Question

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

Answer 1

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: $F_c=115 \ \text{N}$.

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

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

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

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

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