A person bending forward to lift a load "with his back" (Figure a) rather than "with his knees" can be injured by large forces exerted on the muscles and vertebrae. The spine pivots mainly at the fifth lumbar vertebra, with the principal supporting force provided by the erector spinalis muscle in the back. To see the magnitude of the forces involved, and to understand why back problems are common among humans, consider the model shown in Figure b, of a person bending forward to lift a W, = 215-N object. The spine and upper body are represented as a uniform horizontal rod of weight W, = 400 N pivoted at the base of the spine. The erector spinalis muscle, attached at a point two-thirds of the way up the spine, maintains the position of the back. The angle between the spine and this muscle is 12.0°. Back muscle

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Chapter1: Units, Trigonometry. And Vectors
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A person bending forward to lift a load "with his back" (Figure a) rather than "with his knees" can be injured by large forces
exerted on the muscles and vertebrae. The spine pivots mainly at the fifth lumbar vertebra, with the principal supporting
why back problems are common among humans, consider the model shown in Figure b, of a person bending forward to lift
= 400 N pivoted
force provided by the erector spinalis muscle in the back. To see the magnitude of the forces involved, and to understand
a W, = 215-N object. The spine and upper body are represented as a uniform horizontal rod of weight W.
at the base of the spine. The erector spinalis muscle, attached at a point two-thirds of the way up the spine, maintains the
position of the back. The angle between the spine and this muscle is 12.0°.
Back muscle
R,
† 12.0°
Pivot
Wo
W,
b
(a) Find the tension in the back muscle.
kN
(b) Find the compressional force in the spine. (Enter the magnitude.)
kN
Transcribed Image Text:A person bending forward to lift a load "with his back" (Figure a) rather than "with his knees" can be injured by large forces exerted on the muscles and vertebrae. The spine pivots mainly at the fifth lumbar vertebra, with the principal supporting why back problems are common among humans, consider the model shown in Figure b, of a person bending forward to lift = 400 N pivoted force provided by the erector spinalis muscle in the back. To see the magnitude of the forces involved, and to understand a W, = 215-N object. The spine and upper body are represented as a uniform horizontal rod of weight W. at the base of the spine. The erector spinalis muscle, attached at a point two-thirds of the way up the spine, maintains the position of the back. The angle between the spine and this muscle is 12.0°. Back muscle R, † 12.0° Pivot Wo W, b (a) Find the tension in the back muscle. kN (b) Find the compressional force in the spine. (Enter the magnitude.) kN
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