Question

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

Answer 1

`-8/3 N`

Or using correct significant figures:

`-2.7 N`

Explanation:

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

`F_"cent" = m*a_"cent" = (mv^2)/r`

And kinetic energy of an object is:

`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