Rollercoaster Physics: Minimizing h for a Safe Loop-the-Loop Ride

[ledhead86]

Riding a Loop-the-loop. A car in an amusement park ride rolls without friction around the track shown in the figure. It starts from rest at point A at a height h above the bottom of the loop. Treat the car as a particle.

http://community.webshots.com/user/mmaddoxwku"

What is the minimum value of h (in terms of R) such that the car moves around the loop without falling off at the top (point B)?

I have no clue what to do.

 

[lightgrav]

why WOULD it fall off at point B?

What's the shape of the path you WANT it to travel on?

Did you draw a Free-Body-Diagram of the coaster at B?

 

[ledhead86]

i posted a picture. Thats the link.

 

[lightgrav]

What I asked was, did YOU draw the Forces that act on the coaster,
and label them according to what caused them?
Why do we do that all the time?

 

[ledhead86]

YES. I DREW A FREE BODY DIAGRAM. It would fall off if the weight did not equal the centripital force.

 

[lightgrav]

so set the weight equal to m v^2/r, and solve for v needed at top.

Now, how to get that speed there ...
have you done PE and KE , yet? that's the best approach here.

 

[ledhead86]

we just started pe, and ke

 

[lightgrav]

perfect.
The PE_gravitational at the start (height H) + Work done by friction (=0)
becomes PE_grav + KE at point B.

What's the height at B? What KE did you need there?