Question $1$: $(20$ points$)$ Consider a person holding a ball in their hand with the elbow flexed at the right angle with respect to the upper arm $($see figure on the right$).$ Point O designates the axis of rotation at the elbow joint, $M$ is the point of attachment of the biceps muscle to the radius, point $A$ is the center of gravity of the forearm, and point B is the center of gravity of the ball held in the hand.

Assume the arm is stationary and the system is at steady state.

Given:

The distances between the axis of rotation of the elbow joint $($point O $)$ and points $M,A,$ and B are $m=5cm,a=20cm,$ and $b=35cm.$

The total weight of the forearm $(F_A)$ is $56\mathrm{.}5$ N $.$

The magnitude of the muscle force $(F_M)$ is $800$ N

a$.(4$ pts$)$ Define the force $(F_J,F_M,F_A,F_B)$ and position vectors $(r_J,r_M,r_A,r_B)$ for all forces in the system. Use vector notation.

b$.(2$ pts$)$ Write the equation for the conservation of linear momentum in this system.