A model train, with a mass of #2 kg#, is moving on a circular track with a radius of #8 m#. If the train's rate of revolution changes from #1/2 Hz# to #2/5 Hz#, by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2017-02-25T04:15:08

#DeltaF_c = 3pi^2# Newtons

Here, the centripetal force is from the tracks keeping the train in a circle.

Finding the velocity from the frequency
#1/2# #Hz#

#=(1"rotation")/(2"seconds")#

#=(1"rotation")/(2"seconds") * (2pir)/(1"rotation")#

#=8pi# meters per second

Similarly, #2/5# #Hz# = #7.2pi# meters per second

Newtons second law
#F = ma#
#F_c = m*a_c#

Using the equation for centripetal acceleration
#F_c = m*(v^2/r)#

Finding the difference in force

#F_"(at 0.5Hz)" - F_"(at 0.4Hz)" = m*(v_"at0.5Hz"^2/r) - m*(v_"at0.4Hz"^2/r)#

Substituting in values

#DeltaF_c = 2*((8pi)^2/8) - 2*((7.2pi)^2/8)#

#DeltaF_c = 16pi^2 - 13pi^2#

#DeltaF_c = 3pi^2# Newtons

Which is about #30# Newtons