Chapter 17, Problem 100A

To determine

The centripetal force acting on the bug and the agent that provides this force.

Answer to Problem 100A

The centripetal force is $4.61\times {10}^{-7}\text{N}$ that is provided by the frictional force between the bug and the disk.

Explanation of Solution

Given:

The mass of the bug, $m=1.0\text{g}=0.001\text{kg }$

The diameter of the disk, $d=17.2\text{cm = }0.172\text{m}$

The velocity of the bug on the disk, $v=0.63\text{cm/s}=0.0063\text{m/s}$

Formula used:

The centripetal force acting on an object of mass m, moving at a velocity of v in an orbit of radius r, is given by,

  $F=\frac{m{v}^2}{r}$

Calculation:

Using the given values in above formula, the centripetal force acting on the bug will be,

  $\begin{array}{c}{F}_c=\frac{m{v}^2}{r}\\ =\frac{2m{v}^2}{d}\\ =\frac{2\left(0.001\right){\left(0.0063\right)}^2}{0.172}\\ =4.61\times {10}^{-7}\text{N}\end{array}$

This above force is provided by the friction force between the bug and the disk.

Conclusion:

Hence, the centripetal force acting on the bug is $4.61\times {10}^{-7}\text{N}$ . This force is provide by the frictional force.