Ferris Wheel Problem: Calculating Rotation Rate & Force Needed

[luckycharmz]

Cars on a ferris wheel are moving in a verticle circle. The radius of the
wheel in 6 meters. what must be the rotation rate of the wheel in order that riders experience three times their weight at the bottom of the circle? for this rotation rate what will be the required force exerted by the seat belt in the car when the car is at the top of the verticle circle?

 

[buffordboy23]

Hi luckycharmz,

You will have to show an attempt at solving the problem to get help. What have you tried? What physics concepts are applicable to this problem?

 

[thomate1]

To calculate the rotation rate of the ferris wheel, we can use the formula ω = √(g/r), where ω is the rotation rate, g is the acceleration due to gravity, and r is the radius of the wheel. Plugging in the given values of g = 9.8 m/s^2 and r = 6 m, we get a rotation rate of approximately 2.09 radians per second.

To experience three times their weight at the bottom of the circle, the riders would need to experience an acceleration of 3g (three times the acceleration due to gravity). Using the formula a = ω^2r, where a is the centripetal acceleration, ω is the rotation rate, and r is the radius, we can calculate the required centripetal acceleration to be 29.4 m/s^2.

At the top of the vertical circle, the riders would experience zero centripetal acceleration, as they are momentarily at rest before moving downwards. Therefore, the force exerted by the seat belt would be equal to the riders' weight, which is three times their actual weight. Using the formula F = ma, where F is the force, m is the riders' mass, and a is the acceleration, we can calculate the required force to be 294 N.

It is important to note that these calculations assume ideal conditions, and factors such as air resistance and friction may affect the actual rotation rate and force experienced by the riders. Safety precautions, such as the use of seat belts, are necessary to ensure the well-being of the riders and should be determined by trained professionals.