how much work must be done to move the atom from..

Question

An atom is moving radially outward from the origin opposite the pull of force

F= (a)/(r-b)³ - (c)(r⁶)   Where a,b,c are constants and r is the radial distance from the origin 

 

how much work must be done to move the atom from R₁ to R₂ 

Answer 1

Student,

 

From the wording of the problem (i.e. "... opposite the pull of force..."), I am not sure if you provided F or -F.  I will assume you provided F (just reverse the sign otherwise).

 

e_r = unit vector in radial direction

 

F(r) = F(r)e_r

 

The motion is radial, so

 

dr = e_rdr

 

F(r)·dr = F(r)dr

 

W = ∫F(r)dr

 

W = ∫_R1^R2 [a/(r - b)³ - c/r⁶]dr

 

Just evaluate the definite integral using the power rule, which is quite easy.  You should be able to finish from here.