Problem $1$:

Consider someone serving a platter of hot food to family and friends seated around a table. They can choose how to hold the platter in front of them as shown in Positions $1$ and $2$ in Figure $1.$

a$)$ Before doing any calculations, use your biomechanics knowledge to predict whether position $1$ or $2$ would be harder to statically maintain if the person has significant elbow flexor weakness. Explain why.

b$)$ Draw free body diagrams of the elbow joint for each position shown. Include gravitational forces $($forearm and hand weight can be combined into one segment$),$ elbow flexor force, and the joint contact force.

c$)$ For Positions $1$ & $2,$ solve for the elbow flexor force, the magnitude of the joint contact force, and the angle that the joint contact force makes with respect to the horizontal axis. Report your forces in Newtons.

The platter of food weighs $8$ lbs ; the person weighs $200$ lbs and they are $5\text{'}6"$ tall.

$=125$ degrees and the elbow flexor muscle inserts $4$ cm from the elbow joint along the forearm.

Anthropometric studies have shown that the combined weight of the forearm and hand equals $2\mathrm{.}2\%$ of a person's total body weight.

Figure $2$ provides additional anthropometric data to help determine the distances along the forearm where the weight of the arm $($forearm $+$ hand can be assumed to be as one segment$)$ and the platter act. Assume the platter is held in the middle of the hand.

d$)$ Prepare a written summary of your results and relate them back to your predictions from part a$).$ Discuss whether your prediction was accurate or not.

e$)$ Consider the two positions again. In which position are the elbow flexors more effective at creating a moment about the elbow joint? Please explain why.

Source: Roebuck, Kroemer, and Thomson, Engineering Anthropmetry Methods, $1975$

Figure $2.$ Anthropometric data for the forearm and hand.