# A model train, with a mass of #16 kg#, is moving on a circular track with a radius of #9 m#. If the train's kinetic energy changes from #45 j# to #9 j#, by how much will the centripetal force applied by the tracks change by?

The change in centripetal force is

The centripetal force is

The kinetic energy is

The variation of kinetic energy is

The variation of centripetal force is

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The change in kinetic energy is ΔK = K_final - K_initial = 9 J - 45 J = -36 J. The work done by the centripetal force is W = ΔK = F * d, where d is the distance traveled along the circular path. Since the force is always perpendicular to the direction of motion, the displacement and force are in the same direction. So, W = F * d = F * (2 * π * r), where r is the radius of the circular track. Solving for F, we get F = ΔK / (2 * π * r). Substituting the given values, we get F = (-36 J) / (2 * π * 9 m) ≈ -0.637 N. Therefore, the centripetal force applied by the tracks changes by approximately 0.637 N.

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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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