Question

A model train with a mass of `8 kg` is moving along a track at `9 (cm)/s`. If the curvature of the track changes from a radius of `27 cm` to `81 cm`, by how much must the centripetal force applied by the tracks change?

Answer 1

Change in centripetal force `DeltaF=-16000" "`Dynes

Explanation:

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

Solve for `DeltaF`

Replace `F` with `F+DeltaF` and `r` with `r+Deltar`

`F=(mv^2)/r`
`F+DeltaF=(mv^2)/(r+Deltar)`

Subtract `F` from both sides

`F+DeltaF-F=(mv^2)/(r+Deltar)-(mv^2)/r`

`cancelF+DeltaF-cancelF=(mv^2)/(r+Deltar)-(mv^2)/r`

`DeltaF=(mv^2)/(r+Deltar)-(mv^2)/r`

`DeltaF=(mv^2)(1/(r+Deltar)-1/r)`

But `Deltar=81-27=54`

`DeltaF=(8000(9)^2)(1/(27+54)-1/27)`

`DeltaF=-16000" "`Dynes

God bless....I hope the explanation is useful.