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 A?i and R2. The coaster starts from rest at the initial height h. In terms of m, g, h, and Rlt calculate: The magnitude and direction of the force exerted by the track on the coaster at the point A? Justify your answer with a free body diagram. What should be the minimum value of the radius R2 such that the coaster would reach point B without flying from the track? Justify your answer with a free body diagram.

Explanation / Answer

for the first loop we have its weight pointing downward which the track must push equally hard back (Newton's 3rd law)

and the track is supplying centripetal force

Ftot=mv^2/r+mg

Fw=Fcentri

mg=mv^2/r

v=sqrt(g*r)

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