A Ferris wheel with radius 14.0 m is turning about a horizontal axis through its

Question

A Ferris wheel with radius 14.0 m is turning about a horizontal axis through its center, as shown in the figure below. (Figure 1) The linear speed of a passenger on the rim is constant and equal to 6.00 m/s .

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

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

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

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

Part E How much time does it take the Ferris wheel to make one revolution?

Explanation / Answer

here,

radius , r = 14 m

speed , v = 6 m/s

the acceleration of an object in circular motion is always toward the centre of the circle,

so her acceleration will be directly upward at the bottom of the circle (lowest point) and directly downward at the top of the circle (highest point).

a)

at the lowest point

the magnitude of the accelration , a = v^2/r

a = 6^2/14

a = 2.57 m/s^2

b)

the direction of accelration is upwards

c)

the magnitude of acelration is same as 2.57 m/s^2

d)

the direction of accelration is downwards

e)

for one revolution ,

t = 2*pi*r /v

t = 2*pi*14/6

t = 14.65 s

the time taken for one revolution is 14.65 s

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