Torque - Arm and Shoulder

1. Apr 8, 2009

tascja

1. The problem statement, all variables and given/known data
A bodybuilder holds a dumbbell of weight Wd as shown in Figure 9.8a. His arm is extended horizontally and weighs Wa = 31.0 N. The deltoid muscle is assumed to be the only muscle acting and is attached to the arm as shown. The maximum force M that the deltoid muscle can supply to keep the arm horizontal has a magnitude of 1840 N. Figure 9.8b shows the distances that locate where the various forces act on the arm. What is the heaviest dumbbell that can be held, and what are the horizontal and vertical force components, Sx and Sy that the shoulder joint applies to the arm?

2. Relevant equations
3. The attempt at a solution
so i already found that the max weight the dumbbell can be is 86.1 N. but im not sure about the Sx and Sy components. I thought they were the components of the deltoid muscle force.
Sx = 1840sin77 = 1790 N
Sy = 1840cos77 = 410 N
The Sy component is wrong, the answer key says that it should be -297 N downward... im not sure how they are getting this answer??

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