An object with a mass of $6 k g$ $6 kg$ is revolving around a point at a distance of $8 m$ $8 m$ . If the object is making revolutions at a frequency of $6 H z$ $6 Hz$ , what is the centripetal force acting on the object?

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An object with a mass of $6 k g$ $6 kg$ is revolving around a point at a distance of $8 m$ $8 m$ . If the object is making revolutions at a frequency of $6 H z$ $6 Hz$ , what is the centripetal force acting on the object?

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Answer 1 · 2016-07-10T14:46:12

The force acting on the object is $6912 π^{2}$ $6912pi^2$ Newtons.

Explanation:

We'll start by determining the velocity of the object. Since it is revolving in a circle of radius 8m 6 times per second, we know that:

$v = 2 π r \cdot 6$ $v = 2pir*6$

Plugging in values gives us:

$v = 96 π$ $v = 96 pi$ m/s

Now we can use the standard equation for centripetal acceleration:

$a = \frac{v^{2}}{r}$ $a = v^2/r$
$a = \frac{{(96 π)}^{2}}{8}$ $a = (96pi)^2/8$
$a = 1152 π^{2}$ $a = 1152pi^2$ m/s^2

And to finish the problem we simply use the given mass to determine the force needed to produce this acceleration:
$F = m a$ $F = ma$
$F = 6 \cdot 1152 π^{2}$ $F = 6*1152pi^2$
$F = 6912 π^{2}$ $F = 6912pi^2$ Newtons

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An object with a mass of $6 k g$ $6 kg$ is revolving around a point at a distance of $8 m$ $8 m$ . If the object is making revolutions at a frequency of $6 H z$ $6 Hz$ , what is the centripetal force acting on the object?

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Explanation:

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An object with a mass of 6 kg6kg6 kg is revolving around a point at a distance of 8 m8m8 m. If the object is making revolutions at a frequency of 6 Hz6Hz6 Hz, what is the centripetal force acting on the object?

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Explanation:

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An object with a mass of $6 k g$ $6 kg$ is revolving around a point at a distance of $8 m$ $8 m$ . If the object is making revolutions at a frequency of $6 H z$ $6 Hz$ , what is the centripetal force acting on the object?