# A model train, with a mass of #9 kg#, is moving on a circular track with a radius of #15 m#. If the train's kinetic energy changes from #72 j# to #48 j#, by how much will the centripetal force applied by the tracks change by?

The change in centripetal frce 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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To find the change in centripetal force, we can use the formula for centripetal force:

Fc = (mv^2) / r

Given: Initial kinetic energy (Ki) = 72 J Final kinetic energy (Kf) = 48 J Mass (m) = 9 kg Radius (r) = 15 m

We know that kinetic energy is directly proportional to the square of velocity (v). So, we can use the ratio of kinetic energies to find the ratio of velocities:

(Kf / Ki) = (vf^2 / vi^2)

Now, we can rearrange this equation to solve for the final velocity (vf):

vf = vi * sqrt(Kf / Ki)

Given that kinetic energy is given by the formula K = (1/2) * m * v^2, we can find the initial and final velocities:

vi = sqrt((2 * Ki) / m) vf = sqrt((2 * Kf) / m)

Now, we can substitute the values and find the initial and final velocities:

vi = sqrt((2 * 72) / 9) ≈ 8 m/s vf = sqrt((2 * 48) / 9) ≈ 6 m/s

Now, we can find the initial and final centripetal forces:

Fci = (m * vi^2) / r Fcf = (m * vf^2) / r

Substituting the values, we get:

Fci ≈ (9 * 8^2) / 15 ≈ 38.4 N Fcf ≈ (9 * 6^2) / 15 ≈ 21.6 N

Now, we can find the change in centripetal force:

ΔF = Fcf - Fci ΔF ≈ 21.6 - 38.4 ΔF ≈ -16.8 N

Therefore, the centripetal force applied by the tracks will decrease by approximately 16.8 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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- Two objects have masses of #4 MG# and #48 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #7 m# to #2 m#?
- A model train, with a mass of #3 kg#, is moving on a circular track with a radius of #5 m#. If the train's kinetic energy changes from #32 j# to #12 j#, by how much will the centripetal force applied by the tracks change by?
- A model train with a mass of #4 kg# is moving along a track at #18 (cm)/s#. If the curvature of the track changes from a radius of #25 cm# to #14 cm#, by how much must the centripetal force applied by the tracks change?

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