A model train, with a mass of #2 kg#, is moving on a circular track with a radius of #6 m#. If the train's kinetic energy changes from #2 j# to #96 j#, by how much will the centripetal force applied by the tracks change by?

Answer 1

The centripetal force increases by #31 1/3N#

Because the inputs (kinetic energy) and the outputs (centripetal force) don't seem to be related, there must be a link, which we can find by first writing down the equations for each. This is the kind of question that looks complicated when you read it but is simple when you break it down into small steps:

#K.E.=1/2 m v^2#
#F_c=(m v^2)/r#
From this we notice that #v# is the common element. If we find the change in #v# due to the kinetic energy change, we can find the corresponding change in centripetal force.
#K.E._1=1/2 m v_1^2# where #K.E._1 = 2J#
#2J=1/2 2kg * v_1^2#
#v_1=sqrt(2)m//s#

additionally

#K.E._2=1/2 m v_2^2# where #K.E._1 = 96J#
#v_2 = sqrt(96) m//s#

As a result, the centripetal force in the initial and final states can be obtained from:

#F_(c1) = (mv_1^2)/r = (2kg*2m^2//s^2)/(6m) = 2/3N#

additionally

#F_(c2) = (mv_2^2)/r = (2kg*96m^2//s^2)/(6m) = 32N#

Thus, the difference between these two forces represents the change in centripetal force:

Delta F_c is equal to F_(c2)-F_(c1), or 32N -2/3N = 31 1/3N.

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Answer 2

The centripetal force applied by the tracks will change by 192 N.

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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.

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.

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.

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.

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