A model train with a mass of 4 kg is moving along a track at 8 (cm)/s. If the curvature of the track changes from a radius of 54 cm to 27 cm, by how much must the centripetal force applied by the tracks change?

1 Answer
Mar 4, 2017

0.0474N

Explanation:

Firstly let's just put everything in SI units - change the cm to m to make everything easier to solve.

8cms^-1 = 0.08ms^-1
54cm = 0.54m
27 = 0.27m

Now, the equation for centripetal force is

F = ma_c = (mv^2)/r

where F is force, a is acceleration, m is mass, v is velocity and r is radius.

In this case, the radius is changing, so we can say that

DeltaF = (mv^2)/r_2 - (mv^2)/r_1

Putting in the values that we know,

DeltaF = (4*0.08^2)/0.27 - (4*0.08^2)/0.54

= 0.0474N