A model train with a mass of #3 kg# is moving along a track at #16 (cm)/s#. If the curvature of the track changes from a radius of #15 cm# to #32 cm#, by how much must the centripetal force applied by the tracks change?

Question

A model train with a mass of #3  kg# is moving along a track at #16 (cm)/s#.  If the curvature of the track changes from a radius of #15 cm# to #32 cm#, by how much must the centripetal force applied by the tracks change?

Isabella Alvarez · Accepted Answer

The change in centripetal force is #=0.27N#

Centripetal force is what

#F=(mv^2)/r#

The mass, #m=(3)kg#

The speed, #v=(0.16)ms^-1#

The radius, #=(r) m#

The centripetal force fluctuation is

#DeltaF=F_2-F_1#

#F_1=mv^2/r_1=3*0.16^2/0.15=0.512N#

#F_2=mv^2/r_2=3*0.16^2/0.32=0.24N#

DeltaF is 0.512-0.24, or 0.27N.

Layla Ahmed · Answer

undefined To find the change in centripetal force applied by the tracks when the curvature changes, we can use the centripetal force formula:

Centripetal force = (mass × velocity^2) / radius

First, we calculate the initial centripetal force when the curvature radius is 15 cm:

Initial centripetal force = (3 kg × (16 cm/s)^2) / 15 cm

Then, we calculate the final centripetal force when the curvature radius changes to 32 cm:

Final centripetal force = (3 kg × (16 cm/s)^2) / 32 cm

Finally, we find the change in centripetal force by subtracting the initial force from the final force:

Change in centripetal force = Final centripetal force - Initial centripetal force