An object with a mass of $2 k g$ $2 kg$ is revolving around a point at a distance of $4 m$ $4 m$ . If the object is making revolutions at a frequency of $4 H z$ $4 Hz$ , what is the centripetal force acting on the object?

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An object with a mass of $2 k g$ $2 kg$ is revolving around a point at a distance of $4 m$ $4 m$ . If the object is making revolutions at a frequency of $4 H z$ $4 Hz$ , what is the centripetal force acting on the object?

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Answer 1 · 2017-08-19T05:00:49

$F_{c} \approx 5053 N$ $F_c~~5053N$ radially inward.

Explanation:

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

$F_{c} = m a_{c}$ $F_c=ma_c$

where $m$ $m$ is the mass of the object and $a_{c}$ $a_c$ is the centripetal acceleration experienced by the object

The centripetal acceleration is given by:

$a_{c} = \frac{v^{2}}{r}$ $a_c=v^2/r$

which is equivalent to $r ω^{2}$ $romega^2$ . Therefore, we can write:

$F_{c} = m r ω^{2}$ $F_c=mromega^2$

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

The angular velocity can also be expressed as:

$ω = 2 π f$ $omega=2pif$

where $f$ $f$ is the frequency of the revolution

And so our final expression becomes:

$F_{c} = m r {(2 π f)}^{2}$ $color(blue)(F_c=mr(2pif)^2$

We are given:

$\mapsto m = 2 kg$ $|->"m"=2"kg"$
$\mapsto r = 4 m$ $|->"r"=4"m"$
$\mapsto f = 4 s^{- 1}$ $|->f=4"s"^-1$

Substituting these values into the equation we derived above:

$F_{c} = (2 kg) (4 m) {(2 π (4 s^{- 1}))}^{2}$ $F_c=(2"kg")(4"m")(2pi(4"s"^-1))^2$

$= 5053.237 N$ $=5053.237"N"$

$\approx 5053 N$ $~~5053N$ radially inward

This may also be expressed in scientific notation as $5 \times 10^{3} N$ $5xx10^3"N"$ where significant figures are concerned.

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An object with a mass of $2 k g$ $2 kg$ is revolving around a point at a distance of $4 m$ $4 m$ . If the object is making revolutions at a frequency of $4 H z$ $4 Hz$ , what is the centripetal force acting on the object?

1 Answer

Explanation:

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

1 Answer

Explanation:

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An object with a mass of $2 k g$ $2 kg$ is revolving around a point at a distance of $4 m$ $4 m$ . If the object is making revolutions at a frequency of $4 H z$ $4 Hz$ , what is the centripetal force acting on the object?