Question

A model train with a mass of `7 kg` is moving along a track at `15 (cm)/s`. If the curvature of the track changes from a radius of `24 cm` to `45 cm`, by how much must the centripetal force applied by the tracks change?

Answer 1

0.31N

Explanation:

First calculate the Centripetal Force for one of the situations, in this case I will calculate the force required for the 24cm track first.

At this stage you should convert your quantities to standards units, eg meters and meters per second.

So
`24` cm = `0.24`m
`45` cm = `0.45`m
`15` cm/s = `0.15`m/s

Then use the formula:
`F_c = (mv^2)/r`

And substitute the given values:
`F_c = ((7 kg)(0.15m s^-1)^2)/(0.24 m) = 0.656 N`
`F_c = ((7 kg)(0.15m s^-1)^2)/(0.45 m) = 0.350 N`

Now find the difference between the two forces:
`0.656N - 0.350N = 0.31N`