Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_36

⚡ Mecademy AIENG정역학 · ch3  Problem Statement In a procedure to evaluate the strength of the triceps muscle, a person pushes down on a load cell with the palm of his hand as indicated in the figure. If the load-cell reading is 160 N, determine the vertical tensile force F generated by the triceps muscle. The mass of the lower arm is 1.5 kg with mass center at G. State any assumptions. Problem 3/36 (a) Determine the vertical tensile force generated by the triceps muscle ● Calculation Process 1. Present Final Formula: We apply the principle of static equilibrium. By summing the moments about the elbow joint (point ), we can eliminate the unknown joint reaction forces and solve for the muscle force . Taking counter-clockwise (CCW) as the positive direction, the sum of moments is: where: is the triceps force (acting upwards to the left of , creating a clockwise moment). is the weight of the lower arm (acting downwards at ). is the normal reaction force from the load cell (acting upwards on the hand). are the respective horizontal moment arms from point . 2. Substitute Values: From the problem description and diagram: F O F M = ∑ O 0 −F⋅d − F W⋅d + G N⋅d = N 0 FO W=m⋅gG N d ,d ,d FGN O N=160 N m=1.5 kg g= 9.81 m/s 2 d = F 25 mm d = G 150 mm Substituting into the equilibrium equation: 3. Partial Operations: Calculate the individual terms: Weight of lower arm: Moment due to weight: Moment due to load cell reaction: The equation becomes: 4. Final Calculation: Rearrange to solve for :