A model train, with a mass of #2 kg#, is moving on a circular track with a radius of #3 m#. If the train's kinetic energy changes from #3 j# to #5 j#, by how much will the centripetal force applied by the tracks change by?

1 Answer
Feb 15, 2016

Answer:

#=1.dot3N#

Explanation:

For Circular Motion, Centripetal Force #F_c= - mr omega^2#

Where #m# is the mass of the body in circular motion. #r# is the radius of the circle and #omega# is angular velocity.
#-# sign means that the force is opposite to the radius vector and is directed towards the center.
Now velocity #v=romega#
Therefore, magnitude of the force #|F_c|=(mv^2)/r#
Kinetic energy is given by
#KE=1/2mv^2#
Let the velocity of the train change from #v_i# to #v_f#
Given is change in kinetic energy #Delta KE=1/2mv_f^2-1/2mv_i^2#
#1/2mv_f^2-1/2mv_i^2=5-3=2#
or #m/2(v_f^2-v_i^2)=2#
or #m(v_f^2-v_i^2)=4# ........(1)

Change in the centripetal force applied by the tracks #=(mv_f^2)/r-(mv_i^2)/r#
#=m/r(v_f^2-v_i^2)# ........(2)
Inserting value of #m(v_f^2-v_i^2)# from (1) and given value of #r#

Change in the centripetal force applied by the tracks #=1/3*4#
#=1.dot3N#