The SkyView Ferris wheel near Centennial Park has a radius r and rotates clockwi

Question

The SkyView Ferris wheel near Centennial Park has a radius r and rotates clockwise with a constant angular rate omega. President Peterson has mass m and is riding in a gondola that makes an angle of theta = 40 degree with the x-axis as shown. (a) Calculate the magnitude of the parallel component of the contact force exerted by the Ferris wheel on President Peterson. On the diagram, sketch an arrow to represent this parallel component of the contact force acting on President Peterson. (b) What is the magnitude of the perpendicular component of the contact force exerted by the Ferris wheel on President Peterson? (c) The Ferris wheel stops so that President Peterson is suspended motionless at the exact top of the ride. Calculate the vector contact force acting on President Peterson at this instant.

Explanation / Answer

(a) Since the wheel is rotating at a constant angular rate, net parallel force is zero.

So, the parallel component of the contact force is equal to the parallel component of the weight of the President.

So, Fparallel = mgcos40o

(b) The perpendicular component of the contact force provides the centripetal acceleration to the President.

So, Fper = m2r

(c) At the top, the contact force balances the weight of the President.

So, contact force, F = mg (acting downwards)

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