A model train, with a mass of #6 kg#, is moving on a circular track with a radius of #4 m#. If the train's kinetic energy changes from #24 j# to #48 j#, by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2017-03-04T20:23:52

#2.05N#

The kinetic energy of the train is given by

#E = 1/2mv^2#

which we can rearrange to find the velocity (which we need) as

#sqrt((2E)/m)=v#

so, calculating the velocity in both cases (#24J# and #48J#),

#v_1 = sqrt((2xx24)/6) = sqrt8 ~~ 2.83ms^-1#

#v_2 = sqrt((2*48)/6) = sqrt16 = 4ms^-1#

Therefore,

#Deltav# = #v_2-v_2 = 4 - 2.83 = 1.17ms^-1#

The equation of centripetal force is

#F = ma_c = (mv^2)/r#

where #F# is force, #m# is mass, #a_c# is centripetal acceleration, #v# is velocity, and #r# is the radius of the circle.

Therefore we can say that change in centripetal force is

#DeltaF = (m(Deltav)^2)/r#

which, putting in the values we know, is

#DeltaF = (6xx1.17^2)/4 ~~ 2.05N#