Non-central force and work done

[Samia qureshi]

when we start from a point say 'O' cover some distance and back to same point work done in the case is zero.will it be zero too for the non-central force as given below in pic.. am i solving it in the right way?

 

[drvrm]

when we start from a point say 'O' cover some distance and back to same point work done in the case is zero.will it be zero too for the non-central force as given below in pic.. am i solving it in the right way?

i do not understand your differential d(phi) ; how this is defined...
well you have a force which has two parts radial one F(r) and F(theta) the motion is in a plane (r, theta) so any displacement has two parts ;
as it is moving in a circle r is not changing so no work done by the radial force ...as regards theta part as the angle is changing and it returns to the same point after covering 2.pi angle ...
how come the work done will be zero ...so try to analyse your answer.

 

[Samia qureshi]

i do not understand your differential d(phi) ; how this is defined...
well you have a force which has two parts radial one F(r) and F(theta) the motion is in a plane (r, theta) so any displacement has two parts ;
as it is moving in a circle r is not changing so no work done by the radial force ...as regards theta part as the angle is changing and it returns to the same point after covering 2.pi angle ...
how come the work done will be zero ...so try to analyse your answer.

means if angle changes work done will not b zero? if angle changes and still it returns to same point then will it b zero?

 

[Chestermiller]

when we start from a point say 'O' cover some distance and back to same point work done in the case is zero.will it be zero too for the non-central force as given below in pic.. am i solving it in the right way?

Is the circle that it travels along centered at the origin?