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 $2 H z$ $2 Hz$ , 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 $2 H z$ $2 Hz$ , what is the centripetal force acting on the object?

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Answer 1 · 2016-02-17T11:15:23

I found: $7580 N$ $7580N$

Explanation:

Centripetal Force is:
$F_{c} = m \frac{v^{2}}{r}$ $F_c=mv^2/r$
where:
$m =$ $m=$ mass;
$v =$ $v=$ linear velocity;
$r =$ $r=$ radius.

The frequency tells us the number of complete revolutions in one seconds (here 2 revolutions).
We can ask ourselves what will be the Angular Velocity $ω$ $omega$ of our object, i.e., a kind of "curved" velocity involving not linear distance but angle described in time!

So we get:

$ω = \frac{angle}{time} = \frac{2 π}{T}$ $omega="angle"/"time"=(2pi)/T$

Where $T$ $T$ will be the Period of time for a complete revolution (time to describe $2 π$ $2pi$ radians).

The good thing is that the period is connected to frequency as $frequency = ν = \frac{1}{T}$ $"frequency"=nu=1/T$
and also the angular velocity can be changed into linear velocity simply considering at what distance from the center you are travelling....(basically, you include the radius)!!!!
so:
$v = ω \cdot r$ $v=omega*r$

in our case we get (collecting all our stuff):

$F_{c} = m \frac{{(ω \cdot r)}^{2}}{r} = m ω^{2} r = m {(2 π ν)}^{2} r = 6 \cdot {(2 \cdot 3.14 \cdot 2)}^{2} \cdot 8 \approx 7580 N$ $F_c=m(omega*r)^2/r=momega^2r=m(2pinu)^2r=6*(2*3.14*2)^2*8~~7580N$

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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 $2 H z$ $2 Hz$ , 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 6kg6 kg is revolving around a point at a distance of 8m8 m. If the object is making revolutions at a frequency of 2Hz2 Hz, what is the centripetal force acting on the object?

1 Answer

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 $2 H z$ $2 Hz$ , what is the centripetal force acting on the object?