The woman at the right is lifting a 30lb barbell A mechanica

The woman at the right is lifting a 30-lb barbell. A mechanical model of her upper body is shown below the picture. The beam is her backbone and the cable represents her back muscles (a complex set of muscles in the real back). The Earth\'s gravitational force on her upper body at its center of mass is 30 lb. The Earth\'s gravitational force on her head, arms, and the barbell is 50 lb at the end of the beam. The back muscle (rope) connects 0.20 m from the right end of the 0.60-m long beam (the backbone) and makes a 15 degree angle with the beam. Apply the conditions of equilibrium to the beam and use them to estimate the force that one primary back muscle (it is a complex system) exerts on the backbone and the compression of the beam at its joint on the left side. (Each year more than half a million Americans get serious back problems by lifting this way.)

Solution

Let the tension in the rope be T

therefore taking moment along the hinge on left hand side

50 x 0.6 + 30 x 0.3 = Tsin 15 x 0.4

=> T = 377 lb This the muscle force used

Compressive strength = T cos 15 = 363.87 lb