Project 1: Part 1: Aspen Extreme

Honors Project

Joe Bob runs a ski resort with the best ski hills in the area. The only thing he lacks is an awesome tubing hill with a tuber lodge at the top. Joe hires your group to design a hill with a mechanism to pull tubers from the back of the hill up to the top so people can slide down the other side and have lots of fun.

Due to budget cuts, Joe Bob cannot produce enough snow to cover the entire hill. There is a 5 meter segment of dirt at the base of the hill. Keep in mind that in order to stay within safety regulations, the tubes should not go faster than 3 $m/s$ during any part of the lift. Joe needs to know the projected cost of the operation of your mechanism.

Tutor Questions:

Question:
Expected Answer:

Question:The mechanism breaks and a tuber is stranded on the hill. How would the work done by the mechanism change if the tube was pulled at an angle from the second floor of the lodge at the top of the hill? Illustrate what will happen with a force vs. distance graph and a work vs. distance graph that models this situation.

Expected Answer:The work depends on the angle between the direction of the force applied and the direction of the change in distance. &W = Fcos(θ)*d$

Question:How much power does the mechanism need to operate successfully?

Expected Answer:

$$t=d/v$$ $$t=(h)sin(θ)/(v)$$ $$P = W_{motor}/t (watts)$$

Question: How would you change your system to use energy to solve this problem?

Expected Answer:

$$Work -> System: Tube$$ $$Energy -> System: Earth+Tube+Motor$$

Question: Explain how you determined the sign of each component doing work on your system.

Expected Answer:
$W>0$ if force acts in same direction of displacement $(W_{motor})$
$W<0$ if force acts in opposite direction of displacement $(W_{grav}$ & $W_{friction})$

Question: How would the work done by gravity change when the tuber slides down the hill if you increased or decreased the angle of the hill?
Expected Answer: It doesn't change because the height of the hill remains the same so the work done by gravity remains the same. $(K=W_{surr})$

Common Difficulties:

Main Points:

Once you are the top of hill, Joe wants the fun to begin. In order to keep up with the competition, the tubing hill needs to be exciting. There is a ramp at the bottom of the hill where the tubers will be launched through the air. A 5m diameter flaming hoop is located 15m from the ramp and 10m off the ground. Ensure the tubers complete this stunt through the hoop safely. Totally rad dude!!