Finding total energy in an RCT physics model roller coaster

[listera]

Does anyone know anything about building roller coasters on Roller Coaster Tycoon? We have to build them in Physics and I'm stuck on finding the sum of PE and KE for the model.

 

[HallsofIvy]

What information do you have to work with? PE is mgh: mass time g (acceleration due to gravity) times height. KE is 1/2 mass time speed squared. Of course, assuming no friction (and not taking into accout work done to lift the coaster up a slope), PE+ KE is a constant.

 

[Tom McCurdy]

I believe if you go into the testing mode for the coaster it tell you the speed in mph of the coaster... not sure if you can change it into m/s or something but if not you may want to convert manually for KE Calculations. Or you can cheat... again assuming no friction like HallsofIvy pointed out KE + PE = constant number so just wait until the coaster reaches the top where it is not moving then

$$KE_i + PE_i =constant$$

let the constant = X

$$\frac{1}{2}mv^2 + mgh =constant$$
but KE goes to zero because of lack of velocity

so then you know KE anywhere on the coaster assuming no breaking, boosters, or friction

to find KE anywhere else on the coaster just do

X - mgh = KE

but you may realize that if you know the KE then you will know the velocity as well

$$X - mgh = \frac{1}{2}mv^2$$

$$\frac{2(X-mgh)}{m}=v^2$$

$$\sqrt{\frac{2(X-mgh)}{m}}=v$$

remeber everything needs to be in meters for height

also there is a way you can cancel out mass... try to figure this out it makes calculations quicker.