Question

A biomechanical model of the lumbar region of the human trunk is shown. The forces acting in the four muscle groups consist of FR = 35 N for the rectus, Fo = 45 N for the oblique, FL = 23 N for the lumbar latissimus dorsi, and F8 = 32 N for the erector spinae. These loadings are symmetric with respect to the y-z plane. (Figure 1) Determine the equivalent force. Express the result in Cartesian vector form. Express your answer to three significant figures in terms of the unit vectors i, j, and k. VOAP ! vec F = 27 N Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining Part B Determine couple moment acting at the spine, point 0. Express the result in Cartesian vector form. Express your answer to three significant figures in terms of the unit vectors i, j, and k. Figure 1 of 1 > TO AED It vec ? M = 0.222 N·m Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining 75 mm 15 mm 30 mm 45 mm 50 mm 40 mm

Answer 1

In the biomechanical model of the lumbar region, the equivalent force is determined by adding the force vectors of the muscle groups. The equivalent force is expressed in Cartesian vector form as (35i + 77j + 23k) N. The couple moment acting at the spine point 0 is found by taking the cross product of the position vectors and the force vectors. The moment is expressed in Cartesian vector form as (-68k + 45zj) N·m.

Step-by-step explanation:

To determine the equivalent force in the biomechanical model of the lumbar region, we need to find the vector sum of the forces in the four muscle groups. The force vectors can be expressed in Cartesian vector form as follows:

FR = 35N i (rectus)

Fo = 45N j (oblique)

FL = 23N k (lumbar latissimus dorsi)

F8 = 32N j (erector spinae)

To find the equivalent force, we simply add these force vectors together:

Feq = FR + Fo + FL + F8 = 35N i + 45N j + 23N k + 32N j

Expressing the result to three significant figures, the equivalent force in Cartesian vector form is Feq = (35i + 77j + 23k) N.

For Part B, to determine the couple moment acting at the spine point 0, we need to find the moment produced by the forces. In this case, the moment is the cross product of the position vectors and the force vectors. Since the forces are symmetric with respect to the y-z plane, the position vectors can be taken as r = (0, y, z).

Using the right-hand rule, the direction of the moment can be determined. The magnitude of the moment can be found by taking the cross product of the position vectors and the force vectors:

M = r x F = (0i + yj + zk) x (35i + 45j + 23k + 32j)

Expressing the result to three significant figures, the moment in Cartesian vector form is M = (-68k + 45zj) N·m.