A roller coaster car has the mass m when is fully loaded with passengers. The ca

Question

A roller coaster car has the mass m when is fully loaded with passengers. The car moves along the frictionless path shown in the figure. The radii of the circular segments are R1and R2. The coaster starts from rest at the initial height h. In terms of m, g, R1, and R2, caclulate:

a) The maximum value of the height h such that the coaster would reach point B without flying from the track?

b) For a known value of height h, what is the magnitude and direction of the force exerted by the track on the coaster at the point A?

path shown in the figure. The radii of the circular segments are Ri and R2. The coaste initial height h. In terms of m, g, R,, and R2, calculate: The maximum value of the height h such that the coaster would reach point B track? Justify your answer with a free body diagram For a known value of the height h, what is the magnitude and direction of the t track on the coaster at the point A? Justify your answer with a free body diagr a) b)

Explanation / Answer

at bottom point A all poential energy will be convert into KE

mgh = 1/2*mv^2

at point A

Fnet = N - mg

Fnet = mv^/R1

mv^2 = 2mgh

2mgh/R1 = N - mg

2mgh = R1( N - mg )

h = R1(N-mg)/2mg

part b )

The forces on mass m, the roller-coaster vehicle, are its weight mg pointing down and the force the track exerts Fn pointing up

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