# A model train with a mass of #2 kg# is moving along a track at #2 (cm)/s#. If the curvature of the track changes from a radius of #7 cm# to #12 cm#, by how much must the centripetal force applied by the tracks change?

The change in centripetal force is

The centripetal force is

The variation in centripetal force is

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To calculate the change in centripetal force, use the formula:

ΔF = m(v²/ r2 - v²/ r1),

where: ΔF is the change in centripetal force, m is the mass of the train (2 kg), v is the velocity of the train (2 cm/s), r1 is the initial radius of curvature (7 cm), and r2 is the final radius of curvature (12 cm).

Substituting the given values into the formula:

ΔF = 2 * [(2²/12) - (2²/7)] ΔF = 2 * [(4/12) - (4/7)] ΔF = 2 * [0.333 - 0.571] ΔF = 2 * (-0.238) ΔF = -0.476 N.

Therefore, the centripetal force applied by the tracks must decrease by 0.476 Newtons.

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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.

- A model train with a mass of #9 kg# is moving along a track at #15 (cm)/s#. If the curvature of the track changes from a radius of #46 cm# to #35 cm#, by how much must the centripetal force applied by the tracks change?
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- 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 #3 j# to #5 j#, by how much will the centripetal force applied by the tracks change by?
- Two objects have masses of #3 MG# and #15 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #130 m# to #24 m#?
- An object with a mass of #4 kg# is revolving around a point at a distance of #2 m#. If the object is making revolutions at a frequency of #5 Hz#, what is the centripetal force acting on the object?

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