- #1

Gabriel Henrique

- 1

- 0

- Homework Statement
- 3.1 (Kibble's Classical Mechanics) Find which of the following forces are conservative, and for those that

are find the corresponding potential energy function (a and b are constants)

- Relevant Equations
- Fx = ax + by², Fy = az + 2bxy, Fz = ay + bz²

Fr = 2ar sin θ sin ϕ, Fθ = ar cosθ sin ϕ, Fϕ = ar cosϕ

The first force components:

Fx = ax + by², Fy = az + 2bxy, Fz = ay + bz²

I calculated the integral V=-∫Fdr, using dr=(dx,dy,dz)

The result I found was

-(1/2(ax²)+2azy+2bxy²+1/3bz³)

The answer in the book (Kibble's Classical Mechanics): -(1/2(ax²)+azy+bxy²+1/3bz³)The second force:

Fr = 2ar sin θ sin ϕ, Fθ = ar cosθ sin ϕ, Fϕ = ar cosϕ

I calculated the integral V=-∫Fdr, using dr=(dr,rdθ,rsinθdϕ)

The result I found was

-arsinθsinϕ(r+1)

The answer in the book (Kibble's Classical Mechanics): -ar²sinθsinϕ

Me and my colleagues can't find where we have mistaken. Can you help us? Our solutions are incorrect?

Fx = ax + by², Fy = az + 2bxy, Fz = ay + bz²

I calculated the integral V=-∫Fdr, using dr=(dx,dy,dz)

The result I found was

-(1/2(ax²)+2azy+2bxy²+1/3bz³)

The answer in the book (Kibble's Classical Mechanics): -(1/2(ax²)+azy+bxy²+1/3bz³)The second force:

Fr = 2ar sin θ sin ϕ, Fθ = ar cosθ sin ϕ, Fϕ = ar cosϕ

I calculated the integral V=-∫Fdr, using dr=(dr,rdθ,rsinθdϕ)

The result I found was

-arsinθsinϕ(r+1)

The answer in the book (Kibble's Classical Mechanics): -ar²sinθsinϕ

Me and my colleagues can't find where we have mistaken. Can you help us? Our solutions are incorrect?