Iso Excersice, a person places a hand on a scale and pushes vertically downward,

Question

Iso Excersice,
a person places a hand on a scale and pushes vertically downward, keeping the forearm horizontal. This is possible because the triceps muscle applies an upward force M perpendicular to the arm. The forearm weights 22.0 N and has a center of gravity . The scale registers 111 N . Determine the magnitude of M.

Dimension: from Triceps muscle to center of elbow joint is 0.0250 m
Dimension: from center of elbow joint to center of gravity is 0.150 m
Dimension: from center of elbow joint to center of hand is 0.300 m

Explanation / Answer

Considering the forces on the arm:
M is up, the weight of the forearm is down, and the pressure from the scale is up.

For vertical equilibrium, there must be a downward force at the elbow joint, but as we are not interested in that, take moments about that point.

M * 0.025 = 111 * 0.3 - 22 * 0.15
M = 1200N.

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