Given:
The radius of the circle the dog makes is,
[tex]r=0.62\text{ m}[/tex]The dog runs in the circle 10 times in
[tex]t=7.0\text{ seconds}[/tex]The mass of tha bandanna is,
[tex]m=0.024\text{ kg}[/tex]To find:
a) time period
b) speed of the dog
c) centripetal acceleration
d) the centripetal foce on the bandanna
Explanation:
a)
The time period of the dog is,
[tex]\begin{gathered} T=\frac{Total\text{ time}}{Total\text{ number of cycle}} \\ =\frac{7.2}{10} \\ =0.72\text{ s} \end{gathered}[/tex]Hence, the period of the dog is 0.72 s.
b)
The speed of the dog is,
[tex]\begin{gathered} \omega=\frac{2\pi}{T} \\ =\frac{2\pi}{0.72} \\ =8.72\text{ rad/s} \end{gathered}[/tex]Hence, the speed of the dog is 8.72 rad/s.
c)
The centripetal acceleration is,
[tex]\begin{gathered} a=\omega^2r \\ =(8.72)^2\times0.62 \\ =47.1\text{ rad/s}^2 \end{gathered}[/tex]Hence, the centripetal acceleration is,
[tex]47.1\text{ rad/s}^2[/tex]d)
The centripetal foce on the bandanna is,
[tex]\begin{gathered} F=ma \\ =0.024\times47.1 \\ =1.13\text{ N} \end{gathered}[/tex]Hence, the force is 1.13 N.
