Problems involving Elasticity

  1. Parn is exploring a dark underground dungeon when he enters a very tall room -- so tall that the ceiling is invisible in the darkness. There is an aluminum wire of radius r = 8 mm hanging in the middle of the room. The wire runs up into the darkness, so Parn can't see the upper end. The lower end of the wire is exactly h1 = 1.50 m above the floor.

    Parn grabs onto the wire and climbs a short distance upwards. His companion, Ghim the dwarf, sees the bottom end of the wire drop slightly as Parn hangs from the wire. The wire is now only h2 = 1.48 above the floor.

    Ghim pulls out his HP-15C and punches a few buttons. He looks up and says, "Yo, Parn, take your time. That's going to be a loo-oo-oo-ong climb."

                 Q:  How long is the wire?  

  2. Polly has a nice diamond ring. It's an unusual cut: the diamond is a cube, 5 mm on each side.

    Polly wonders what will happen if she places her diamond into the special high-pressure anvil in the geophysics research lab. "It ought to shrink," she figures, "but by how much?" Polly doesn't know that the bulk modulus of diamond is B = 4.4 x 10^(11) N/m^2.

    Polly sets the anvil to P = 500,000 atmospheres and presses the "Crush" button. She watches carefully and sees that her diamond DOES shrink ...

                 Q:  What is the new size of her diamond?

  3. Joe Anoxia is trapped in a crevasse on the alpine glacier! You're the leader of a rescue team. You must climb up to the crevasse, lower a cable a distance of L = 100 m to Joe, and pull him up. Unfortunately, the climb to reach the crevasse is technical work over sheer rock faces. You figure you can allow at most M = 5 kg for the mass of the cable, in addition to all the other equipment you must carry.

    You know all about stress and strain. Even a tiny amount of stretching could throw everyone off balance, so you want to minimize the change in the cable's length as it hoists Joe to safety.

    Which Material of Engineering Interest would make the best cable for your purpose? Assume that you purchase cables made of spun fibers of any of these materials.