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A model train, with a mass of #3 kg#, is moving on a circular track with a radius of #4 m#. If the train's rate of revolution changes from #3 Hz# to #2 Hz#, by how much will the centripetal force applied by the tracks change by?

Answer 1

Nathan Ashcroft

The answer is #=473.7N#

The centipetal force is

#F=mr omega^2#

#m=# mass

#r=# radius

The variation in centripetal force is

#Delta F=mr (Delta omega)^2#

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

#Delta F=3*4*(2pi)^2=473.7N#

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Answer 2

Sebastian Acosta

To find the change in centripetal force, we first calculate the initial centripetal force (F_initial) using the formula:

F_initial = m * (v_initial)^2 / r

Where: m = mass of the train = 3 kg v_initial = initial velocity = 2 * π * r * frequency_initial r = radius of the track = 4 m frequency_initial = initial frequency = 3 Hz

Then, we calculate the final centripetal force (F_final) using the same formula but with the final frequency:

v_final = 2 * π * r * frequency_final frequency_final = final frequency = 2 Hz

Finally, we find the change in centripetal force by subtracting F_initial from F_final:

ΔF = F_final - F_initial

Substitute the values and calculate.

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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.