A model train, with a mass of $3$ $3$ $k g$ $kg$ , is moving on a circular track with a radius of $3$ $3$ $m$ $m$ . If the train's kinetic energy changes from $18$ $18$ $J$ $J$ to $0$ $0$ $J$ $J$ , by how much will the centripetal force applied by the tracks change by?

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A model train, with a mass of $3$ $3$ $k g$ $kg$ , is moving on a circular track with a radius of $3$ $3$ $m$ $m$ . If the train's kinetic energy changes from $18$ $18$ $J$ $J$ to $0$ $0$ $J$ $J$ , by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2016-02-04T06:32:31

The centripetal force is given by $F = \frac{m v^{2}}{r}$ $F=(mv^2)/r$ . We are given the mass and the radius and can calculate the velocity from the kinetic energy. The change is $- 12$ $-12$ $N$ $N$ .

Explanation:

The centripetal force on an object of mass $m$ $m$ $k g$ $kg$ in circular motion at velocity $v$ $v$ $m s^{- 1}$ $ms^-1$ in a circle of radius $r$ $r$ $m$ $m$ is given by:

$F = \frac{m v^{2}}{r}$ $F=(mv^2)/r$

In this case we know the mass is $3$ $3$ $k g$ $kg$ and the radius is $3$ $3$ $m$ $m$ , but the velocity is not immediately obvious. We are given the kinetic energy at two moments in time, though, and we know that kinetic energy is:

$E_{k} = \frac{1}{2} m v^{2}$ $E_k=1/2mv^2$

We can rearrange this to make $v$ $v$ the subject:

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

Since the kinetic energy at the second time is $0$ $0$ $J$ $J$ , the velocity is also $0$ $0$ $m s^{- 1}$ $ms^-1$ , and therefore the centripetal force is also $0$ $0$ $N$ $N$ .

At the first time, the kinetic energy is $18$ $18$ $J$ $J$ , so:

$v = \sqrt{\frac{2 \cdot 18}{3}} = \sqrt{\frac{36}{3}} = \sqrt{12}$ $v=sqrt((2*18)/3)=sqrt(36/3)=sqrt12$ $m s^{- 1}$ $ms^-1$

This means the centripetal force is:

$F = \frac{m v^{2}}{r} = \frac{3 \cdot 12}{3} = 12$ $F=(mv^2)/r = (3*12)/3 = 12$ $N$ $N$ (since ${(\sqrt{12})}^{2} = 12$ $(sqrt12)^2=12$ )

So the centripetal force was $12$ $12$ $N$ $N$ at the beginning and $0$ $0$ $N$ $N$ at the end. Its change was therefore $- 12$ $-12$ $N$ $N$ .

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A model train, with a mass of $3$ $3$ $k g$ $kg$ , is moving on a circular track with a radius of $3$ $3$ $m$ $m$ . If the train's kinetic energy changes from $18$ $18$ $J$ $J$ to $0$ $0$ $J$ $J$ , by how much will the centripetal force applied by the tracks change by?

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Explanation:

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A model train, with a mass of 333 kgkgkg, is moving on a circular track with a radius of 333 mmm. If the train's kinetic energy changes from 181818 JJJ to 000 JJJ, 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 $3$ $3$ $k g$ $kg$ , is moving on a circular track with a radius of $3$ $3$ $m$ $m$ . If the train's kinetic energy changes from $18$ $18$ $J$ $J$ to $0$ $0$ $J$ $J$ , by how much will the centripetal force applied by the tracks change by?