Question

question 16
1 pts
a student whirls a small rubber stopper around their head so that it completes 13 revolutions. their lab partner records a total time of 22 seconds to complete these revolutions. if the students string is 0.9 meters long, how fast must the rubber stopper be moving in meters per second?

Explanation:

Step1: Calculate the total distance

The circumference of a circle is \(C = 2\pi r\), where \(r = 0.9\) m. For \(n=13\) revolutions, the total distance \(d=n\times2\pi r\).

$$d = 13\times2\pi\times0.9$$

$$d=13\times1.8\pi$$

$$d = 23.4\pi$$

Step2: Calculate the speed

Speed \(v=\frac{d}{t}\), where \(t = 22\) s.

$$v=\frac{23.4\pi}{22}$$

$$v=\frac{23.4\times3.14}{22}$$

$$v=\frac{73.476}{22}$$

Answer:

\(v\approx3.34\) m/s