1) A person with a weight of 715 N hangs from a climbing rope 9.2 mm in diameter.
a) What is the cross-sectional area of the rope in m2?
b) What is the stress applied to the rope?
2) A particular 60 m climbing rope stretches by 0.15 m when a 715 N person hangs from it.
a) What is the strain in the rope?
b) What is the strain in the rope as a percentage?
3) Label the following features in the stress-strain curve of a hypothetical material seen below:
- Toe region
- Elastic region
- Yield point
- Plastic Region
- Ultimate Strength
- Rupture Point
- Failure Region
Data adapted with permission from rubber band stress-strain data originally acquired by Umpqua Community College Students: Brittany Watts, Ashlie DeHart, Hanna Wicks and Juan Martinez.
4) Use the data in the previous graph to determine the elastic modulus of the hypothetical material. Be sure to convert the strain from % stretch back to fractional stretch before doing your calculations.
5) Answer the following questions regarding the material used to create the created the stress-strain graph above.
a) How much force could be applied to a 2 m x 2 m x 10 m long block of this material before reaching the ultimate strength?
b) When operating in the elastic region, how much additional stress would be required to cause an additional strain of 0.01?
c) What force would cause that amount of stress you found in part b on the 2 m x 2 m block?
d) What actual length would the 10 m long material stretch when put under the strain of 0.01?
e) What is the effective spring constant of this 2 m x 2 m x 10 m long block of this material?