A model train, with a mass of #2 kg#, is moving on a circular track with a radius of #5 m#. If the train's rate of revolution changes from #1/9 Hz# to #1/5 Hz#, by how much will the centripetal force applied by the tracks change by?

Question

A model train, with a mass of #2 kg#, is moving on a circular track with a radius of #5 m#.  If the train's rate of revolution changes from #1/9 Hz# to #1/5 Hz#, by how much will the centripetal force applied by the tracks change by?

Julia Aguilar · Accepted Answer

The centripetal force changes by #=3.12N#

Centripetal force is what

#F=mr omega^2#

mass is #m=2kg#

radius #r=5m#

Delta omega is equal to (1/5-1/9)*2pi, or (8/45pi)rad^-1.

The centripetal force fluctuation is

#DeltaF=mr(Delta omega)^2#

#=2*5*(8/45pi)^2#

#=3.12N#

Adam Arnold · 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 train
f = frequency of revolution (in Hz)
r = radius of the circular track

Given:
Initial frequency (f1) = 1/9 Hz
Final frequency (f2) = 1/5 Hz
Mass of the train (m) = 2 kg
Radius of the circular track (r) = 5 m

First, calculate the initial centripetal force (F1) using the initial frequency:
F1 = 2 * (2 * π * (1/9) * 5)^2

Then, calculate the final centripetal force (F2) using the final frequency:
F2 = 2 * (2 * π * (1/5) * 5)^2

Finally, find the change in centripetal force by subtracting the initial force from the final force:
Change in centripetal force = F2 - F1