A model train, with a mass of #6 kg#, is moving on a circular track with a radius of #4 m#. If the train's kinetic energy changes from #24 j# to #42 j#, by how much will the centripetal force applied by the tracks change by?

Answer 1

#\deltaF_c=9N#

Given that we have the involvement of Kinetic energy and centripetal force. Kinetic energy is given by the equation #K=1/2mv^2# and centripetal force by equation #F_c=mv^2/r# From both equations, it can be seen that equation of kinetic energy can be substituted into the equation of centripetal force, and the equation would be #F_c=2K/r#

Given that we have to find just the change in the centripetal force, so #\deltaF_c=2/r\deltaK=2/r(K_f-K_i)#

#K_f=42J# and #K_i=24J#, #r=4m# So, substituting into the equation #\deltaF_c=cancel{2}/cancel{4}^2*(42-24)=18/2=9N#

Thus, the centripetal force change is indicated above.

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Answer 2

Isabella Alvarez

The centripetal force applied by the tracks will change by 18 joules.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.