# A model train, with a mass of 24 kg, is moving on a circular track with a radius of 3 m. If the train's kinetic energy changes from 18 j to 21 j, by how much will the centripetal force applied by the tracks change by?

Mar 5, 2016

2N

#### Explanation:

Mass of the train m= 24kg
The radius of circular path (r)=3m
Initial velocity,${v}_{1}$
final velocity,${v}_{2}$
Initial KE,$= \frac{1}{2} m {v}_{1}^{2}$
final KE,$\frac{1}{2} m {v}_{2}^{2}$
Change in KE =$\frac{1}{2} m {v}_{2}^{2} - \frac{1}{2} m {v}_{1}^{2} = 21 - 18 = 3 J$
Dividing both sides of this equation by radius (r)of circular path and multiplying both sides by 2 we have
$m {v}_{2}^{2} / r - m {v}_{1}^{2} / r = 2 \cdot \frac{3}{r}$
We see that left side of the equation is the change in centripetal force
So The change in centripetal force is $= 2 \cdot \frac{3}{r} = \frac{2.3}{3} \frac{N . m}{m} = 2 N$