A model train, with a mass of #4 kg#, is moving on a circular track with a radius of #6 m#. If the train's kinetic energy changes from #16 j# to #80 j#, by how much will the centripetal force applied by the tracks change by?

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Answer 1 · 2018-03-11T19:14:41

the centripetal force changes by four times of the initial value.

the centripetal force on the circular track is given by

#f = m. v^2/r# where m is mass ,r the radius and v the speed

initially it was # f1 = 4kg. v^2 /(6m #

therefore #v^2 = (6/4) f1#

The initial Kinetic energy # = (1/2)m. v^2 # = 16 joule(J)

Therefore # (1/2) .4kg. (6/4) f1 = 16J #

so f1 the initial centripetal force # = 16/3 N #

now if the kinetic energy is increased to 80 J the train will

speed up and # f2 = (4/6 ).vel. ^2#

thereby # (1/2)m.vel.^2 = 80 J #

putting up value of velocity ,we get

                  #(1/2). 4kg.( 6/4 ). f2 = 80J#

                                        #f2= 80/3 N#

so the change in centripetal force is 4 times the initial value.