Question

panchor36601 minute agoPhysicsCollegeDog is chasing his tail. The radius of the circle that dog makes is 0.62 meters. The dog runs in a circle 10 times in 7.2 seconds.a) What is the period of motion of the dog?b) What is the speed of the dog?c) What us the centripetal acceleration of the dog?d) If the dog has a bandanna tied to his neck, mass is 0.024 kg, then what is the centripetal forceacting on the bandanna?

Answer 1

Given:

The radius of the circle the dog makes is,

`r=0.62\text{ m}`

The dog runs in the circle 10 times in

`t=7.0\text{ seconds}`

The mass of tha bandanna is,

`m=0.024\text{ kg}`

To find:

a) time period

b) speed of the dog

c) centripetal acceleration

d) the centripetal foce on the bandanna

Step-by-step explanation:

a)

The time period of the dog is,

`\begin{gathered} T=\frac{Total\text{ time}}{Total\text{ number of cycle}} \\ =(7.2)/(10) \\ =0.72\text{ s} \end{gathered}`

Hence, the period of the dog is 0.72 s.

b)

The speed of the dog is,

`\begin{gathered} \omega=(2\pi)/(T) \\ =(2\pi)/(0.72) \\ =8.72\text{ rad/s} \end{gathered}`

Hence, the speed of the dog is 8.72 rad/s.

c)

The centripetal acceleration is,

`\begin{gathered} a=\omega^2r \\ =(8.72)^2*0.62 \\ =47.1\text{ rad/s}^2 \end{gathered}`

Hence, the centripetal acceleration is,

`47.1\text{ rad/s}^2`

d)

The centripetal foce on the bandanna is,

`\begin{gathered} F=ma \\ =0.024*47.1 \\ =1.13\text{ N} \end{gathered}`

Hence, the force is 1.13 N.