A model train, with a mass of $8 k g$ $8 kg$ , is moving on a circular track with a radius of $2 m$ $2 m$ . If the train's kinetic energy changes from $8 j$ $8 j$ to $36 j$ $36 j$ , by how much will the centripetal force applied by the tracks change by?

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A model train, with a mass of $8 k g$ $8 kg$ , is moving on a circular track with a radius of $2 m$ $2 m$ . If the train's kinetic energy changes from $8 j$ $8 j$ to $36 j$ $36 j$ , by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2017-11-09T23:13:01

The centripetal force increases by 28 N, from 8 N to 36 N.
Details follow.

Explanation:

Centripetal force is given by

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

For this train, we know the mass of the train, $m$ $m$ and the radius $r$ $r$ of the circular path it is following. What we need is the speed of the train $v$ $v$ .

Since the kinetic energy $K$ $K$ is given, we can use this to calculate the speed:

$K = \frac{1}{2} m v^{2}$ $K = 1/2 mv^2$

which I will rewrite as

$v^{2} = \frac{2 K}{m}$ $v^2 = (2 K)/m$

(because we will need $v^{2}$ $v^2$ for the centripetal force formula, rather than $v$ $v$ ).

When the energy is 8 J, $v^{2} = \frac{2 \cdot 8}{8} = 2$ $v^2 = (2 *8)/8 = 2$

and the centripetal force is $F_{c} = \frac{m v^{2}}{r} = \frac{8 \cdot 2}{2} = 8 N$ $F_c=(mv^2)/r= (8*2)/2 = 8 N$

When the energy is 36 J, $v^{2} = \frac{2 \cdot 36}{8} = 9$ $v^2 = (2 *36)/8 = 9$

and the centripetal force is $F_{c} = \frac{m v^{2}}{r} = \frac{8 \cdot 9}{2} = 36 N$ $F_c=(mv^2)/r= (8*9)/2 = 36 N$

The change in centripetal force will be $36 - 8 = 28 N$ $36-8=28 N$

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A model train, with a mass of $8 k g$ $8 kg$ , is moving on a circular track with a radius of $2 m$ $2 m$ . If the train's kinetic energy changes from $8 j$ $8 j$ to $36 j$ $36 j$ , 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 8kg8 kg, is moving on a circular track with a radius of 2m2 m. If the train's kinetic energy changes from 8j8 j to 36j36 j, 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 $8 k g$ $8 kg$ , is moving on a circular track with a radius of $2 m$ $2 m$ . If the train's kinetic energy changes from $8 j$ $8 j$ to $36 j$ $36 j$ , by how much will the centripetal force applied by the tracks change by?