Question

A model train with a mass of `4 kg` is moving along a track at `8 (cm)/s`. If the curvature of the track changes from a radius of `54 cm` to `27 cm`, by how much must the centripetal force applied by the tracks change?

Answer 1

`0.0474N`

Explanation:

Firstly let's just put everything in SI units - change the `cm` to `m` to make everything easier to solve.

`8cms^-1 = 0.08ms^-1`
`54cm = 0.54m`
`27 = 0.27m`

Now, the equation for centripetal force is

`F = ma_c = (mv^2)/r`

where `F` is force, `a` is acceleration, `m` is mass`,`v`is velocity` and `r` is radius.

In this case, the radius is changing, so we can say that

`DeltaF = (mv^2)/r_2 - (mv^2)/r_1`

Putting in the values that we know,

`DeltaF = (4*0.08^2)/0.27 - (4*0.08^2)/0.54`

`= 0.0474N`