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forces physics problem - Please Help ASAP

The radius of curvature of a loop-the-loop for a roller coaster is 14.0 m. At the top of the loop, the force that the seat exerts on a passenger of mass m is 0.35mg. Find the speed of the roller coaster at the top of the loop. (Enter your answers from smallest to largest.)

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1 Answer

At the top of the coaster, there is a net force on the passenger of 0.35mg.     The centifugal force is of course mV^2/r.  The force exerted by seat on passenger can be either a downward or an upward net force.  We solve each case separately

Doing a force balance on the chair in the Y direction at the top of the loop

mV^2/r = .35mg + mg   (downward seat force on passenger)

mV^2/r = -0.35mg + mg  (upward seat on passenger)

Solve separately to get two different values for velocity.  In each case the values of m will cancel out.