An object with a mass of $2 kg$ is revolving around a point at a distance of $4 m$ . 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 · 2017-08-19T05:00:49

$F_c~~5053N$ radially inward.

The centripetal force is given in accordance with Newton's second law as:

$F_c=ma_c$

where $m$ is the mass of the object and $a_c$ is the centripetal acceleration experienced by the object

The centripetal acceleration is given by:

$a_c=v^2/r$

which is equivalent to $romega^2$ . Therefore, we can write:

$F_c=mromega^2$

where $r$ is the radius and $omega$ is the angular velocity of the object

The angular velocity can also be expressed as:

$omega=2pif$

where $f$ is the frequency of the revolution

And so our final expression becomes:

$color(blue)(F_c=mr(2pif)^2$

We are given:

Substituting these values into the equation we derived above:

$F_c=(2"kg")(4"m")(2pi(4"s"^-1))^2$

$=5053.237"N"$

$~~5053N$ radially inward

This may also be expressed in scientific notation as $5xx10^3"N"$ where significant figures are concerned.

An object with a mass of 2 kg2 kg is revolving around a point at a distance of 4 m4 m. If the object is making revolutions at a frequency of 4 Hz4 Hz, what is the centripetal force acting on the object?