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A 85.0kg man and a 65, 0kg woman are riding a Ferris wheel with a radius of 20.0m. What is the Ferris wheels tangential velocity if the net centripetal force on the woman is 115N

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Answer:

The Ferris wheel's tangential (linear) velocity if the net centripetal force on the woman is 115 N is 3.92 m/s.

Explanation:

Let's use Newton's 2nd Law to help solve this problem.

  • F = ma

The force acting on the Ferris wheel is the centripetal force, given in the problem: [tex]F_c=115 \ \text{N}[/tex].

The mass "m" is the sum of the man and woman's masses: [tex]85+65= 150 \ \text{kg}[/tex].

The acceleration is the centripetal acceleration of the Ferris wheel: [tex]a_c=\displaystyle \frac{v^2}{r}[/tex].

Let's write an equation and solve for "v", the tangential (linear) acceleration.

  • [tex]\displaystyle 115=m(\frac{v^2}{r} )[/tex]
  • [tex]\displaystyle 115 = (85+65)(\frac{v^2}{20})[/tex]
  • [tex]\displaystyle 115=150(\frac{v^2}{20} )[/tex]
  • [tex].766667=\displaystyle(\frac{v^2}{20} )[/tex]
  • [tex]15.\overline{3}=v^2[/tex]
  • [tex]v=3.9158[/tex]

The Ferris wheel's tangential velocity is 3.92 m/s.

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