A model train, with a mass of #4# #kg#, is moving on a circular track with a radius of #3# #m#. If the train's kinetic energy changes from #12# #J# to #48# #J#, by how much will the centripetal force applied by the tracks change by?

1 Answer

Answer:

Centripetal force changes from #8N# to #32N#

Explanation:

Kinetic energy #K# of an object with mass #m# moving at a velocity of #v# is given by #1/2mv^2#. When Kinetic energy increases #48/12=4# times, velocity is hence doubled.

The initial velocity will be given by #v=sqrt(2K/m)=sqrt(2xx12/4)=sqrt6# and it will become #2sqrt6# after increase in kinetic energy.

When an object moves in a circular path at a constant speed, it experiences a centripetal force is given by #F=mv^2/r#, where: #F# is centripetal force, #m# is mass, #v# is velocity and #r# is radius of circular path. As there is no change in mass and radius and centripetal force is also proportional to square of velocity,

Centripetal force at the beginning will be #4xx(sqrt6)^2/3# or #8N# and this becomes #4xx(2sqrt6)^2/3# or #32N#.

Hence centripetal force changes from #8N# to #32N#