Question

1) Explain why A) If the wo rk done by a force in any closed loop is zero then it must be conservative. Su Pate is taken th user Le te samt B) It is not possible to define potential energy for any force that is not conservative

Answer 1

a) work done by a force F along a closed path is not always zero. It is zero only when the force (and the system) is conservative. A system cannot be conservation if function or other dissipation forces are present, so a closed integral force Contourintegral F ds cannot vanish. When, work w is independent of the path of integration between the end points land 2 and can be expressed as the end points 1 and 2 and can be expresses as the change in a quantity which depends only upon the position of end points, the word done over a closed orbit is zero. For a conservative system the work done by the forces is w(1 rightarrow 2) = v_1 - v_2 w(2 rightarrow 1) = v_2 - v_1 Total workdone w(1 rightarrow 2) + w(2 rightarrow 1) = 0 b) with a non conservative force field the energy used in moving from one point to another is path dependent.