A model train, with a mass of #3 kg#, is moving on a circular track with a radius of #8 m#. If the train's rate of revolution changes from #1/9 Hz# to #1/2 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 #8 m#.  If the train's rate of revolution changes from #1/9 Hz# to #1/2 Hz#, by how much will the centripetal force applied by the tracks change by?

Emily Abbate · Accepted Answer

The centripetal force changes by #=143.3N#

Centripetal force is what

#F=mr omega^2#

The mass is #m=3kg#

The radius #r=8m#

The angular velocity change is

Delta omega is equal to (1/2-1/9)*2pi, or (7/9pi)rad^-1.

The centripetal force fluctuation is

#DeltaF=mr(Delta omega)^2#

#=3*8*(7/9pi)^2#

#=143.3N#

Layla Ahmed · Answer

undefined To find the change in centripetal force, use the formula $ F = \frac{{m \cdot v^2}}{r} $, where $ F $ is the centripetal force, $ m $ is the mass, $ v $ is the velocity, and $ r $ is the radius of the circular track. Since $ v = 2\pi r \cdot f $, where $ f $ is the frequency, we can calculate the initial and final velocities using the initial and final frequencies. Then, calculate the initial and final centripetal forces using the given data. Finally, subtract the initial force from the final force to find the change in centripetal force.