A model train with a mass of #8 kg# is moving along a track at #9 (cm)/s#. If the curvature of the track changes from a radius of #27 cm# to #81 cm#, by how much must the centripetal force applied by the tracks change?

1 Answer

Answer:

Change in centripetal force #DeltaF=-16000" "#Dynes

Explanation:

From #F=(mv^2)/r#

Solve for #DeltaF#

Replace #F# with #F+DeltaF# and #r# with #r+Deltar#

#F=(mv^2)/r#
#F+DeltaF=(mv^2)/(r+Deltar)#

Subtract #F# from both sides

#F+DeltaF-F=(mv^2)/(r+Deltar)-(mv^2)/r#

#cancelF+DeltaF-cancelF=(mv^2)/(r+Deltar)-(mv^2)/r#

#DeltaF=(mv^2)/(r+Deltar)-(mv^2)/r#

#DeltaF=(mv^2)(1/(r+Deltar)-1/r)#

But #Deltar=81-27=54#

#DeltaF=(8000(9)^2)(1/(27+54)-1/27)#

#DeltaF=-16000" "#Dynes

God bless....I hope the explanation is useful.