When you bend over, a series of large muscles, the erector spinae, pull on your

Question

When you bend over, a series of large muscles, the erector spinae, pull on your spine to hold you up. The following figure shows a simplified model of the spine as a rod of length L that pivots at its lower end. In this model, the center of gravity of the 270N weight of the upper torso is at the center of the spine. The 140 N weight of the head and arms acts at the top of the spine. The erector spinae muscles are modeled as a single muscle that acts at a 12-degree angle to the spine. Suppose the person in the figure bends over to an angle of 30 degrees from horizontal.

The center of gravity is half the length, and the center of gravity for the upper torso is 2/3 of the length

A. What is the tension in the erector muscle?

B. A force from the pelvic girdle acts on the base of the spine. What is the component of this force in the direction parallel to the spine? This large force is the cause of many back injuries.

Explanation / Answer

Torque summation around pivot:

140*L*cos30º 270*(½L)*cos30º - F*(L)*sin12º = 0

F*()*sin12º = [140 + 270*(½)]*cos30º

F = 1.718*10^3 N

The force along the length of the spine is the sum of force components along the spine from the three forces

270*sin30º + 140*sin30º + 1718*cos12º =1.885*10^3 N

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.