A circular-motion addict of mass 85 kg rides a Ferris wheel around in a vertical circle of radius 10 m at a constant speed of 6.1 m/s.
(a) What is the period of the motion?
__________s
(b) What is the magnitude of the normal force on the addict from the seat when both go through the highest point of the circular path?
_________N
(c) What is it when both go through the lowest point?
__________ N
speed is 2PIr/T solve for T
normal seat at top=mg-mv^2/r
lowert point mg+mv^2/r
To answer these questions, we need to apply the concepts of centripetal force, gravitational force, and Newton's second law.
(a) To find the period of the motion, we can use the formula for the period of uniform circular motion:
T = 2π * r / v
Where T is the period, r is the radius of the circular path, and v is the velocity of the object.
Using the given values, we substitute r = 10 m and v = 6.1 m/s into the formula:
T = 2π * 10 m / 6.1 m/s
= 20π / 6.1
≈ 10.3 s
So, the period of the motion is approximately 10.3 s.
(b) At the highest point of the circular path, the normal force and gravitational force combine to provide the necessary centripetal force. Since the rider is not accelerating vertically, the vertical components of the forces cancel out, resulting in the equation:
N - mg = 0
Where N is the magnitude of the normal force and mg is the gravitational force (mass multiplied by acceleration due to gravity).
Substituting the given mass m = 85 kg and acceleration due to gravity g = 9.8 m/s², we can solve for N:
N - (85 kg * 9.8 m/s²) = 0
N - 833 N = 0
N ≈ 833 N
So, the magnitude of the normal force on the addict from the seat when both go through the highest point is approximately 833 N.
(c) At the lowest point of the circular path, the normal force and gravitational force add up to provide the necessary centripetal force. In this case, the equation becomes:
N + mg = 0
Substituting the same values as before, we find:
N + (85 kg * 9.8 m/s²) = 0
N + 833 N = 0
N ≈ -833 N
The negative value of the magnitude of the normal force indicates that it acts in the opposite direction to the gravitational force. Therefore, the magnitude of the normal force on the addict from the seat when both go through the lowest point is approximately 833 N in the upward direction.