What Forces Act on a Roller-Coaster Car in Nonuniform Circular Motion?

[afterjames]

A roller-coaster car has a mass of 500 kg when fully loaded with passengers. (a) If the vehicle has a speed of 20.0 m/s at point A, what is the force exerted by the track on the car at this point? (b) What is the maximum speed the vehicle can have at point B and still remain on the track?

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Is the answer to (b) dependent on the tangential acceleration?For part (a), I found the force exerted on the car by the track to be
m( g - ( v^2 ) / R1 ) = 500( 9.8 - ( 20.0 / 10.0 ) ) = 3900 N.

Then for part (b), I have
0 = mg( ( vmax^2 ) / ( R2 * g ) - cos 0 ) -> vmax = ( g * R2 )^( 1 / 2 ) =
( 9.8 * 15 )^( 1 / 2 ) = 12.1 m/s.

Am I in the ball-park?

 

[lightgrav]

well, your first statement implies that if it was moving FASTER at A,
the track would push LESS hard ... by 100 m/s it wouldn't even NEED a track.

mg is a real Force, downward (left side of eqn)
. . . . v^2/R is an acceleration (on right side of eqn)
. . . . F_track is a real Force (on the left side of eqn)

same sign mistake in "2"