A force F = x2y2i + x2y2j (N) acts on a particle which moves in the XY plane (a) - Physics - Work Energy And Power

Question

A force F = x 2 y 2
i + x 2 y 2
j (N) acts on a particle which moves in the XY plane
(a) Determine F is conservative or not and
(b) Find the work done by F as it moves the particle from A to C
(fig ) along each of the paths ABC, ADC, and AC

Kiruthika · Accepted Answer

Dear student,

(a)If F is conservative then
Fx=-δUδx,Fy=-δUδySo δFxδy=-δ2Uδyδx=-δ2Uδxδy=δFyδxBut for the given force,δFxδy=2x2y,δFyδx=2xy2Hence the given force is not conservative
(b)The work done by the given force is
W=∫F ds =∫(x2y2i+x2y2j)
dx i+dy jW=∫x2y2 dx+∫x2y2 dy

Along AB, y=0 so WAB =0,
Along BC,dx =0 so WBC=∫0aa2y2dy =a53j
Thus work done is WABC=WAB+WBC=a53
Along AD,x=0, WAD =0
Along DC,dy=0
WDC=∫0ax2a2dx=a53Thus WADC =a53j
Along AC,x=y,dx=dy
WAC=2∫0ax4dx=2a53j

â€‹Regards

A force F = x 2 y 2 i + x 2 y 2 j (N) acts on a particle which moves in the XY plane. (a) Determine F is conservative or not and (b) Find the work done by F as it moves the particle from A to C (fig.) along each of the paths ABC, ADC, and AC.

A force F = x ² y ² i + x ² y ² j (N) acts on a particle which moves in the XY plane.
(a) Determine F is conservative or not and
(b) Find the work done by F as it moves the particle from A to C (fig.) along each of the paths ABC, ADC, and AC.