Question

A Ferris wheel with radius 14.0 m is turning about a horizontal axis through its center (the figure (Figure 1)). The linear speed of a passenger on the rim is constant and equal to 7.49 m/s

1-What is the magnitude of the passenger's acceleration as she passes through the lowest point in her circular motion?

2-What is the direction of the passenger's acceleration as she passes through the lowest point in her circular motion?

3-What is the magnitude of the passenger's acceleration as she passes through the highest point in her circular motion?

4-What is the direction of the passenger's acceleration as she passes through the highest point in her circular motion?

5-How much time does it take the Ferris wheel to make one revolution?

Answer 1

Part A.

When person is at the lowest point in her circular motion:

ac = Centripetal acceleration = V^2/R

V = linear Speed of passenger = 7.49 m/s

R = radius of wheel = 14.0 m

So,

ac = 7.49^2/14.0

ac = 4.01 m/s^2 = magnitude of acceleration

Part B.

remember centripetal acceleration is always towards the center, So when the person is at the lowest point then at that moment center of wheel is in upward direction, So acceleration will be upward

Part C.

When person is at the highest point in her circular motion:

ac = Centripetal acceleration = V^2/R

V = linear Speed of passenger = 7.49 m/s

R = radius of wheel = 14.0 m

So,

ac = 7.49^2/14.0

ac = 4.01 m/s^2 = magnitude of acceleration

Part D.

remember centripetal acceleration is always towards the center, So when the person is at the highest point then at that moment center of wheel is in downward direction, So acceleration will be downward

Part E.

Time period is given by:

T = 2*pi/w = 2*pi*R/V

T = 2*pi*14.0/7.49

T = 11.7 sec = time taken by ferris wheel to make one revolution