A model train, with a mass of $8$ $8$ $k g$ $kg$ , is moving on a circular track with a radius of $1$ $1$ $m$ $m$ . If the train's kinetic energy changes from $32$ $32$ $J$ $J$ to $0$ $0$ $J$ $J$ , by how much will the centripetal force applied by the tracks change?

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A model train, with a mass of $8$ $8$ $k g$ $kg$ , is moving on a circular track with a radius of $1$ $1$ $m$ $m$ . If the train's kinetic energy changes from $32$ $32$ $J$ $J$ to $0$ $0$ $J$ $J$ , by how much will the centripetal force applied by the tracks change?

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Answer 1 · 2016-06-24T23:19:25

The centripetal force is given by $F = \frac{m v^{2}}{r}$ $F=(mv^2)/r$ , and we can calculate the change in $v$ $v$ from the change in the kinetic energy, $E_{k} = \frac{1}{2} m v^{2}$ $E_k=1/2mv^2$ . The change in the centripetal force acting is $- 64$ $-64$ $N$ $N$ .

Explanation:

The kinetic energy is given by $E_{k} = \frac{1}{2} m v^{2}$ $E_k=1/2mv^2$ , and we can rearrange to make $v$ $v$ the subject:

$v = \sqrt{\frac{2 E_{k}}{m}}$ $v=sqrt((2E_k)/m)$

The final kinetic energy is zero and therefore the final velocity is zero.

We can use the mass, radius and initial kinetic energy to calculate the initial velocity:

$v = \sqrt{\frac{2 E_{k}}{m}} = \sqrt{\frac{2 \cdot 32}{8}} = \sqrt{\frac{64}{8}} = \sqrt{8} \approx 2.8$ $v=sqrt((2E_k)/m)=sqrt((2*32)/8) = sqrt (64/8) =sqrt8~~2.8$ $m s^{- 1}$ $ms^-1$

Since the final velocity is zero, the final centripetal force will be zero. The initial centripetal force will be:

$F = \frac{m v^{2}}{r} = \frac{8 \cdot {2.8}^{2}}{1} = 64$ $F=(mv^2)/r=(8*2.8^2)/1=64$ $N$ $N$ .

Since the final centripetal force is $0$ $0$ $N$ $N$ , the change in the centripetal force is:

final - initial = $0 - 64 = - 64$ $0-64=-64$ $N$ $N$

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A model train, with a mass of $8$ $8$ $k g$ $kg$ , is moving on a circular track with a radius of $1$ $1$ $m$ $m$ . If the train's kinetic energy changes from $32$ $32$ $J$ $J$ to $0$ $0$ $J$ $J$ , by how much will the centripetal force applied by the tracks change?

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Explanation:

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A model train, with a mass of 888 kgkgkg, is moving on a circular track with a radius of 111 mmm. If the train's kinetic energy changes from 323232 JJJ to 000 JJJ, by how much will the centripetal force applied by the tracks change?

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Explanation:

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A model train, with a mass of $8$ $8$ $k g$ $kg$ , is moving on a circular track with a radius of $1$ $1$ $m$ $m$ . If the train's kinetic energy changes from $32$ $32$ $J$ $J$ to $0$ $0$ $J$ $J$ , by how much will the centripetal force applied by the tracks change?