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Mary and her younger brother Alex decide to ride the 26 ft diameter carousel at the State Fair. Mary sits on one of the horses in the outer section at a distance of 11.5 feet from the center. Alex decides to play it safe and chooses to sit in the inner section at a distance of 6 feet from the center. What is Mary's centripetal acceleration aM compared to that of Alex's centripetal acceleration aA?

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Answer:

[tex]a_M=1.92a_A[/tex]

Explanation:

[tex]\omega_M=\omega_A[/tex] = Angular speed

[tex]r_M[/tex] = Distance of Mary = 11.5 ft

[tex]r_A[/tex] = Distance of Alex = 6 ft

Ratio of centripetal acceleration is given by

[tex]\dfrac{a_M}{a_A}=\dfrac{\omega_M^2r_M}{\omega_A^2r_A}\\\Rightarrow \dfrac{a_M}{a_A}=\dfrac{r_M}{r_A}\\\Rightarrow a_M=a_A\dfrac{r_M}{r_A}\\\Rightarrow a_M=\dfrac{11.5}{6}a_A\\\Rightarrow a_M=1.92a_A[/tex]

Mary's centripetal acceleration is 1.92 times the centripetal acceleration of Alex

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