Question

A force F~ = Fx ˆı + Fy ˆ acts on a particle that

Answer 1

Answer:

W = 46 J

Explanation:

We need to find the angle between the two vectors Force vector and displacement vector.

First we will find the angle α of the force vector

$tan\alpha =\frac{1}{8} \\\\\\alpha =7.125 deg$

Then we find the angle β of the displacement vector

$tan\beta=\frac{2}{6} \\\\beta = 18.43 deg$

With these two angles we can find the angle between the two vectors

∅ = α + β = 25.56 deg

The definition of work is given by the expression

$W=F*d*cos (theta)$

The absolute value of F will be:

$F=\sqrt{8^{2}+1^{2} } \\F= 8.06 N$

The absolute value of d will be:

$d=\sqrt{(6 )^{2}+(2)^{2} } \\d= 6.32m$

Now we have:

$W=8.06*6.32*cos(25.56)\\W=46 J$