Question

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?

Answer 1

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

Explanation:

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.