a child on a spinning ride at a playground has a centripetal acceleration of 0.80 m/s². the child completes…

a child on a spinning ride at a playground has a centripetal acceleration of 0.80 m/s². the child completes a full circle every 4.2 s. how far from the center of the ride is the child? 0.068 m 0.085 m 0.27 m 0.36 m

a child on a spinning ride at a playground has a centripetal acceleration of 0.80 m/s². the child completes a full circle every 4.2 s. how far from the center of the ride is the child? 0.068 m 0.085 m 0.27 m 0.36 m

Answer

Explanation:

Step1: Find the angular velocity

The child completes a full - circle ($\theta = 2\pi$ radians) in $T = 4.2$s. The angular velocity $\omega=\frac{\theta}{T}$. So, $\omega=\frac{2\pi}{4.2}\text{ rad/s}\approx1.5\text{ rad/s}$.

Step2: Use the centripetal - acceleration formula

The centripetal - acceleration formula is $a_c=\omega^{2}r$. We know $a_c = 0.80\text{ m/s}^2$ and $\omega\approx1.5\text{ rad/s}$, and we want to find $r$. Rearranging the formula for $r$ gives $r=\frac{a_c}{\omega^{2}}$. Substitute $a_c = 0.80\text{ m/s}^2$ and $\omega\approx1.5\text{ rad/s}$ into the formula: $r=\frac{0.80}{(1.5)^{2}}=\frac{0.80}{2.25}\approx0.36\text{ m}$.

Answer:

0.36 m