The next illustration shows a person lifting a barbell. (Warning: don\'t try thi

Question

The next illustration shows a person lifting a barbell. (Warning: don't try this yourself. Each year more than half a million Americans sustain serious back injuries by lifting this way.) The other illustration is a mechanical model of the person's upper body. The beam represents the backbone, and the cable represents the back muscles (the real back is a complex set of muscles). The gravitational force that the Earth exerts on the person's upper body at its center of mass is 30 lb. The gravitational force that the Earth exerts on the person's head, arms, and the barbell is 50 lb at the end of the beam. The back muscles (cable) connect 0.20 m from the left end of the 60 m long beam (the backbone) and make a 15 degree angle with the beam. Apply the conditions of equilibrium to the beam and use them to estimate the force that the back muscle exerts on the backbone and the compression force of the beam at its joint on the left side.

Explanation / Answer

Take the moments about the joint

T*sin15 *0.4 = 50*4.45*0.60+ 30*4.45*0.30

T= 1676.36 N

So horizontal component of the force at the joint = 1676.36 * cos15 = 1619.24 N

For vertcial component

20*4.45+30*4.45= 1676.36 sin15 + Y

Y = -77.87 Negative means downwards

Net force = Sqrt( 1619.24^2 + 77.87^2)= 1621.11 N = 364.39 lb

I have multipled by 4.45 to convert lb to newtons

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