A model train, with a mass of #2 kg#, is moving on a circular track with a radius of #3 m#. If the train's kinetic energy changes from #4 j# to #5 j#, by how much will the centripetal force applied by the tracks change by?

Answer 1

The centripetal force will increase by a factor of 5/4.

The formulas for both kinetic energy #KE = 1/2*m*v^2# and centripetal force #F_c = m*v^2/r# have a #v^2# term. If the #v^2# term used in the calculation of kinetic energy is increased by a factor of 5/4, the #v^2# term used in the calculation of centripetal force will also increase by a factor of 5/4.

I hope this helps, Steve

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Answer 2

The change in kinetic energy is ( \Delta KE = KE_f - KE_i = 5 J - 4 J = 1 J ). The centripetal force is given by ( F = \frac{{mv^2}}{r} ). Since the mass and radius remain constant, the change in centripetal force is directly proportional to the change in kinetic energy. Therefore, the change in centripetal force is ( \Delta F = \frac{{\Delta KE}}{r} = \frac{1 J}{3 m} ). So, the change in centripetal force applied by the tracks is approximately ( \frac{1}{3} ) 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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