Calculating Centripetal Force: 40.0kg Child on 9.0m Ferris Wheel

[jesuslovesu]

A 40.0 kg child on a Ferris wheel rotates four times each minute and the wheel has a radius of 9.0 m.

What force does the seat exert on the child when the child is halfway between the top and bottom?

The answer is 397 N which is 5 N more than the weight of the child, but I have not idea how they got that, anyone have any ideas?

 

[Tide]

HINT: The seat also supplies the centripetal force to keep the child moving in a circular path.

 

[quicknote]

I would first clarify the given information and assumptions. The problem states that the child has a mass of 40.0 kg and the Ferris wheel has a radius of 9.0 m. It also mentions that the wheel rotates four times per minute, but it does not specify the speed or angular velocity of the wheel. Therefore, we cannot accurately calculate the centripetal force without this information.

Assuming that the wheel is rotating at a constant speed, we can use the equation F = mω^2r to calculate the centripetal force. Here, m represents the mass of the child, ω is the angular velocity, and r is the radius of the wheel. Since the child is halfway between the top and bottom of the wheel, we can assume that the child is at a 90-degree angle from the center of rotation, making the radius 9.0 m.

To find the angular velocity, we can use the formula ω = 2πf, where f is the frequency of rotations per minute. In this case, f = 4 rotations per minute, so ω = 2π(4) = 8π radians per minute.

Plugging in the values, we get F = (40.0 kg)(8π radians per minute)^2(9.0 m) = 9,027 N. However, this is the total force acting on the child, including the child's weight. To find the force exerted by the seat on the child, we need to subtract the weight of the child, which is 40.0 kg x 9.8 m/s^2 = 392 N. Therefore, the force exerted by the seat on the child is 9,027 N - 392 N = 8,635 N.

This is slightly different from the answer given in the problem (397 N). It is possible that the given answer assumes a different value for the child's weight or the angular velocity of the wheel. Without further information, it is difficult to determine the exact reason for the discrepancy. As scientists, it is important to always double check our calculations and assumptions to ensure accuracy and avoid errors.