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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A person bending forward to lift a load “with his back” (Fig. P8.23a) 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 P8.23b of a person bending forward to lift a 200.-N object The spine and upper body are represented as a uniform horizontal rod of weight 350. 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°. Find (a) the tension in the back muscle and (b) the compressional force in the spine.

images

Figure P8.23

(a)

To determine
The tension in the back muscle.

Explanation

Given info: The weight of the load is 200N and the spine and upper body weight is 350N .

Explanation: The vertical component of tension in the muscle can be determined by the relation of rotational equilibrium. The torque on the system is τ=0=[(2/3)L]Ty(L/2)WLWload , from which the tension in the muscle is calculated.

The formula for the vertical component of the tension in the muscle is,

Ty=3W+32Wload

  • W is the spine and upper body weight.
  • Wload is weight of the load.

Substitute 350N for W and 200N for Wload to find Ty

(b)

To determine
The compressional force in the spine.

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