A model train with a mass of #4 kg# is moving along a track at #3 (cm)/s#. If the curvature of the track changes from a radius of #4 cm# to #27 cm#, by how much must the centripetal force applied by the tracks change?

Question

A model train with a mass of #4  kg# is moving along a track at #3 (cm)/s#.  If the curvature of the track changes from a radius of #4 cm# to #27 cm#, by how much must the centripetal force applied by the tracks change?

Sebastian Acosta · Accepted Answer

The centripetal force changes by #=0.077N#

The centripetal force is

#F=(mv^2)/r#

mass, #m=4kg#

speed, #v=0.03ms^-1#

radius, #=r#

The variation in centripetal force is

#DeltaF=F_2-F_1#

#F_1=4*0.03^2/0.04=0.09N#

#F_2=4*0.03^2/0.27=0.013N#

#DeltaF=0.09-0.013=0.077N#

Nathan Ashcroft · Answer

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

$$ F_c = \frac{{m \cdot v^2}}{r} $$

Where:
- $ F_c $ is the centripetal force,
- $ m $ is the mass of the train (4 kg),
- $ v $ is the velocity of the train (3 cm/s),
- $ r $ is the radius of curvature of the track.

First, calculate the initial centripetal force when the radius is 4 cm:
$$ F_{c1} = \frac{{4 \, \text{kg} \cdot (3 \, \text{cm/s})^2}}{{4 \, \text{cm}}} $$

Then, calculate the final centripetal force when the radius is 27 cm:
$$ F_{c2} = \frac{{4 \, \text{kg} \cdot (3 \, \text{cm/s})^2}}{{27 \, \text{cm}}} $$

Finally, find the difference between the initial and final centripetal forces:
$$ \Delta F_c = F_{c2} - F_{c1} $$