A model train, with a mass of #12 kg#, is moving on a circular track with a radius of #9 m#. If the train's rate of revolution changes from #6 Hz# to #4 Hz#, by how much will the centripetal force applied by the tracks change by?

1 Answer
Joseph W.
Aug 8, 2017

The centripetal force will decrease by a factor of #9/4# or more exactly, by 8640N

Explanation:

Just learnt circular motion today so . . . umm, answer might not be 100% correct. Anyhow, we first need to find the angular speed to find centripetal force. Angular speed is found using

#omega=(2pi)/T#, where #omega# is the angular speed, and #T# is time taken for 1 rotations. When a object has 6#Hz# for circular motion, than it means it rotates around the path 6 time per second and thus. will only take #1/6# for 1 rotation. Likewise, 4#Hz# will have a #T# value of #1/4#. Finding the angular speed for both, we get

#omega=12pi# for the 6#Hz# train

#omega=8pi# for the 4#Hz# train

Now to find centripidal force, we need the equation

#F=momega^2r#, were #m=# mass (kg) and #r=#radius of rotation.

Placing our values into this formula, we get

#F=15552piN# for the 6#Hz# train

#F=6912piN# for the 4#Hz# train

Thus, we can now find the difference between the centripetal force applied by the tracks.

Hope this helps.

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