A Ferris wheel has radius 5.0 m and makes one revolution every 8.0 s with uniform rotation. A person who normally weighs 670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent weight of the person as she passes through the highest point of her motion

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Answer: The apparent weight of the person as she passes through the highest point of her motion is 458.81 N

Explanation: Please see the attachments below

Ver imagen Abdulazeez10
Ver imagen Abdulazeez10

The apparent weight of the person as she passes through the highest point of her motion is 460 N.

The given parameters;

  • radius of the wheel, r = 5.0 m
  • time of motion, t = 8.0 s
  • weight of the person, W = 670 N

The apparent weight of the person as she passes through the highest point of her motion is calculated as follows;

[tex]R = m(g - a)[/tex]

The mass of the person;

[tex]m = \frac{W}{g}\\\\m = \frac{670}{9.8} = 68.37 \ kg[/tex]

The acceleration of the person is calculated as;

[tex]a_c = (\omega^2)r\\\\a_c = (\frac{1 \ rev}{8 \ s} \times \frac{2\pi \ rad}{1 \ rev} )^2 \times 5\ m\\\\a_c = 3.08 \ m/s^2[/tex]

The apparent weight is calculated as;

[tex]R = 68.37(9.8 - 3.08)\\\\R = 460 \ N[/tex]

Thus, the apparent weight of the person as she passes through the highest point of her motion is 460 N.

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