A model train, with a mass of $4 k g$ $4 kg$ , is moving on a circular track with a radius of $15 m$ $15 m$ . If the train's kinetic energy changes from $32 j$ $32 j$ to $12 j$ $12 j$ , by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2017-06-10T13:56:53

$- \frac{8}{3} N$ $-8/3 N$

Or using correct significant figures:

$- 2.7 N$ $-2.7 N$

We know that the centripetal force on an object moving in a circle is:

$F_{cent} = m \cdot a_{cent} = \frac{m v^{2}}{r}$ $F_"cent" = m*a_"cent" = (mv^2)/r$

And kinetic energy of an object is:

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

$therefore 2KE= mv^2$

We can substitute this into our first equation to give us:

$F_"cent" = (2KE)/r$

And therefore,

$DeltaF_"cent" = (2DeltaKE)/r = (2(12J - 32J))/(15m) = -40/15 N = -8/3N$

Now, since the problem gives us 2 sig. figs, the answer needs 2 sig. figs as well.

$-2.7 N$

Final Answer

A model train, with a mass of 4 kg4kg4 kg, is moving on a circular track with a radius of 15 m15m15 m. If the train's kinetic energy changes from 32 j32j32 j to 12 j12j12 j, by how much will the centripetal force applied by the tracks change by?