Goal: Understand radial acceleration and radial force in a non-uniform situation

Question

Goal: Understand radial acceleration and radial force in a non-uniform situation. After the dizzying ride on a roller coaster, the student decides to take a more relaxing ride on a Ferris wheel, shown at right. The wheel has a diameter of 12 m and spins at a constant rate making three complete revolutions per minute. Determine (i) the speed of the student, and (ii) the magnitude of the acceleration of the student. If the acceleration of the student is zero, state so explicitly. The physics student, wishing to test Newtons laws of motion, sits on a bathroom scale as the Ferris wheel moves through a complete circle. At the highest point in the motion, the scale reads 600 N. Determine the mass of the student (in kg).

Explanation / Answer

here,
Radius, r = 6 m
peroid , T = 3/60 = 0.05 s

as we know :
Linear Speed,v = (2*pi*r)/T

v = (2*3.14*6)/0.5
v = 75.36 m/s
The Velocity of the student 75.36 m/s

Acceleration in circular motion is :
Ac = V^2/r
Ac = 75.36^2/6
Ac = 946.521 m/s^2
The acceleration of student is 946.521 m/s^2

At heighest point F = mg
600 = m *9.8
m = 61.224 kg

mass of student is 61.224 kg

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