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A model train, with a mass of #15 kg#, is moving on a circular track with a radius of #3 m#. If the train's rate of revolution changes from #7 Hz# to #3 Hz#, by how much will the centripetal force applied by the tracks change by?

Answer 1

Nathan Ashcroft

The centripetal force changes by #=28424.46N#

The centripetal force is

#F=mr omega^2#

mass is #m=15kg#

radius #r=3m#

#Delta omega=(7-3)*2pi=(8pi)rads^-1#

The variation in centripetal force is

#DeltaF=mr(Delta omega)^2#

#=15*3*(8pi)^2#

#=28424.46N#

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Answer 2

Carson Alexander

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

F = m * (2 * π * r * f)^2

Where: F = centripetal force m = mass of the train r = radius of the track f = frequency of revolution

First, calculate the initial centripetal force with the initial frequency: F_initial = 15 kg * (2 * π * 3 m * 7 Hz)^2

Then, calculate the final centripetal force with the final frequency: F_final = 15 kg * (2 * π * 3 m * 3 Hz)^2

Finally, find the difference between the final and initial centripetal forces: ΔF = F_final - F_initial

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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.