A model train, with a mass of #8 kg#, is moving on a circular track with a radius of #2 m#. If the train's kinetic energy changes from #8 j# to #36 j#, by how much will the centripetal force applied by the tracks change by?

1 Answer
Dwight
Nov 9, 2017

The centripetal force increases by 28 N, from 8 N to 36 N.
Details follow.

Explanation:

Centripetal force is given by

#F_c = (mv^2)/r#

For this train, we know the mass of the train, #m# and the radius #r# of the circular path it is following. What we need is the speed of the train #v#.

Since the kinetic energy #K# is given, we can use this to calculate the speed:

#K = 1/2 mv^2#

which I will rewrite as

#v^2 = (2 K)/m#

(because we will need #v^2# for the centripetal force formula, rather than #v#).

When the energy is 8 J, #v^2 = (2 *8)/8 = 2#

and the centripetal force is #F_c=(mv^2)/r= (8*2)/2 = 8 N#

When the energy is 36 J, #v^2 = (2 *36)/8 = 9#

and the centripetal force is #F_c=(mv^2)/r= (8*9)/2 = 36 N#

The change in centripetal force will be #36-8=28 N#

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