# An object with a mass of 4 kg is revolving around a point at a distance of 5 m. If the object is making revolutions at a frequency of 5 Hz, what is the centripetal force acting on the object?

Aug 2, 2017

Centripetal force is $19739.21 N$

#### Explanation:

Centripetal force acting on a body in circular motion is given by

${F}_{c} = \frac{m {v}^{2}}{r}$, where$m$ is mass, $v$ is velocity and $r$ is the radius

As object moves at a frequency of $f H z$, it means it moves

$2 \pi r \times f$ in $1$ second and hence $v = 2 \pi r f$

and ${F}_{c} = \frac{m}{r} \times 4 {\pi}^{2} {r}^{2} {f}^{2} = 4 {\pi}^{2} m r {f}^{2}$

aas $m = 4 k g$, $f = 5 H z$ and $r = 5 m$

${F}_{c} = 4 {\pi}^{2} \times 4 \times 5 \times {5}^{2} = 2000 {\pi}^{2} = 19739.21 N$

Aug 2, 2017

The centripetal force is $= 19.739 k N$

#### Explanation:

The centripetal force is

$F = m {v}^{2} / r = m r {\omega}^{2}$

The mass is $m = 4 k g$

The radius is $r = 5 m$

The angular velocity is $\omega = 2 \pi f = 10 \pi$

Therefore,

$F = 4 \cdot 5 \cdot {\left(10 \pi\right)}^{2} = 19739 N$