Applications of Mechanical Engineering
4) Compare the hip abductor muscle force magnitude and hip joint reaction force magnitude if a person is carrying a weight of W, in each hand (Case A) or in just one hand (Case B) during a single-leg stance. = Case A is a 5-force system. The three-force parallel system made of the gravitational forces (W2 = total body weight - weight of right leg; W. = weight in each hand) can be combined into a single resultant force acting at point G'. In Figure 5.31, points Mand N are the right and left hand, respectively, where the external forces We are applied. Point G is the CoG of the upper body and left leg (notice it is shifted to the left of the dashed midline). If W., W, 17, and la are known, the location of point G' can be calculated using the CoG of system Σ Wx; Σ W, method Xcg Now the system is a non-parallel 3-force system so the lines of action can be extended to find the point of intersection. Once this point is found, geometry can be used to determine ' = 75°. Therefore, we can solve for the two remaining unknowns (Fma and F,x) using a concurrent three-force system. Case B can be analyzed in a similar way with Q' = 70° and W4 = W2 + We to determine F, тв and FJB = Compare the cases by calculating the ratio of results with: W2 = 675 N; W. = 110N; O = 65° Case A Case B W;=W2+2W M N M N f GY 1 W. W Wo FM ' W Wo W2 FJ 12 Fj W W. Fig. 5.31 W3 is the resultant of the three-force system w FM F) Answers: FJA F, is approximately 1.75 times larger in Case B than in Case A (i.e., = 0.57) FJB FMA FM is approximately 2.3 times larger in Case B than in Case A (i.e., = 0.43) FMB
Applications of Mechanical Engineering
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