The constant forces Fi = x + 2y + 3z (newtons) and F2 = 4x - 5y - 2z (newtons) a

Question

The constant forces Fi = x + 2y + 3z (newtons) and F2 = 4x - 5y - 2z (newtons) act together on a particle during a displacement from the point A = (20,15,0) (m) to the point B = (0,0,7) (m). The forces do work on the particle; the work is given by F . r, where F is the resultant force (here F = F1+F2 ) and r is the displacement. (What is the work done (in joules) on the particle? Suppose the same forces were acting, but the displacement went from B to A. What is the work done (in joules) on the particle in this case?

Explanation / Answer

Fresultant =F1+F2= 5x^-3y^+z^

r =(20-0)x^+(15-0)y^+(0-7)z^=20x^+15y^-7z^

W=F.r=(5x^-3y^+z^).(20x^+15y^-7z^)=100-45-7=48J

b)r=-20x^-15y^+7z^

W=F.r=(5x^-3y^+z^).(-20x^-15y^+7z^) =-100+45+7 =-48J

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