What is the maximum force on a rod that links the center of a ferris wheel of radius 10 m to the end where a mass of 200 kg is attached to it if the wheel is turning at 4 rpm.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A ferris wheel rotates in a vertical plane, as a result a mass attached at the end of the wheel has two forces acting on it; one of them is the centrifugal force due to the rotation of the wheel and the other is the gravitational force of attraction due to the Earth acting on the mass. The maximum force on a rod linking the center of the ferris wheel to the end where a mass is attached to it is equal to the sum of the gravitational force and the centrifugal force. The force exerted on the rod by the mass varies as the wheel rotates and is at its maximum when the mass is at the lowest position.

At the bottom, the force exerted on the rod by the mass is equal to F = m*g + m*w^2*r where m is the mass, g is the gravitational acceleration, w is the angular velocity and r is the distance of the mass from the center.

w = 2*pi*(4/60) = 0.419 rad/s

The force F = 200*9.81 + 200*(0.419)^2*10 = 2312.9 N

The maximum force that the rod linking the center of the ferris wheel to the mass of 200 kg at the edge of the wheel is 2312.9 N

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