A model train, with a mass of #6 kg#, is moving on a circular track with a radius of #7 m#. If the train's rate of revolution changes from #1 Hz# to #2 Hz#, by how much will the centripetal force applied by the tracks change by?

Question

A model train, with a mass of #6 kg#, is moving on a circular track with a radius of #7 m#.  If the train's rate of revolution changes from #1 Hz# to #2 Hz#, by how much will the centripetal force applied by the tracks change by?

Charles Aeschliman · Accepted Answer

The centripetal force applied is #F_c=1654.8#Newtons.

Centripetal force is defined as #F_c=mromega^2#. Angular acceleration #omega= 2pi#(change in frequency) #=>omega=2pi(nu_2-nu_1)#. Now the centripetal force becomes #F_c=mr[2pi(nu_2-nu_1)]^2#. #F_c= 4mrpi^2(nu_2-nu_1)^2# Substituting the given values we get, #F_c= 4(2kg)(7m)(3.14)^2[(2Hz)-(1Hz)]^2# #:. F_c = 1654.8#Newtons.

Charlotte Aaron · Answer

undefined To find the change in centripetal force applied by the tracks, we need to consider the change in angular velocity (ω) of the train as it moves from 1 Hz to 2 Hz.

Given:
Mass of the train (m) = 6 kg
Radius of the circular track (r) = 7 m
Initial frequency (f_initial) = 1 Hz
Final frequency (f_final) = 2 Hz

Angular velocity (ω) is related to frequency (f) by the equation:

Angular velocity = 2π × Frequency

Initial angular velocity (ω_initial) = 2π × 1 Hz = 2π rad/s
Final angular velocity (ω_final) = 2π × 2 Hz = 4π rad/s

The centripetal force is given by the formula:

Centripetal force = Mass × (Angular velocity)^2 × Radius

Initial centripetal force (F_initial) = 6 kg × (2π rad/s)^2 × 7 m
                                    = 84π^2 N

Final centripetal force (F_final) = 6 kg × (4π rad/s)^2 × 7 m
                                  = 336π^2 N

Change in centripetal force (ΔF) = Final centripetal force - Initial centripetal force
                                  = 336π^2 N - 84π^2 N
                                  = 252π^2 N

So, the change in centripetal force applied by the tracks is 252π^2 Newtons.

Adrian Ayala · Answer

undefined The centripetal force applied by the tracks will change by a factor of 4.