# A model train with a mass of #8 kg# is moving along a track at #9 (cm)/s#. If the curvature of the track changes from a radius of #180 cm# to #63 cm#, by how much must the centripetal force applied by the tracks change?

The change in centripetal force is

The centripetal force is

The radii are

and

The variation in centripetal force is

The centripetal forces are

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To find the change in centripetal force, we first need to calculate the initial centripetal force using the initial radius of curvature and velocity, and then calculate the final centripetal force using the final radius of curvature. The formula for centripetal force is F = (mv^2) / r, where F is the centripetal force, m is the mass, v is the velocity, and r is the radius of curvature.

Initial centripetal force: F_initial = (m * v^2) / r_initial

Final centripetal force: F_final = (m * v^2) / r_final

Change in centripetal force: ΔF = F_final - F_initial

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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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- An object with a mass of #5 kg# is revolving around a point at a distance of #8 m#. If the object is making revolutions at a frequency of #4 Hz#, what is the centripetal force acting on the object?

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