Q. 51

Expert-verifiedFound in: Page 201

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

In an amusement park ride called The Roundup, passengers stand inside a 16-m-diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, as shown in FIGURE P8.51.

a. Suppose the ring rotates once every 4.5 s. If a rider’s mass is 55 kg, with how much force does the ring push on her at the top of the ride? At the bottom? b. What is the longest rotation period of the wheel that will prevent the riders from falling off at the top?

a) Ring push on her at the top of the ride with force T_{top}= 0.32 kN and at the bottom T_{bottom} =1.4 KN

b) Longest rotation period of the wheel that will prevent the riders from falling off at top is T= 5.67 sec.

Given that ring rotates once every 4.5 s.

And mass of rider is 55 kg

Diameter of ring = 16 m

First draw free body diagram and the equate forces

From the diagram we can get

We can find v by using v=ω r

We have period as 4.5 s So

And

Now substitute the given values in equation (1) and (2)

Similarly

Given that ring rotates once every 4.5 s.

Mass of rider = 55 kg

Diameter of ring = 16 m

We have calculated velocity = 11.17 m/s

For longest rotation period prevent riders to fall means resultant force is zero

Substitute the values given we get

We know

Substitute values we get

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