Question

1. determine the centripetal acceleration of a whistle on a string. the whistle takes three seconds to make one rotation, and the length of the string is 0.75 m.

o 2.79 m/s²
o 1.57 m/s
o 3.29 m/s²
o 2.09 m/s²

Explanation:

Step1: Calculate the linear - speed

The distance traveled in one rotation is the circumference of the circle $C = 2\pi r$, where $r$ is the length of the string. Given $r=0.75\ m$, so $C = 2\pi\times0.75= 1.5\pi\ m$. The time taken for one rotation $t = 3\ s$. The linear - speed $v=\frac{s}{t}$, and $s = C$, so $v=\frac{1.5\pi}{3}=0.5\pi\ m/s$.

Step2: Calculate the centripetal acceleration

The formula for centripetal acceleration is $a_c=\frac{v^{2}}{r}$. Substitute $v = 0.5\pi\ m/s$ and $r = 0.75\ m$ into the formula. $v^{2}=(0.5\pi)^{2}=0.25\pi^{2}\ m^{2}/s^{2}$, then $a_c=\frac{0.25\pi^{2}}{0.75}=\frac{\pi^{2}}{3}\approx\frac{9.8696}{3}\approx3.29\ m/s^{2}$.

Answer:

$3.29\ m/s^{2}$