An object with a mass of $7 k g$ $7 kg$ is revolving around a point at a distance of $8 m$ $8 m$ . If the object is making revolutions at a frequency of $12 H z$ $12 Hz$ , what is the centripetal force acting on the object?

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An object with a mass of $7 k g$ $7 kg$ is revolving around a point at a distance of $8 m$ $8 m$ . If the object is making revolutions at a frequency of $12 H z$ $12 Hz$ , what is the centripetal force acting on the object?

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Answer 1 · 2016-05-30T20:48:26

$F_{C} = 32256 π^{2}$ $F_C=32256 pi^2$

Explanation:

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$m = 7 k g$ $m=7 " "kg$
$r = 8 m$ $r=8" "m$

$f = 12 H z$ $f=12" "Hz$

$v = \frac{2 π r}{T} \frac{v}{r} = \frac{2 π}{T} (1)$ $v=(2pir)/T" "v/r=(2pi)/T" "(1)$

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

$using (1) and (2)$ $"using (1) and (2)"$

$\frac{v}{r} = ω v = ω r v^{2} = ω^{2} r^{2}$ $v/r=omega" "v=omega r" "v^2=omega^2 r^2$

$F_{C} = m \cdot \frac{v^{2}}{r} centripetal force$ $F_C=m*v^2/r" centripetal force"$

$F_{C} = \frac{m \cdot ω^{2} \cdot r^{2}}{r}$ $F_C=(m*omega^2*r^2)/r$

$F_{C} = m \cdot ω^{2} \cdot r$ $F_C=m*omega^2*r$

$F_{C} = m \cdot ω^{2} \cdot r ω = 2 π f ω = 2 π \cdot 12 ω^{2} = 4 π^{2} \cdot 144$ $F_C=m*omega^2*r" "omega=2pi f" "omega=2 pi*12" "omega^2=4pi^2*144$

$ω^{2} = 576 π^{2}$ $omega^2=576pi^2$

$F_{C} = 7 \cdot 576 π^{2} \cdot 8$ $F_C=7*576pi^2*8$

$F_{C} = 32256 π^{2}$ $F_C=32256 pi^2$

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An object with a mass of $7 k g$ $7 kg$ is revolving around a point at a distance of $8 m$ $8 m$ . If the object is making revolutions at a frequency of $12 H z$ $12 Hz$ , what is the centripetal force acting on the object?

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An object with a mass of 7 kg7kg7 kg is revolving around a point at a distance of 8 m8m8 m. If the object is making revolutions at a frequency of 12 Hz12Hz12 Hz, what is the centripetal force acting on the object?

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An object with a mass of $7 k g$ $7 kg$ is revolving around a point at a distance of $8 m$ $8 m$ . If the object is making revolutions at a frequency of $12 H z$ $12 Hz$ , what is the centripetal force acting on the object?