Question

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?

Answer 1

`a_M=1.92a_A`

Step-by-step explanation:

`\omega_M=\omega_A` = Angular speed

`r_M` = Distance of Mary = 11.5 ft

`r_A` = Distance of Alex = 6 ft

Ratio of centripetal acceleration is given by

`(a_M)/(a_A)=(\omega_M^2r_M)/(\omega_A^2r_A)\\\Rightarrow (a_M)/(a_A)=(r_M)/(r_A)\\\Rightarrow a_M=a_A(r_M)/(r_A)\\\Rightarrow a_M=(11.5)/(6)a_A\\\Rightarrow a_M=1.92a_A`

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