COLLEGE PHYSICS
COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 9, Problem 78QAP
To determine

(a)

To identify about who will suffer more transverse break in a bone in human or a cow.

Expert Solution
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Answer to Problem 78QAP

The human suffers more transverse break in a bone than a cow

Explanation of Solution

Given:

Ultimate stress in the transverse direction for human bone =133×106N/m2

Ultimate stress in the transverse direction for cow bone =178×106N/m2

Formula used:

  Ultimate strength=FmaxAmin

Here, all alphabets are in their usual meanings.

Calculation:

Since, Ultimate strength1Amin

Here, human has less area of the cross-section than cow and their ultimate stresses in the transverse direction are nearly equal as compare to their area of the cross-sections.

Hence, human suffers more transverse break in a bone than a cow

Conclusion:

Thus, the human suffers more transverse break in a bone than a cow.

To determine

(b)

To explain, how cow's bones are much more capable of supporting their extreme weight than human.

Expert Solution
Check Mark

Answer to Problem 78QAP

The cow's bones are much more capable of supporting their extreme weight than human because of high longitudinal ultimate stress and wider bone.

Explanation of Solution

Given:

Longitudinal yield stress for human bone =182×106N/m2

Longitudinal ultimate stress for human bone =195×106N/m2

Longitudinal yield stress for cow bone =196×106N/m2

Longitudinal ultimate stress for cow bone =237×106N/m2

Formula used:

  Ultimate strength=FmaxAmin

Here, all alphabets are in their usual meanings.

Calculation:

Since, Ultimate strength1Amin

Here, cow has more area of the cross-section and wider bone (or thicker) than man but longitudinal ultimate stress for cow bone is237×106N/m2 which is more than the longitudinal ultimate stress for human bone (195×106N/m2).

Hence, the cow's bones are much more capable of supporting their extreme weight than human.

Conclusion:

Thus, the cow's bones are much more capable of supporting their extreme weight than human because of high longitudinal ultimate stress and wider bone.

To determine

(c)

The compressive force before the breaking the bone.

Compressed length of the bone.

Expert Solution
Check Mark

Answer to Problem 78QAP

The compressive force before the breaking the bone is 4.0×104N.

Compressed length of the bone is 0.5mm.

Explanation of Solution

Given:

Compressive ultimate stress for human bone =133×106N/m2

Longitudinal elastic modulus of human bone Y=9.6×109N/m2

Area of cross-section of woman's leg A=3.00×104m2

Length of bone L=35cm=35×102m

Let ΔL be the compressed length and Let Fmax be the compressed force

Formula used:

  Ultimate compressivestrength=compressedforceareaofcrosssection=FmaxA(i)

Longitudinal elastic modulus Y=(110Fmax)/AΔL/L(ii)

Here, all alphabets are in their usual meanings.

Calculation:

Substituting the given values in above formula,

  Ultimate compressivestrength=FmaxA

  or,Fmax=(Ultimate compressivestrength)×Aor,Fmax=(133×106N/m2)×(3.00×104m2)or,Fmax=4.0×104N

Now, using equation (ii),

  Y=(110Fmax)/AΔL/L

  or,ΔL=( F max10A)×LYor,ΔL=(4.0× 10 4N10×( 3.00× 10 4 m 2 ))×(35× 10 2m)(9.6× 10 9N/ m 2)or,ΔL=4.9×104m=0.5mm

Hence, the compressive force before the breaking the bone is 4.0×104N.

Compressed length of the bone is 0.5mm.

Conclusion:

Thus, the compressive force before the breaking the bone is 4.0×104N.

Compressed length of the bone is 0.5mm.

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