*Conservative force and its potential energy function Consider the components of a position dependent force F(r): Fx = ayz + bx + c Fy = axz + bz Fz = axy + by. (a) Show that this force is conservative. (b) Find its corresponding potential energy function, V (r)
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Expert's answer
2021-08-29T16:55:10-0400
Given:
Fx=ayz+bx+cFy=axz+bzFz=axy+by
(a) For conservative field
curlF=0
In our case
curlF=∣∣i^∂x∂Fxj^∂y∂Fyk^∂z∂Fz∣∣
=∣∣i^∂x∂ayz+bx+cj^∂y∂axz+bzk^∂z∂axy+by∣∣
=i^(ax+b−ax−b)+j^(ay−ay)+k^(az−az)=0
(b) The potential energy function satisfies equation
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