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

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To ensure a car completes a loop-the-loop ride without falling off at the top, it must maintain sufficient speed at point B. The minimum height h from which the car starts must be calculated in relation to the loop's radius R. A free-body diagram reveals that the gravitational force must equal the centripetal force at the top of the loop to prevent the car from falling. The discussion emphasizes using potential energy (PE) and kinetic energy (KE) principles to derive the necessary speed at point B. Understanding these physics concepts is crucial for determining the minimum height required for a safe ride.
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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.
 
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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?
 
i posted a picture. Thats the link.
 
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?
 
YES. I DREW A FREE BODY DIAGRAM. It would fall off if the weight did not equal the centripital force.
 
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.
 
we just started pe, and ke
 
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?
 
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