# A model train with a mass of #2 kg# is moving along a track at #9 (cm)/s#. If the curvature of the track changes from a radius of #6 cm# to #25 cm#, by how much must the centripetal force applied by the tracks change?

##### 2 Answers

The change in centripetal force is

#### Explanation:

The centripetal force is

The mass is of the train

The velocity of the train is

The radii of the tracks are

and

The variation in the centripetal force is

The centripetal forces are

#### Explanation:

Consider a diagram:

We know that centripetal acceleration, towards the centre, is

Now, use the formula to find the acceleration in each case for each radius.

Let

Now, since the acceleration will be towards the centre of the circle, resolve forces towards the centre using Newton's Second Law

So the increase in centripetal force is: