A force is represented by the vector F=3i(x2-y2)+2j(x+y) where all coordinate va

ID: 1430096 • Letter: A

Question

A force is represented by the vector F=3i(x2-y2)+2j(x+y) where all coordinate values are in meters and magnitude of the force is in Newtons.

1.) Calculate the work done in joules by this force in a displacement along the line y=0 from the point (0,0) to the point (2,0)

2.) Calculate the work done in joules by this force in a displacement along the line x=2 from the point (2,0) to the point (2,2)

3.) Calculate the work done in joules by this force in a displacement along the line y=x from the point (0,0) to the point (2,2)

AF the vector F=3i(x^2-y^2)+2i(x+y)*I(2-0)+j(0)

w=Fd

(1)

w=3i(x^2-0)+2xj*2i+j0

(3i x^2+2xj)*2i

=3x^2+2xj*i

=3x^2+0

W=3x^2 joules

(2)

For x=2

w=3i(4-y^2)+2j(2+y)*i(2-2)+j(2-0)

w=[3i(4-y^2)+2j(2+y)]*i(0) +j2

w=3i*2j(4-y^2)+2j*j(8+4y)

w=8+4y joule(answer)

(3)

For y=x then

w=3i(x^2-x^2)+2j(x+x).i(2-0)

w=0+2i*2j(2x)

w=8x joule (answer)

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