A model train with a mass of #4 kg# is moving along a track at #18 (cm)/s#. If the curvature of the track changes from a radius of #25 cm# to #42 cm#, by how much must the centripetal force applied by the tracks change?

1 Answer
Oct 20, 2016

Answer:

The centripetal force changes in a factor of #25/42#, i.e. approximately #0.6# times greater.

Explanation:

The centripetal force acting on a moving mass #m# traveling a circular path with radius #r# at a constant speed #v# is given by the formula:

#F_c = m v^2/r#

If the path's radius is modified from a #r_1# value to a #r_2# one, the initial centripetal force #F_{c1}# changes to a new value #F_{c2}# which can be compared using the above formula:

#{F_{c2}}/{F_{c1}} = {m v^2/r_2}/{m v^2/r_1} = {1/r_2}/{1/r_1}=r_1 / r_2#

Thus:

#{F_{c2}}/{F_{c1}} = r_1 / r_2 = {25 cm} / {42 cm} ~~0.595... rArr F_{c2} ~~0.595 F_{c1}#