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. (Figure 1) 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 330 N weight of the upper torso is at the center of the spine. The 170 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 an 12? angle to the spine. Suppose the person in (Figure 1) bends over to an angle of 30? from the horizontal.

A -

What is the tension in the erector muscle? Hint: Align your x-axis with the axis of the spine.

Express your answer to two significant figures and include the appropriate units.

B -

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

Express your answer to two significant figures and include the appropriate units.

Problem 8.47 Part A When you bend over, a series of large muscles, the erector spinae, pull on your spine to hold you up. (Figure 1) 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 330 N weight of the upper torso is at the center of the spine. The 170 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 an 12 What is the tension in the erector muscle? Hint: Align your z-axis with the axis of the spine Express your answer to two significant figures and include the appropriate units. angle to the spine. Suppose the person in (Figure 1) bends over to an angle of 30° from the horizontal TValue Units Submit My Answers Give Up Incorrect; Try Again; 5 attempts remaining Part B Figure 1 of 1 A force from the pelvic girdle acts on the base of the spine. What is the component of this force in the direction of the spine? (This large force is the cause of many back injuries) Express your answer to two significant figures and include the appropriate units Effective location of erector spinae muscles 30° LA Center of gravity of head and arms | Fp.g= 1 Value Units /// Center of gravity of upper torso Submit My Answers Give Up Incorrect; Try Again; 5 attempts remaining

Explanation / Answer

Part-A

W=330N

w=170N

Torque summation around pivot:

2/3LTsin[180o-12o]-L/2 W sin[180o-60o]-L w sin[180o-60o]=0

0.139T-165*0.866-170*0.866=0

0.139T-142.9-147.2=0

0.139T-290.12=0

0.139T=290.12

T=2087.2N

Part -B

Force summation along the x and y axis

Fx=0;

we get; Nx-Tcos[30o-12o]=0

Nx=T*cos [18o]=2087.2*cos [18o]= 1985.05N

Fy=0;

we get; Ny-W-w-Tsin[30o-12o]=0

Ny-330-170-2087.2*sin[18o]=0

Ny-500-644.98=0

Ny=1144.98N

F= N= [ Nx2+Ny2]1/2=[1985.052+1144.982]1/2=2291.6N

F= 2300N [ in two significant figures]

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