A model train with a mass of #3 kg# is moving along a track at #16 (cm)/s#. If the curvature of the track changes from a radius of #12 cm# to #32 cm#, by how much must the centripetal force applied by the tracks change?

Answer 1

The change in centripetal force is #=0.4N#

Centripetal force is what

#F=(mv^2)/r#
mass, #m=3kg#
speed, #v=0.16ms^-1#
radius, #=(r) m#

The centripetal force fluctuation is

#DeltaF=F_2-F_1#
#F_1=mv^2/r_1=3*0.16^2/0.12=0.64N#
#F_2=mv^2/r_2=3*0.16^2/0.32=0.24N#
#DeltaF=0.64-0.24=0.4N#
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Answer 2

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

ΔF = m * Δv^2 / r

Where: ΔF = Change in centripetal force m = Mass of the train (3 kg) Δv = Change in velocity (final velocity - initial velocity) r = Radius of curvature (final radius - initial radius)

Calculating Δv: Initial velocity (v1) = 16 cm/s Final velocity (v2) = 16 cm/s (since speed is constant)

Δv = v2^2 - v1^2

Calculating Δv^2: Δv^2 = (v2^2 - v1^2)^2

Substitute the values into the formula and solve for ΔF:

ΔF = 3 * ((16^2 - 16^2)^2) / (32 - 12)

ΔF = 0

Therefore, the change in centripetal force applied by the tracks is 0.

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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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