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?

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Answer 1 · 2016-01-28T18:05:21

Data:-

Mass $=m=7kg$
Distance $=r=8m$
Frequency $=f=4Hz$
Centripetal Force $=F=??$

Sol:-

We know that:

The centripetal acceleration $a$ is given by
$F=(mv^2)/r................(i)$

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 $v=romega$

Where $omega$ is the angular velocity.

Put $v=romega$ in $(i)$

$implies F=(m(romega)^2)/r implies F =mromega^2...........(ii)$

The relation between angular velocity and frequency is

$omega=2pif$

Put $omega=2pif$ in $(ii)$

$implies F=mr(2pif)^2$
$implies F=4pi^2rmf^2$

Now, we are given with all the values

$implies F=4(3.14)^2*8*7*(4)^2=4*9.8596*8*16=35336.8064$

$implies F=35336.8064N$

An object with a mass of 7 kg7 kg is revolving around a point at a distance of 8 m8 m. If the object is making revolutions at a frequency of 4 Hz4 Hz, what is the centripetal force acting on the object?