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

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Answer 1 · 2017-10-09T11:41:01

The force will change by $15150 N$ $15150N$

Explanation:

The equation for centripetal force is

$F_{c} = \frac{m v^{2}}{r} = m ω^{2} r$ $F_c = (mv^2)/r = momega^2r$

where $v$ $v$ is linear velocity, $ω$ $omega$ is angular velocity, $r$ $r$ is radius and $m$ $m$ is mass.

We know that the mass is $6 k g$ $6kg$ and the radius is $2 m$ $2m$ . We will use angular velocity for these calculations, but we could equally do it with linear velocity.

We know that

$ω = 2 π f$ $omega = 2pif$

where $f$ $f$ is the frequency, which we have.

For $f = 2 H z$ $f = 2Hz$

then

$ω = 2 π \cdot 2 = 12.6 \frac{rad}{sec}$ $omega = 2pi*2 = 12.6"rad"/"sec"$
$F_{c} = 6 \cdot {12.6}^{2} \cdot 2 = 1905 N$ $F_c = 6 * 12.6^2 * 2 = 1905N$

whereas with $f = 6 H z$ $f = 6Hz$

$ω = 2 π f = 2 π \cdot 6 = 37.7 \frac{rad}{sec}$ $omega = 2pif = 2pi * 6 = 37.7 "rad"/"sec"$

so

$F_{c} = 6 \cdot {37.7}^{2} \cdot 2 = 17055 N$ $F_c = 6 * 37.7^2 * 2 = 17055N$

Therefore the centripetal force will change by

$DeltaF_c = 17055N - 1905N = 15150N$

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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 $2 m$ $2 m$ . If the train's rate of revolution changes from $2 H z$ $2 Hz$ to $6 H z$ $6 Hz$ , 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 2 m2m2 m. If the train's rate of revolution changes from 2 Hz2Hz2 Hz to 6 Hz6Hz6 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 $2 m$ $2 m$ . If the train's rate of revolution changes from $2 H z$ $2 Hz$ to $6 H z$ $6 Hz$ , by how much will the centripetal force applied by the tracks change by?