A company is designing a new, very large ferris wheel. The radius R will be 90 m

Question

A company is designing a new, very large ferris wheel. The radius R will be 90 m, which will exceed the current record holder (the "High Roller" in Las Vegas). The rim and cars in which people sit are held to the center by a series of steel, radial struts. Which expression describes how much force the strut exerts on the chairs at the top? How fast would the wheel need to be turning so that seatbelts would be required to hold people in their seats (not just being a good idea for safety)? (A) v^2/r must be larger than 9.8 m/s^2 (B) You would always need seatbelts. (C) Gravity will always hold you in the seat, so you never need seatbelts. (D) v^2/r must be less than 9.8 m/s^2. Consider two speeds of rotation, v and 2v. (A) At 2v the radial struts do twice compared to the case where it was turning at v. (B) At 2v the radial struts do four times as much work while the wheel compared to the case where it was turning at v. (C) At 2v the radial struts do just as much work as the case where it was turning at v, but the work is not zero. (D) There is no work done by the radial struts. While the wheel is being constructed, a worker at the top drops a bolt that gets caught in the circular frame and slides all the way around the wheel from top to the very bottom. (A) Ignoring friction, the bolt will be travelling slower when it hits the bottom than if he dropped it straight down. (B) Ignoring friction, the bolt will be travelling faster when it hits the bottom than if he dropped it straight down. (C) Ignoring friction, the bolt will be travelling just as fast when it hits the bottom as if he dropped it straight down. Which is true while the wheel is in motion? (A) The struts exert the most force when the cars are at the top (B) The struts exert the most force when the cars are straight out (i.e. at a level with the central hub) (C) The struts exert the most force when the cars are at the bottom (D) The struts exert the same force in all cases since the wheel is in uniform motion.

Explanation / Answer

(8)

At the top, the centripetal foce acts upwards and weigh acts downward. These two forces constitute net normal reaction.

N = mv^2 / r - mg

Thus, the correct option is ( A )

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( 9 )

The gravitaional accelration acts always downward. In order to hold seat belts, the wheel must accelerate with a centipetal accleration, v^2 /r that must greater than gravitaional acceleration to avoid fall down situation

Thus, the correct option is ( A )

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(10 ) Work done is product of force and displacement. There is no radial displacement about the struts. Hence the work done is zero by the struts.

Thus, the correct option is ( D )

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(11)

As bolt dropes down, there exist only gravitaional accleration acts on the bolt. The gravitaional accelration is constant through out the motion of fallin object, Hence, the bolt will travelling just as fast when it hits the bottom as if dropped in straightline. ( Note that here fricitonal forces are not considered )

Thus, the correct option is ( c)

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(12 )

At the bottom, tehy exertes more force. In this case, centripetal force and weight acts downward which are result in normal force. Hence to lift upward the the structs need apply more force.

Thus, the correct option is ( c)

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