A model train, with a mass of #4 kg#, is moving on a circular track with a radius of #3 m#. If the train's kinetic energy changes from #8 j# to #48 j#, by how much will the centripetal force applied by the tracks change by?

Answer 1

#deltaF=26.6666666666.......N#

Given we have to find the centripetal force on a model train of mass #m=4kg# which is moving in a circular track of radius #r=3m#
The centripetal force of a body is #F=mv^2/r# and the kinetic energy of a body is #K=1/2mv^2\implies2k=mv^2# Substituting #K# in #F#, we get #F=2K/r# or #deltaF=2/r\deltaK#
Here, #deltaK=48-8=40J# So, change in centripetal force applied by tracks change by #deltaF=2*40/3#
Um.....yeah, that's why you end up with #666666#s
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Answer 2

To find the change in centripetal force applied by the tracks, use the relationship between kinetic energy and centripetal force.

  1. Calculate the initial and final centripetal forces: Initial centripetal force = initial kinetic energy / (radius of the circular track) Final centripetal force = final kinetic energy / (radius of the circular track)

  2. Find the difference between the final and initial centripetal forces.

Given:

  • Mass of the train (m) = 4 kg
  • Radius of the circular track (r) = 3 m
  • Initial kinetic energy (KE_initial) = 8 J
  • Final kinetic energy (KE_final) = 48 J
  1. Initial centripetal force = 8 J / 3 m = 2.67 N Final centripetal force = 48 J / 3 m = 16 N

  2. Change in centripetal force = Final centripetal force - Initial centripetal force = 16 N - 2.67 N ≈ 13.33 N

So, the centripetal force applied by the tracks will change by approximately 13.33 Newtons.

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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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