# Homework Help: Loop in a Rollercoaster

1. Apr 13, 2010

### Breanne

1. The problem statement, all variables and given/known data
I am trying to calculate the speed and force needed to make a marble complete a loop in the rollercoaster that i have been instructed to make. I do not know how to calculate f though. I can not use v=d/t becuase I cant find time until the rollercoaster is built which I cannot build until I find the force needed to get the marble to go through the loop. How do i find f?
= 0.11 m
mass = approx 3.56g

2. Relevant equations
T = 1/f
v = 2πr/T
FR =mv^2 / r

3. The attempt at a solution
v = 2πr/T
= 2πr/(1/f)
= 2π0.11/(1/f)
=0.6911503838/(1/f)
FR = mv^2/r
= 3.56v^2 / 0.11
= 32.36363636v^2
= 32.36363636(0.6911503838/(1/f))

π is supposed to be pi, the alt code I found did not work sorry

2. Apr 14, 2010

### PhanthomJay

You need to determine the height of the top of the takeoff ramp such that its speed at the top of the circle is just enough to prevent the marble from falling when it reaches the top of the loop. Once youi calculate the theoretical value of the marble's speeed, there will be friction and drag to consider. Use conservation of energy and the centripetalacceleration equation, and assume no contact force at the top. You'll probably have to experiment to determine the proper height, or make the ramp high enough or the radius larger to exceed the minimum value for the speed.

3. Apr 18, 2010

### Breanne

Thank you for the help, the links where especially useful :)

Last edited: Apr 18, 2010
4. Apr 18, 2010

### sean-820

I would use F=(mv^2) /r

m=mass
v=velocity