A model train with a mass of #7 kg# is moving along a track at #15 (cm)/s#. If the curvature of the track changes from a radius of #32 cm# to #45 cm#, by how much must the centripetal force applied by the tracks change?

Question

A model train with a mass of #7  kg# is moving along a track at #15 (cm)/s#.  If the curvature of the track changes from a radius of #32 cm# to #45 cm#, by how much must the centripetal force applied by the tracks change?

Amelia Adams · Accepted Answer

The change in centripetal force is #=0.41N#

Centripetal force is what

#F=(mv^2)/r#

The mass is of the train #m=7kg#

The velocity is #v=0.15ms^-1#

The radii are

#r_1=0.32m#

additionally

#r_2=0.45m#

The centripetal force's variance is

#DeltaF=F_2-F_1#

What are the centripetal forces?

#F_1=7*0.15^2/0.32=0.49N#

#F_2=7*0.15^2/0.45=0.35N#

#DeltaF=0.49-0.35=0.14N#

Lily Adams · Answer

undefined The centripetal force required to keep an object moving in a circular path is given by the formula:

$$ F = \dfrac{{mv^2}}{r} $$

Where:
- $ F $ is the centripetal force
- $ m $ is the mass of the object
- $ v $ is the velocity of the object
- $ r $ is the radius of the circular path

Given that the mass of the model train $ m = 7 $ kg, the initial radius $ r_1 = 32 $ cm, the final radius $ r_2 = 45 $ cm, and the initial velocity $ v = 15 $ cm/s, we can calculate the initial centripetal force $ F_1 $ and the final centripetal force $ F_2 $. Then, we can find the change in centripetal force by subtracting the initial from the final:

$$ \Delta F = F_2 - F_1 $$