Question

You and four of your classmates are a team on Survivors. You must cross a chasm that is twenty feet wide using the following materials and some information given to you on a 3x5 card. The reward to get across the ravine is great, however nobody wants to lose their life crossing. Since you took Emch 213 way back in college, you must convince them that you can design a safe passage across for the five of you and a 4-wheeler. Given: Person 1 Person 2 Person 3 Person 4 Person 5 1 Four-wheeler 400lbs (40" wide by 48" long) 100lbs 150lbs 150lbs 200lbs 250lbs (2) 24-foot-long trees with a diameter of 5 inches weighing 12 lbs/foot (assume they are columns of uniform diameter) (3) 4' x 8' x 3/4" pieces of plywood weighing 30lbs each. (1) rope, 50 feet long, rated at 500 lbs. (1) Knife Young's modulus of these"green" trees is 2x106 psi, allowed shear stress is 2000 psi parallel to the grain and the allowed normal stress is 5000 psi (T) parallel to the grains and 2000 psi (T) perpendicular to the grains. The allowed shear in the plywood is 2000 psi and the allowed normal stress is 6000 psi in any direction and the Young's modulus is 3 x 106 psi. There is a weird net-like material stretched taut located 3" below the edges of the ledge (which are at the same level). You are told that your bridge may not touch the net or something catastrophic will happen. You must prove to all the team that you can safely pass all teammates and the four-wheeler across the chasm by showing them the calculations for deflection and maximum shear stress and maximum normal stress and the factor of safety for all possible modes of failure. Since these are trees after all, the team will want to understand the factors of safety. Of course, it is imperative that you state all your assumptions. You must also describe in 200 words or less how you will construct this bridge of passage.

Answer 1