A 36.0-kg child takes a ride on a Ferris wheel that rotates four times each minu

Question

A 36.0-kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 20.0 m. (a) What is the centripetal acceleration of the child? Magnitude m/s^2 direction (b) What force (magnitude and direction) does the seat exert on the child at the lowest point of the ride? magnitude N direction (c) What force does the seat exert on the child at the highest point of the ride? magnitude N direction (d) What force does the seat exert on the child when the child is halfway between the top and button? (Assume the Ferris wheel is rotating clockwise and the child is moving upward.) magnitude N direction degree counter-clockwise from the horizontal

Explanation / Answer

cenAngular velocity = 4 rev / min

V = 4*2*pi*R / 60 = 4.188 m/s

centripetal force = mv^2 /R = 36*4.188^2 / 10 = 63.166 m/s^2

Fc = ma

Centripetal acceleration (a) = 63.166/36 = 1.754 m/s

b.) net force the seat exert = Fc + mg

F = 63.166 + 36*9.81 = 416.326 N

c.) force exert by the seat at top of the circle = Fc - Mg

F = 63.166 - 36* 981 = 289 .994 N

d.) F = sqrt ( Fc^2 + (mg)^2 )

F = 358.76 N

315o couner clockwise from horizontal

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