A model train with a mass of #1 kg# is moving along a track at #24 (cm)/s#. If the curvature of the track changes from a radius of #72 cm# to #180 cm#, by how much must the centripetal force applied by the tracks change?

Question

A model train with a mass of #1  kg# is moving along a track at #24 (cm)/s#.  If the curvature of the track changes from a radius of #72 cm# to #180 cm#, by how much must the centripetal force applied by the tracks change?

William Audy · Accepted Answer

The change in centripetal force is #=0.048N#

Centripetal force is what

#vecF_C=(mv^2)/r*vecr#

The mass is of the train #m=1kg#

The velocity of the train is #v=0.24ms^-1#

The tracks' respective radii are

#r_1=0.72m#

additionally

#r_2=1.80m#

The centripetal force's variance is

#DeltaF=F_2-F_1#

What are the centripetal forces?

#||F_1||=1*0.24^2/0.72=0.08N#

#||F_2||=1*0.24^2/1.80=0.032N#

#DeltaF=F_1-F_2=0.08-0.0032=0.048N#

Nathan Ashcroft · Answer

undefined To calculate the change in centripetal force, use the formula:

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

Where:
- $ F $ is the centripetal force
- $ m $ is the mass of the train
- $ v $ is the velocity of the train
- $ r $ is the radius of curvature of the track

Given:
- $ m = 1 $ kg
- $ v = 24 $ cm/s
- Initial radius $ r_1 = 72 $ cm
- Final radius $ r_2 = 180 $ cm

Calculate the initial centripetal force $ F_1 $ using $ r_1 $, and the final centripetal force $ F_2 $ using $ r_2 $. Then find the difference between $ F_2 $ and $ F_1 $.

$$ F_1 = \frac{m \cdot v^2}{r_1} $$

$$ F_2 = \frac{m \cdot v^2}{r_2} $$

$$ \Delta F = F_2 - F_1 $$

Substitute the given values into the equations and calculate to find the change in centripetal force.