A model train, with a mass of #16 kg#, is moving on a circular track with a radius of #3 m#. If the train's kinetic energy changes from #15 j# to #9 j#, by how much will the centripetal force applied by the tracks change by?

Answer 1

The centripetal force changes by #=4N#

The centripetal force is

#F=(mv^2)/r#

The kinetic energy is

#KE=1/2mv^2#

The variation of kinetic energy is

#Delta KE=1/2mv^2-1/2m u^2#
#=1/2m(v^2-u^2)#

The variation of centripetal force is

#DeltaF=m/r(v^2-u^2)#
#DeltaF=2m/r1/2(v^2-u^2)#
#=(2)/r*1/2m(v^2-u^2)#
#=(2)/r*Delta KE#
#=2/3*(15-9)N#
#=4N#
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Answer 2

The change in kinetic energy of the train is ( \Delta KE = KE_{\text{final}} - KE_{\text{initial}} = 9 , \text{J} - 15 , \text{J} = -6 , \text{J} ). The work done by the centripetal force is equal to this change in kinetic energy. Therefore, ( W = \Delta KE = -6 , \text{J} ). Since work is equal to the force multiplied by the displacement, and the displacement is along the direction of the force, ( W = F \cdot d ). In the case of circular motion, the displacement is along the circumference of the circle, so ( d = 2\pi r ). Therefore, ( F = \frac{\Delta KE}{d} = \frac{-6 , \text{J}}{2\pi r} = \frac{-6 , \text{J}}{2\pi \cdot 3 , \text{m}} ). Solving for ( F ) gives ( F \approx -0.318 , \text{N} ). The negative sign indicates that the force decreases by approximately ( 0.318 , \text{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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