulus of the nylon rope is 156.8 N/m^2 and the change in diameter is 0.3%. These calculations can help us understand the strength and flexibility of the material and how it will behave under different loads. It is important for mountaineers and other users of nylon rope to be aware of these properties in order to ensure their safety and the proper use of the material.
 

1. How do you calculate Young's Modulus of a nylon rope?

To calculate Young's Modulus, also known as the modulus of elasticity, of a nylon rope, you need to measure the stress and strain of the rope. The formula for Young's Modulus is stress divided by strain. Stress is the force applied to the rope divided by the cross-sectional area of the rope, and strain is the change in length of the rope divided by its original length.

2. What is the significance of Young's Modulus for a nylon rope?

Young's Modulus is a measure of the stiffness and elasticity of a material. For a nylon rope, it determines how much stretch and deformation the rope can withstand before breaking. A higher Young's Modulus indicates a stiffer and stronger rope.

3. How does the diameter of a nylon rope affect its Young's Modulus?

The diameter of a nylon rope has a direct impact on its Young's Modulus. A thicker rope will have a higher Young's Modulus, meaning it is stiffer and stronger, compared to a thinner rope. This is because a thicker rope has a larger cross-sectional area, allowing it to withstand more stress without deforming.

4. Can the Young's Modulus of a nylon rope change over time?

The Young's Modulus of a nylon rope can change over time due to factors such as exposure to UV light, moisture, and repeated use. These factors can cause the nylon fibers in the rope to degrade and lose their elasticity, resulting in a decrease in Young's Modulus.

5. How can the change in diameter of a nylon rope be calculated?

The change in diameter of a nylon rope can be calculated by measuring the rope's diameter before and after subjecting it to a known amount of stress. The difference in diameter divided by the original diameter gives the percentage change in diameter, which can then be used to calculate the change in Young's Modulus.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
5K
  • Introductory Physics Homework Help
Replies
2
Views
940
  • Introductory Physics Homework Help
Replies
6
Views
2K
Replies
23
Views
2K
  • Introductory Physics Homework Help
Replies
19
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
5K
  • Introductory Physics Homework Help
Replies
1
Views
2K
Back
Top