Final answer:
The expression for the sum of vertical forces (∑Fy) when upward is positive is written as fbiceps - mforearm·g - mball·g = 0, reflecting the static equilibrium of the system.
Step-by-step explanation:
To write an expression for the sum of vertical forces (also known as ∑Fy), where upward forces are considered positive, we analyze the forces acting on an arm holding a weight. Assuming the arm is in static equilibrium (not moving), then according to Newton's second law, the net force acting on the arm is zero. This means that the upward forces must be balanced by the downward forces. The upward force is provided by the bicep's force (fbiceps), and the downward forces include the weight of the forearm (mforearm multiplied by gravity g) and the weight of the ball (mball multiplied by g).
The expression based on these variables would be: fbiceps - mforearm·g - mball·g = 0. Here, fbiceps represents the muscle force exerted by the biceps, mforearm is the mass of the forearm, mball is the mass of the ball being held, and g is the acceleration due to gravity (approximately 9.81 m/s^2 on Earth's surface).
In a scenario where there is no muscle force from the elbow (felbow), or if it is negligible, it would not appear in the expression. However, if there is an elbow force acting upward, it would be added to the fbiceps term as they both provide lifting effects against gravity. The free-body diagram for this situation would show fbiceps and felbow, if relevant, pointing upward, and the weights of the forearm and ball pointing downward. The net sum of the vertical forces would be the sum of all the vertical components of these forces.