A model train, with a mass of $4$ $4$ $k g$ $kg$ , is moving on a circular track with a radius of $3$ $3$ $m$ $m$ . If the train's kinetic energy changes from $12$ $12$ $J$ $J$ to $48$ $48$ $J$ $J$ , by how much will the centripetal force applied by the tracks change by?

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A model train, with a mass of $4$ $4$ $k g$ $kg$ , is moving on a circular track with a radius of $3$ $3$ $m$ $m$ . If the train's kinetic energy changes from $12$ $12$ $J$ $J$ to $48$ $48$ $J$ $J$ , by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2016-03-06T07:19:23

Centripetal force changes from $8 N$ $8N$ to $32 N$ $32N$

Explanation:

Kinetic energy $K$ $K$ of an object with mass $m$ $m$ moving at a velocity of $v$ $v$ is given by $\frac{1}{2} m v^{2}$ $1/2mv^2$ . When Kinetic energy increases $\frac{48}{12} = 4$ $48/12=4$ times, velocity is hence doubled.

The initial velocity will be given by $v = \sqrt{2 \frac{K}{m}} = \sqrt{2 \times \frac{12}{4}} = \sqrt{6}$ $v=sqrt(2K/m)=sqrt(2xx12/4)=sqrt6$ and it will become $2 \sqrt{6}$ $2sqrt6$ after increase in kinetic energy.

When an object moves in a circular path at a constant speed, it experiences a centripetal force is given by $F = m \frac{v^{2}}{r}$ $F=mv^2/r$ , where: $F$ $F$ is centripetal force, $m$ $m$ is mass, $v$ $v$ is velocity and $r$ $r$ is radius of circular path. As there is no change in mass and radius and centripetal force is also proportional to square of velocity,

Centripetal force at the beginning will be $4 \times \frac{{(\sqrt{6})}^{2}}{3}$ $4xx(sqrt6)^2/3$ or $8 N$ $8N$ and this becomes $4 \times \frac{{(2 \sqrt{6})}^{2}}{3}$ $4xx(2sqrt6)^2/3$ or $32 N$ $32N$ .

Hence centripetal force changes from $8 N$ $8N$ to $32 N$ $32N$

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A model train, with a mass of $4$ $4$ $k g$ $kg$ , is moving on a circular track with a radius of $3$ $3$ $m$ $m$ . If the train's kinetic energy changes from $12$ $12$ $J$ $J$ to $48$ $48$ $J$ $J$ , 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 444 kgkgkg, is moving on a circular track with a radius of 333 mmm. If the train's kinetic energy changes from 121212 JJJ to 484848 JJJ, 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 $4$ $4$ $k g$ $kg$ , is moving on a circular track with a radius of $3$ $3$ $m$ $m$ . If the train's kinetic energy changes from $12$ $12$ $J$ $J$ to $48$ $48$ $J$ $J$ , by how much will the centripetal force applied by the tracks change by?