# Chapter 3 - Equilibrium of a Particle - Section 3.4 - Three-Dimensional Force Systems - Problems - Page 113: 49

$m=102Kg$

#### Work Step by Step

We can determine the required maximum mass as follows: $F_{AD}=-\frac{2}{3}F_{AD}\hat i+\frac{2}{3}F_{AD}\hat j+\frac{1}{3}F_{AD}\hat k$ The sum of the forces in the x-direction is given as $\Sigma F_x=0$ $\implies -\frac{2}{3}F_{AD}+F_{AB}=0$..eq(1) The sum of the forces in the y-direction is given as $\Sigma F_y=0$ $\implies \frac{2}{3}F_{AD}-F_{AC}=0$.eq(2) The sum of the forces in the z-direction is given as $\Sigma F_z=0$ $\implies \frac{1}{3}F_{AD}-m(9.81)=0$.eq(3) It is given that the maximum force is $3KN$, so let $F_{AD}=3KN$. Then we plug in this value in eq(1) and eq(2) to obtain: $F_{AB}=F_{AC}=2KN$ Now we plug in the known values in eq(3) to obtain: $\frac{1}{3}(3000)-m(9.81)=0$ This simplifies to: $m=102Kg$

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