A model train, with a mass of $6 k g$ $6 kg$ , is moving on a circular track with a radius of $7 m$ $7 m$ . If the train's rate of revolution changes from $1 H z$ $1 Hz$ to $2 H z$ $2 Hz$ , by how much will the centripetal force applied by the tracks change by?

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A model train, with a mass of $6 k g$ $6 kg$ , is moving on a circular track with a radius of $7 m$ $7 m$ . If the train's rate of revolution changes from $1 H z$ $1 Hz$ to $2 H z$ $2 Hz$ , by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2016-11-18T06:24:39

The centripetal force applied is $F_{c} = 1654.8$ $F_c=1654.8$ Newtons.

Explanation:

Centripetal force is defined as $F_{c} = m r ω^{2}$ $F_c=mromega^2$ .
Angular acceleration $ω = 2 π$ $omega= 2pi$ (change in frequency)
$\Rightarrow ω = 2 π (ν_{2} - ν_{1})$ $=>omega=2pi(nu_2-nu_1)$ .
Now the centripetal force becomes
$F_{c} = m r {[2 π (ν_{2} - ν_{1})]}^{2}$ $F_c=mr[2pi(nu_2-nu_1)]^2$ .
$F_{c} = 4 m r π^{2} {(ν_{2} - ν_{1})}_{2}^{2}$ $F_c= 4mrpi^2(nu_2-nu_1)^2$
Substituting the given values we get,
$F_{c} = 4 (2 k g) (7 m) {(3.14)}^{2} {[(2 H z) - (1 H z)]}^{2}$ $F_c= 4(2kg)(7m)(3.14)^2[(2Hz)-(1Hz)]^2$
$:. F_c = 1654.8$ Newtons.

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A model train, with a mass of $6 k g$ $6 kg$ , is moving on a circular track with a radius of $7 m$ $7 m$ . If the train's rate of revolution changes from $1 H z$ $1 Hz$ to $2 H z$ $2 Hz$ , by how much will the centripetal force applied by the tracks change by?

1 Answer

Explanation:

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A model train, with a mass of 6 kg6kg6 kg, is moving on a circular track with a radius of 7 m7m7 m. If the train's rate of revolution changes from 1 Hz1Hz1 Hz to 2 Hz2Hz2 Hz, by how much will the centripetal force applied by the tracks change by?

1 Answer

Explanation:

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A model train, with a mass of $6 k g$ $6 kg$ , is moving on a circular track with a radius of $7 m$ $7 m$ . If the train's rate of revolution changes from $1 H z$ $1 Hz$ to $2 H z$ $2 Hz$ , by how much will the centripetal force applied by the tracks change by?