Edison Tech Center Pi Day Quiz 2019

This year the Edison Tech Center is working on a mapping machine to compete in DARPA’s Subterranean Challenge. This could be used for search and rescue missions, so this year the Pi Day Quiz is all about engineering for rescues.

1) A 100m long rope is wrapped around a perfectly round tree which is 2m away from a 90m deep hole. Approximately how much rope is wrapped around the tree with a 1m diameter, if four wraps are used?

2) Will the rope from question 1 reach the bottom of the hole?

3) A rope is wrapped around a perfectly round tree. If the amount of friction which holds the rope is (Number of Wraps x (coefficient of friction of rope on tree) x circumference of tree) + (Number of Wraps-1)x(coefficient of friction of rope on rope) x circumference of tree)), what happens if we go from 3 wraps around the tree to 4?

In this example, use these values:

diameter of tree=20 units

coefficient of friction of rope on rope = 0.5

coefficient of friction of rope on tree = 0.3

4) A rope is wrapped around a perfectly round tree. What happens if we find a tree which has a diameter of 24 units instead of 12 units? Use the equation the amount of friction which holds the rope is (Number of Wraps)x(coefficient of friction of rope on tree) x circumference of tree) + (Number of Wraps-1)x(coefficient of friction of rope on rope) x circumference of tree)).

In this example, use these values:

Number of Wraps=3

coefficient of friction of rope on rope = 0.5

coefficient of friction of rope on tree = 0.3

5) Caver Static Rope is designed to minimize rope stretch. As a result, it is stronger when straight than when in a knot. Design a rope hauling system that only uses three knots.

6) Design a rope hauling system using gears to lift ten times the weight that can be lifted with no gears.

7) A rappel rack is a device which winds rope around metal cylinders, known as bars, to create friction to control the speed of rope moving through. Using the equation friction = (coefficient of friction of rope on bar)x(rope on bar contact area), how much more friction would there be if the diameter of the bars were doubled?

8) Design a hauling system which only uses rope, anchors, and pulleys to lift ten times the weight that can be lifted using only rope.