Building a roller coaster
-The roller coaster must have at least 4 different hillls or troughs,each at different heights,and at least 1 loop.
-at one point in time,the speed of the rollarcoaster has to be greater than 40 m/s.
-To comply with federal safety standards,the speed of the dollar coaster must not exceed 60 m/s.
-we would like to limit the cost of running the roller coaster at $100.
Motor type Lifting speed Cost to run
Dc brushes motor 1 m/s $0.20/w
Ac brushed motor 2 m/s $0.35/w
Dc stepper motor 3 m/s $0.70/w
Brake type. Max chane in vel. Cost
Friction brakes 50 m/s $0.80/j
Magnetic brakes 30 m/s $0.20/j
Must include
1.A full sketch of roller coaster
2.label important dimensions
A) height of initial hills and each subsequent
B)length and angle of lift hills
C)radius of loop
3.number of cars in trains,mass of each car
4.toatl length of ride track
5,locations of braking system
6.choice for lift system and braking system
7.following values correctly calculated
A) power required to lift dollarcoaster train to the top of the hill
B)velocity of roller coaster at each hill,through and right before it hits teh brakes.
C)energy dissipated by the braking system
D)cost per lauch
Answers & Comments
Verified answer
I think your first step will be to find how high the coaster might climb, knowing power costs and limit of $100.00. It costs nothing for it to come down. Then you can find PE. You need to decide which power system is cheapest, knowing all 3 have different ascent velocities. I assume the heights it rises is vertical height.
From there it could be best that the first descent should cause the maximum 60m/sec., the 40m/sec. could be going around the loop at the bottom (remember it must have enough V to not fall off the top), then you can arrange hills from there that will not stop it rising, finally arrange to have reserve for the cheapest braking for the least change in energy (the slowest V for braking from).
Actually, you might have to figure the braking cost allowed for from a set V that you decide, so use the cheapest for the final V it seems is allowed (30m/sec., magnetic brakes) and subtract that from the $100.00 before you figure the PE. It has to brake from 30m/sec., it seems. That can be done horizontally (at the ground) to minimise costs.
It sounds like fun, but I can't do it for you.