Question

Mini Project 3:
You wake up to find yourself in the Marvel Universe (Earth-43), under the tutelage of the Avengers. Nick Fury’s Helicarrier, the Bellerophon, is now a make-shift academy for budding super-heroines/heroes. During an attack by Dr. Doom, you and your groupmates must abandon the helicarrier. All the flying superheroes have bailed out, and the aircraft are destroyed. Luckily you found a supply closet with a plot device for cutting indestructible metals as well as giant spools of Unobtainium, Vibranium, and Adamantium.
You and you group rush to the edge of the ship. The one of you, with the uncanny power to judge distances very accurately, guesses the ship is currently at an altitude of 2.0 kilometers. You need to cut the exact length of cable to reach the ground below, if you waste any of these materials, Agent Fury will definitely kick you out of the program. You just sat through a lecture on rare metals and know that each metal has a simple cubic structure as well as the following facts about the metals on the spools:

Elements Below

Element: Adamantium
Bond Length (m):2.3x10^10
Effective Bond Stiffness (N/m):
4.7x10^2

Element: Unobtainium
Bond Length (m):3.5x10^10
Effective Bond Stiffness (N/m): 3.8x10^2

Element: Vibranium
Bond Length (m):4.3x10^10
Effective Bond Stiffness (N/m):
1.2x10^2

Each cable has a diameter of 2.0 cm, and you can cut it to any length you choose. Pick a cable material, and calculate how long it will need to be to reach from the edge of the ship to the ground.

Answer 1

I would choose Vibranium, as it has the highest value of bond length. As the situation makes it mandatory that we are not to waste any material, Vibranium is the best option, as we would need to use less quantity of it.

Length of Vibranium required: Distance between edge of the ship and ground = 2 km = 2000m

The stength/tolerance capacity of the metal =Bond length/Bond stiffness = 4.3x10^10/1.2x10^2

As I'm unable to understand the meaning of the symbol "^", I'm not doing the calculation. Kindly assist to do it from your end.

Length required (in meters) = (Tolerance capacity x diameter (0.002 m)) / 2000