An object with a mass of $16 k g$ $16 kg$ is revolving around a point at a distance of $3 m$ $3 m$ . If the object is making revolutions at a frequency of $13 H z$ $13 Hz$ , what is the centripetal force acting on the object?

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An object with a mass of $16 k g$ $16 kg$ is revolving around a point at a distance of $3 m$ $3 m$ . If the object is making revolutions at a frequency of $13 H z$ $13 Hz$ , what is the centripetal force acting on the object?

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Answer 1 · 2016-01-28T13:47:11

I found: $320, 250 N$ $320,250N$

Explanation:

Centripetal force is equal to mass time centripetal acceleration:
$F_{c} = m \cdot a_{c} = m \cdot \frac{v^{2}}{r}$ $F_c=m*a_c=m*v^2/r$
where:
$m = 16 k g =$ $m=16kg=$ mass;
$v = ? =$ $v=?=$ linear velocity;
$r = 3 m =$ $r=3m=$ radius.

Now:
Angular Velocity $ω$ $omega$ (a kind of circular velocity!) will be equal to distance divided time or:
$ω = \frac{2 π}{T}$ $omega=(2pi)/T$

in this case the distance will be the circumference of $2 π$ $2pi$ radians divided by the time or period $T$ $T$ to desribe it.
But period is related to frequency $ν$ $nu$ as:
$ν = \frac{1}{T}$ $nu=1/T$ so we can write:
$ω = 2 π ν$ $omega=2pinu$

But we want a Linear velocity!
We simply introduce the radius into the $ω$ $omega$ to get:
$v = ω r = 2 π ν r$ $v=omegar=2pinur$
The centripetal force will then become:
$F_{c} = m (4 π^{2}) ν^{2} r^{2} \frac{)}{r} = m (4 π^{2}) (ν^{2}) r = 16 \cdot (4 π^{2}) (13^{2}) \cdot 3 = 320, 248.9 N \approx 320, 250 N$ $F_c=m(4pi^2)nu^2r^2)/r=m(4pi^2)(nu^2)r=16*(4pi^2)(13^2)*3=320,248.9N~~320,250N$

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An object with a mass of $16 k g$ $16 kg$ is revolving around a point at a distance of $3 m$ $3 m$ . If the object is making revolutions at a frequency of $13 H z$ $13 Hz$ , what is the centripetal force acting on the object?

1 Answer

Explanation:

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Humanities

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An object with a mass of 16kg16 kg is revolving around a point at a distance of 3m3 m. If the object is making revolutions at a frequency of 13Hz13 Hz, what is the centripetal force acting on the object?

1 Answer

Explanation:

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An object with a mass of $16 k g$ $16 kg$ is revolving around a point at a distance of $3 m$ $3 m$ . If the object is making revolutions at a frequency of $13 H z$ $13 Hz$ , what is the centripetal force acting on the object?