Find the work done by the force field F in moving an object from P(-5, 9) to Q(3, 5).

Expert Answers
crmhaske eNotes educator| Certified Educator

First we must parametrize the path:

r(t) = (-5,9) + t(8,-4) =(-5+8t,9-4t) for t [0,1]

Now, in order to solve for work:

W = `int_rF*dr=int_0^1((-10+16t)/(9-4t),(-5+8t)^2/(9-4t)^2)*(8,-4)dt`

` `

Solve the dot product `F*R:`





This integral can be solved using integration by partial fractions:



The first integral is solved using simple integration:

-48(1-0) = -48


The second integral is solved using integration by substitution:

z = 4t-9 and dz = 4dt therefore dt = dz/4 




The last integral is also solved using integration by substitution:

z = 4t - 9 and dz = 4 dt therefore dt = dz/4

`int_0^1(676/(4t-9))dt = int_0^1(676/z^2)(dz/4) = int_0^1(169/z^2)dz`



Therefore the solution is:

W = -48-(-25.58)-15 = -37.4

alainnass | Student


F(x,y)= (2x/y) i - (x^2/y^2) j