Hello and thank you in advance for your help!
I am taking an introductory algebra-based physics class and am trying to solve this problem:
Suppose an arm holds an 5.8-kg mass. The total mass of the arm is 3.3 kg. Gravity acts from the center of the arm, which is 24 cm away from the joint. To support the mass, the deltoid muscle exerts a leftward force 15° above the horizontal, and 12 cm away from the joint. The joint itself exerts a rightward force subtending an unspecified angle from the horizontal.
What force, FM, is required of the deltoid muscle, assuming the mass is 52 cm from the shoulder joint?
Since there is no motion,
Tau = 0
Torques about the shoulder joint:
Tau = perpendicular force * length from joint
FG = mg
For forces at an angle:
Fnet = √(Fx)2+(Fy)2
The Attempt at a Solution
There seem to be too many variables to calculate Fm.
The best equation system I could come up with was:
(y+ is up, x+ is rightward)
Taunet = (FM sin 15°)(0.12 m) - (FJsin θ)(x) - (3.3g)(0.24 m) - (5.8g)(0.52 m)
FXnet = (FM sin 15°) - (FJsin θ) - (9.1g)
FYnet = (FJcos θ) - (FM cos 15°)
I know there must be some way to cut the variables down to three and then solve the system, but neither FJ, the angle it subtends, or the lever arm of its vertical force is given. I can't figure out how to work around this.
I hope the image upload works: