Chapter 4, Problem 40P

A waiter extends his arm to hand a plate of food to his customer. The free- body diagram is shown in Fig. P4.40 where $F_m=250\sqrt{2}N$ is the force in the deltoid muscle, $W_a=35$ N is the weight of the arm, $W_p=15$ N is the weight of the plate of food, $R_x$ and $R_y$ are the

x- and y-components of the reaction forces at the shoulder, and $\theta =45°$.

(a) Using the x-y coordinate system shown in Fig. P4.40, write the deltoid muscle force ${\stackrel{\to }{F}}_m$. the weight of the arm ${\stackrel{\to }{W}}_a$, and the weight of the plane ${\stackrel{\to }{W}}_p$, in the standard vector notation (i.e.. using unit vectors i and j ). (b) Determine the values of $R_x$ and $R_y$, required for static equilibrium: $\stackrel{\to }{R}+{\stackrel{\to }{F}}_m+{\stackrel{\to }{W}}_a+{\stackrel{\to }{W}}_p=0$. Also compute the magnitude and direction to $\stackrel{\to }{R}$.