A model train, with a mass of #8# #kg#, is moving on a circular track with a radius of #1# #m#. If the train's kinetic energy changes from #32# #J# to #0# #J#, by how much will the centripetal force applied by the tracks change?

1 Answer
David G.
Jun 24, 2016

The centripetal force is given by #F=(mv^2)/r#, and we can calculate the change in #v# from the change in the kinetic energy, #E_k=1/2mv^2#. The change in the centripetal force acting is #-64# #N#.

Explanation:

The kinetic energy is given by #E_k=1/2mv^2#, and we can rearrange to make #v# the subject:

#v=sqrt((2E_k)/m)#

The final kinetic energy is zero and therefore the final velocity is zero.

We can use the mass, radius and initial kinetic energy to calculate the initial velocity:

#v=sqrt((2E_k)/m)=sqrt((2*32)/8) = sqrt (64/8) =sqrt8~~2.8# #ms^-1#

Since the final velocity is zero, the final centripetal force will be zero. The initial centripetal force will be:

#F=(mv^2)/r=(8*2.8^2)/1=64# #N#.

Since the final centripetal force is #0# #N#, the change in the centripetal force is:

final - initial = #0-64=-64# #N#

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