# 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?

Mar 11, 2018

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 ${v}^{2} = \left(\frac{6}{4}\right) f 1$

The initial Kinetic energy $= \left(\frac{1}{2}\right) m . {v}^{2}$ = 16 joule(J)

Therefore $\left(\frac{1}{2}\right) .4 k g . \left(\frac{6}{4}\right) f 1 = 16 J$

so f1 the initial centripetal force $= \frac{16}{3} N$

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

speed up and $f 2 = \left(\frac{4}{6}\right) . v e l {.}^{2}$

thereby $\left(\frac{1}{2}\right) m . v e l {.}^{2} = 80 J$

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.