# An object with a mass of 7 kg is revolving around a point at a distance of 8 m. If the object is making revolutions at a frequency of 4 Hz, what is the centripetal force acting on the object?

Jan 28, 2016

Data:-

Mass$= m = 7 k g$
Distance$= r = 8 m$
Frequency$= f = 4 H z$
Centripetal Force=F=??

Sol:-

We know that:

The centripetal acceleration $a$ is given by
$F = \frac{m {v}^{2}}{r} \ldots \ldots \ldots \ldots \ldots . \left(i\right)$

Where $F$ is the centripetal force, $m$ is the mass, $v$ is the tangential or linear velocity and $r$ is the distance from center.

Also we know that $v = r \omega$

Where $\omega$ is the angular velocity.

Put $v = r \omega$ in $\left(i\right)$

$\implies F = \frac{m {\left(r \omega\right)}^{2}}{r} \implies F = m r {\omega}^{2.} \ldots \ldots \ldots . \left(i i\right)$

The relation between angular velocity and frequency is

$\omega = 2 \pi f$

Put $\omega = 2 \pi f$ in $\left(i i\right)$

$\implies F = m r {\left(2 \pi f\right)}^{2}$
$\implies F = 4 {\pi}^{2} r m {f}^{2}$

Now, we are given with all the values

$\implies F = 4 {\left(3.14\right)}^{2} \cdot 8 \cdot 7 \cdot {\left(4\right)}^{2} = 4 \cdot 9.8596 \cdot 8 \cdot 16 = 35336.8064$

$\implies F = 35336.8064 N$