A Ferris wheel has a radius R of 6.3 m and rotates four times each minute. There

Question

A Ferris wheel has a radius R of 6.3 m and rotates four times each minute. There is a rider with a mass of 41.5 kg. What is the centripetal acceleration (m/s2) of the rider? Find the magnitude of the force (N) that the seat exerts on the rider at the lowest point of the ride. Find the direction (degrees from the vertical) of the force that the seat exerts on the rider at the lowest point of the ride. Find the magnitude of the force (N) that the seat exerts on the rider at the highest point of the ride. Find the direction (degrees from the vertical) of the force that the seat exerts on the rider at the highest point of the ride. Find the magnitude of the force (N) that the scat exerts on the rider half way between top and bottom (3 o'clock). Find the direction (degrees from the vertical) of the force that the seat exerts on the rider half way between the top and the bottom on the way down.

Explanation / Answer

a)a=v2/r=2r=(2*4/60)2*9.3=1.63m/s2

b)F=mg+mv2/r=41.5*9.8+41.5*(2*4*9.3/60)2/9.3=474.4N

c) Upward i.e. 0 degrees with the vertical

d)F=mg-mv2/r=339N

e)Direction is downward.

f)F=sqrt((mg)2+(mv2/r)2)=412.3N

g)Direction is Tan-1[(v2/r)/g]=9.4 degrees with the vertical or 170.56 degrees with the vertical

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