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 17m , and you use your watch to find that each loop around takes 26s

What is your speed?

Express your answer to two significant figures and include the appropriate units.

What is the magnitude of your acceleration?

Express your answer to two significant figures and include the appropriate units.

What is the ratio of your weight at the top of the ride to your weight while standing on the ground?

Express your answer using two significant figures.

Explanation / Answer

Tangential speed is equal to the circumference multiplied bythe revolutions per second:

V = (1 rev / 26s)*(2?*17m) = 4.10 m/s

Centripetal acceleration is equal to:

ac = V2 /R          whereV is tangential velocity and R is the radius of the circle

ac = (4.10m/s)2 / 17m = 0.988m/s2

At the top of the ride, using newton's equation ofmotion:

mac = -Fn + mg

Apparent Weight = Fn = m*(g - ac) =m*(9.81m/s2 - .988m/s2) =m*8.822m/s2

Apparent Weight / True Weight =(m*8.86m/s2) /(m*9.81m/s2) = 0.899

At the bottom:

mac = Fn - mg

Fn = m*(g+ac) =m*(9.81m/s2 + .988m/s2) =m*10.798m/s2

Apparent Weight / True Weight =(m*10.798m/s2) /(m*9.81m/s2) = 1.10

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