If a particle of mass m is moving in a horizontal circle of radius r with a centripetal force (k/r2), the total energy is:

Asked by Arushi Juyal 12th November 2017, 2:56 PM

Answered by Expert

Answer:

If a particle of mass m is moving in a horizontal circle of radius r with a centripetal force (k/r2), the total energy is:

$begin mathsize 12px style Centripetal space force space equals space mv squared over straight r equals straight k over straight r squared space... left parenthesis given right parenthesis Kinetic space Energy space equals space 1 half mv squared equals space 1 half straight k over straight r Potential space Energy space equals negative space integral subscript infinity superscript straight r straight F space dr The space lower space limit space has space been space taken space as space infinity space because space potential space energy space is space zero space at space infinity equals negative integral subscript infinity superscript straight r space straight k over straight r squared dr equals negative straight k space integral subscript infinity superscript straight r space straight r to the power of negative 2 end exponent space dr equals negative straight k space open vertical bar fraction numerator straight r to the power of negative 1 end exponent over denominator negative 1 end fraction close vertical bar subscript infinity superscript straight r equals fraction numerator negative straight k over denominator straight r end fraction Total space energy space equals space fraction numerator straight k over denominator 2 straight r end fraction minus straight k over straight r equals negative fraction numerator straight k over denominator 2 straight r end fraction end style$