Question

landon and jocelyn are partners in pair figure skating. last weekend, they perfected the death spiral element for inclusion in their upcoming competition. during this maneuver, landon holds jocelyn by the hand and swings her in a circle while she maintains her blades on the ice stretched out in a nearly horizontal orientation. determine the net force that must be applied to jocelyn (m = 50.7 kg) if her center of mass rotates in a circle with a radius of 0.715 m once every 1.10 seconds. net force

Explanation:

Step1: Find the angular velocity

The formula for angular velocity $\omega$ is $\omega=\frac{2\pi}{T}$, where $T$ is the time period. Given $T = 1.10\ s$, so $\omega=\frac{2\pi}{1.10}\ rad/s\approx 5.71\ rad/s$.

Step2: Find the centripetal acceleration

The formula for centripetal acceleration $a_{c}=\omega^{2}r$. Given $r = 0.715\ m$ and $\omega\approx 5.71\ rad/s$, then $a_{c}=(5.71)^{2}\times0.715\ m/s^{2}\approx 5.71\times5.71\times0.715\ m/s^{2}\approx 23.1\ m/s^{2}$.

Step3: Find the net force

According to Newton's second law $F = ma$, where $m = 50.7\ kg$ and $a=a_{c}$. So $F=50.7\times23.1\ N\approx 1171\ N$.

Answer:

$1171$