A model train, with a mass of $2 kg$ , is moving on a circular track with a radius of $8 m$ . If the train's rate of revolution changes from $1/2 Hz$ to $2/5 Hz$ , by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2017-02-25T04:15:08

$DeltaF_c = 3pi^2$ Newtons

Here, the centripetal force is from the tracks keeping the train in a circle.

Finding the velocity from the frequency
$1/2$ $Hz$

$=(1"rotation")/(2"seconds")$

$=(1"rotation")/(2"seconds") * (2pir)/(1"rotation")$

$=8pi$ meters per second

Similarly, $2/5$ $Hz$ = $7.2pi$ meters per second

Newtons second law
$F = ma$
$F_c = m*a_c$

Using the equation for centripetal acceleration
$F_c = m*(v^2/r)$

Finding the difference in force

$F_"(at 0.5Hz)" - F_"(at 0.4Hz)" = m*(v_"at0.5Hz"^2/r) - m*(v_"at0.4Hz"^2/r)$

Substituting in values

$DeltaF_c = 2*((8pi)^2/8) - 2*((7.2pi)^2/8)$

$DeltaF_c = 16pi^2 - 13pi^2$

$DeltaF_c = 3pi^2$ Newtons

Which is about $30$ Newtons

A model train, with a mass of 2 kg2 kg, is moving on a circular track with a radius of 8 m8 m. If the train's rate of revolution changes from 1/2 Hz1/2 Hz to 2/5 Hz2/5 Hz, by how much will the centripetal force applied by the tracks change by?