While at the county fair, you decide to ride the Ferris wheel. Having eaten too

Question

While at the county fair, you decide to ride the Ferris wheel. Having eaten too many candy apples and elephant ears, you find the motion somewhat unpleasant. To take your mind off your stomach, you wonder about the motion of the ride. You estimate the radius of the big wheel to be 19 m , and you use your watch to find that each loop around takes 26 s .

What is your speed?

What is the magnitude of your acceleration?

What is the ratio of the magnitude of your apparent weight to the magnitude of your true weight at the top of the ride?

Explanation / Answer

Here ,

radius of big wheel , R = 19 m

time period , T = 26 s

angular speed , w = 2pi/T

w = 2pi/26 rad/s

w = 0.241 rad/s

speed = R * w

speed = 0.241 * 19 m/s

speed = 4.59 m/s

the speed is 4.59 m/s

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magnitude of acceleration = v^2/R

magnitude of acceleration = 4.59^2/19 m/s^2

magnitude of acceleration = 1.11 m/s^2

the magnitude of acceleration is 1.11 m/s^2

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ratio of magnitude of your apparent weight to magnitude of true weight at the top = (g - a)/g

ratio of magnitude of your apparent weight to magnitude of true weight at the top = (9.8 - 1.11)/9.8

ratio of magnitude of your apparent weight to magnitude of true weight at the top = 0.89

the ratio of magnitude of your apparent weight to magnitude of true weight at the top is 0.89

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