A model train, with a mass of #3 kg#, is moving on a circular track with a radius of #2 m#. If the train's rate of revolution changes from #5/8 Hz# to #3/4 Hz#, by how much will the centripetal force applied by the tracks change by?

Question

A model train, with a mass of #3 kg#, is moving on a circular track with a radius of #2 m#.  If the train's rate of revolution changes from #5/8 Hz# to #3/4 Hz#, by how much will the centripetal force applied by the tracks change by?

Leo Abeyta · Accepted Answer

The centripetal force change by #=3.7N#

Centripetal force is what

#F=mr omega^2#

The mass is #m=3kg#

The radius #r=2m#

The angular velocity change is

Delta omega is equal to (3/4-5/8)*2pi, or (1/4pi)rad^-1.

The centripetal force fluctuation is

#DeltaF=mr(Delta omega)^2#

#=3*2*(1/4pi)^2#

#=3.7N#

Olivia Askew · Answer

undefined To calculate the change in centripetal force, we need to use the formula for centripetal force:

F = m * (2 * π * f * r)^2

Where:
F = centripetal force
m = mass of the object (in this case, the train) 
f = frequency of revolution (in Hz)
r = radius of the circular track

Using the given values:
Initial frequency (f1) = 5/8 Hz
Final frequency (f2) = 3/4 Hz
Initial centripetal force (F1) = m * (2 * π * (5/8) * 2)^2
Final centripetal force (F2) = m * (2 * π * (3/4) * 2)^2

Substitute the values into the formula and calculate the difference between the final and initial centripetal forces:

ΔF = F2 - F1