College Physics
1st Edition
ISBN: 9781938168000
Author: Paul Peter Urone, Roger Hinrichs
Publisher: OpenStax College
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Chapter 9, Problem 30PE
A person working at a drafting board may hold her head as shown in Figure 9.40, requiring muscle action to support the head. The three major acting forces are shown. Calculate the direction and magnitude of the force supplied by the upper vertebrae FV to hold the head stationary, assuming that this force acts along a line through the center of mass as do the weight and muscle force.
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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 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-195-N object. The spine and upper
body are represented as a uniform horizontal rod of weight W-295 N pivoted at the base of the spine. The erector spinalls 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
Pivot
R₂
T120
T
W
W₂
0
(a) Find the tension in the back muscle.
KN
D
(b) Find the compressional force in the spine. (Enter the magnitude.)
KN
A person working at a drafting board may hold her head as shown in Figure shown, requiring muscle action to support the head. The three major acting forces are shown. Calculate the direction and magnitude of the force supplied by the upper vertebrae FV to hold the head stationary, assuming that this force acts along a line through the center of mass as do the weight and muscle force.
DA man holds a 178-N
ball in his hand, with the arm bone-
22.
Upper
- rlexor muscle
forcarm horizontal (sce the draw-
ing). He can support the ball in
this position because of the flexor
muscle force M, which is applied
perpendicular to the forearm. The
forearm weighs 22.0 N and has a
center of gravity as indicated. Find
(a) the magnitude of M and (b) the
magnitude and direction of the
force applied by the upper arm bone to the forearm at the elbow joint.
Elbow
cg
joint
'0.0890 m
-0.330 m-
0.0510 m
Chapter 9 Solutions
College Physics
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- Even when the head is held erect, as shown in the figure, its center of mass is not directly over the principal point of support (the atlanto-ocipital joint, Point A). The muscles at the back of the neck should, therefore, exert a force to keep the head erect. That is why your head falls forward when you fall asleep in the class. If the head weighs 43 N, calculate the force exerted by the muscles, Fm, using the information in the figure. Assume that x1= 4.9 cm, X2= 2.3 cm, and |Fw|= 43 N. A) Fm= ?? N B) What is the force, Fj, exerted by the pivot on the head?arrow_forwardEven when the head is held erect, as in the figure below, its center of mass is not directly over the principal point of support (the atlanto-occipital joint). The muscles at the back of the neck should therefore exert a force to keep the head erect. That is why your head falls forward when you fall asleep in the class. (a) Calculate the force (in N) exerted by these muscles. (Assume w = 48 N, r1 = 4.8 cm, and r2 = 2.9 cm.) magnitude Ndirection ---Select--- upward downward to the left to the right (b) What is the force (in N) exerted by the pivot on the head? magnitude Ndirection ---Select--- upward downward to the left to the rightarrow_forwardEven when the head is held erect, as shown in the figure, its center of mass is not directly over the principal point of support (the atlanto-occipital joint, Point A). The muscles at the back of the neck should, therefore, exert a force to keep the head erect. That is why your head falls forward when you fall asleep in the class. If the head weighs 55 N, calculate the force exerted by the muscles FM using the information in the figure. Assume that 5.1 cm, x2 2.5 cm, and Fw = 55 N. X1 = -26.96 A F N M = Incorrect M What is the force Fj exerted by the pivot on the head? -81.96 Fj = N Incorrectarrow_forward
- Even when the head is held erect, as shown in the figure, its center of mass is not directly over the principal point of support (the atlanto-occipital joint, Point A). The muscles at the back of the neck should, therefore, exert a force to keep the head erect. That is why your head falls forward when you fall asleep in the class. If the head weighs 51 N, calculate the force exerted by the muscles Fm using the information in the figure. Assume that x1=5.3 cm, x2 = 2.5 cm, and |Fw|= 51 N. What is the force Fj exerted by the pivot on the head? Fj=arrow_forwardA person bending forward to lift a load “with his back”(Fig. P8.23a) rather than “with his knees” can be injured bylarge forces exerted on the muscles and vertebrae. The spinepivots mainly at the fifth lumbar vertebra, with the principalsupporting force provided by the erector spinalis muscle inthe back. To see the magnitude of the forces involved, and tounderstand why back problems are common among humans,consider the model shown in Figure P8.23b of a person bendingforward to lift a 200.-N object. The spine and upper bodyare 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, maintainsthe position of the back. The angle between the spineand this muscle is 12.0°. Find (a) the tension in the back muscleand (b) the compressional force in the spine.arrow_forwardEven when the head is held erect, as shown in the figure, its center of mass is not directly over the principal point of support (the atlanto-occipital joint, Point A). The muscles at the back of the neck should, therefore, exert a force to keep the head erect. That is why your head falls forward when you fall asleep in the class. If the head weighs 55 N, calculate the force exerted by the muscles FM using the information in the figure. Assume that x1 = 4.9 cm, x2 = 1.9 cm, and Fw = 55 N. %3D W X, %3D M M What is the force F exerted by the pivot on the head? |F. W %3Darrow_forward
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- Even when the head is held erect, as shown in the figure, its center of mass is not directly over the principal point of support (the atlanto-occipital joint, Point A). The muscles at the back of the neck should, therefore, exert a force to keep the head erect. That is why your head falls forward when you fall asleep in the class. If the head weighs 43 N, calculate the force exerted by the muscles FM using the information in the figure. Assume that x1 = 5.1 cm, x2 = 2.7 cm, and |Fw = 43 N. N What is the force Fj exerted by the pivot on the head? F; = N Question Credit: OpenStax College Physicsarrow_forwardA 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 Wo = 195-N object. The spine and upper body are represented as a uniform horizontal rod of weight W₁ = 305 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 12.0⁰. Back muscle R₂ T 12.0° 1T Rx Pivot a Wb Wo ..(a).Find the tension in the back muscle. 1.114 Enter a number. differs from the correct answer by more than 10%. Double check your calculations. kN…arrow_forwardA 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 Wo = 210–N object. The spine and upper body are represented as a uniform horizontal rod of weight Wb = 325 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 12.0arrow_forward
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