Home > Physics > Circular Motion

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?

Answer 1

Adrian Ayala

#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

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Layla Ahmed

The centripetal force applied by the tracks will decrease by approximately 16 N.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.