- Homework Statement
- The arm in the figure below weighs 43.2 N. The force of gravity acting on the arm acts through point A. Assume that L1 = 0.0890m, L2 = 0.342m and alpha = 11.0deg.
a) Determine the magnitude of the tension force Ft in the deltoid muscle.
b) Determine the magnitude of the tension force Fs of the shoulder on the humerus (upper-arm bone) to hold the arm in the position shown.
c) Determine the angle of tension force Fs relative to the x-axis.
- Relevant Equations
- Static Equilibrium: Fnet = 0 & Torque net = 0
Torque = radius*sin(angle)*Force
a^2 + b^2 = c^2
arctan = Fsin(angle)/Fcos(angle)
I already solved for part a, setting the sum of the Torques of the arms and deltoid equal to 0 and subbing in values which lead to a tension force of 870N in the deltoid.
For part b, I remembered the law of static equilibrium, so the summation x and y components of all the forces in the system must equal 0. I found that the x component for Fs needs to be 854.019 by multiplying the deltoid tension force by cos(11) and the y component for Fs to be the sum of the weight of the arm and the deltoid tension force*sin(11), which was 209.2. I used Pythagorean theorum to find that the magnitude of Fs is 879.27N.
Now for part c, I tried using the x and y components I got for part b and substituted them into arctan, so arctan(209.2/854.019) which resulted in me getting 13.76deg. However, it is wrong even when I try to answer it as -13.76. Is it the x-y components I messed up on?