Friction is not conservative

Question

A equilateral triangle is formed using 3 wires, !!AB!!, !!BC!! and !!CA!!. They are placed in a vertical plane such that AB is parallel to earth's surface. Coefficient of friction for all the three wires is the same. If !!w_1!! and !!w_2!! are the work done by friction in moving the object from A to B along AB and ACB then:

  • !!w_1=w_2!!
  • !!w_1 > w_2!!
  • !!w_1 < w_2!!
  • Can't say

Question shared by Siddhant Chawla

Solution

This is pretty straight forward question, you just need to calculate the work done by friction when moving in a straight line !!AB!! and when moving along !!ACB!!

The work done in !!AB!! is: !!w_1=muxxmgxxa!!

The work done in !!ACB!! is: !!w_2=muxxNxxa+muxxNxxa!!

!!=muxxmgcos60xxa+muxxmgcos60xxa!!

!!=muxxmgxxa!!

So the work done by friction along !!AB!! is equal to work done along !!ABC!!

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