A model train, with a mass of #4 kg#, is moving on a circular track with a radius of #15 m#. If the train's kinetic energy changes from #32 j# to #12 j#, by how much will the centripetal force applied by the tracks change by?

Question

A model train, with a mass of #4 kg#, is moving on a circular track with a radius of #15 m#.  If the train's kinetic energy changes from #32 j# to #12 j#, by how much will the centripetal force applied by the tracks change by?

Sebastian Acosta · Accepted Answer

#-8/3 N#

Or using correct significant figures:

#-2.7 N# We know that the centripetal force on an object moving in a circle is: #F_"cent" = m*a_"cent" = (mv^2)/r# And kinetic energy of an object is: #KE = 1/2mv^2# #therefore 2KE= mv^2# We can substitute this into our first equation to give us: #F_"cent" = (2KE)/r# And therefore, #DeltaF_"cent" = (2DeltaKE)/r = (2(12J - 32J))/(15m) = -40/15 N = -8/3N# Now, since the problem gives us 2 sig. figs, the answer needs 2 sig. figs as well. #-2.7 N# Final Answer

Xavier Adame · Answer

undefined The change in centripetal force applied by the tracks can be found by using the equation:

ΔF = ΔKE / r

where ΔF is the change in centripetal force, ΔKE is the change in kinetic energy, and r is the radius of the circular track.

ΔF = (12 J - 32 J) / 15 m

ΔF = -20 J / 15 m

ΔF = -1.33 N

The change in centripetal force applied by the tracks is approximately -1.33 Newtons.