Answer :
The upper arm bone shortens by [tex]2.2693* 10^-^6[/tex] meters, or approximately 2.3 micrometers.
How do we calculate?
shortening = (force * distance) / (bone stiffness * bone area)
The force applied to the bone is equal to the weight of the wrestler, which is 151 kg * 9.81 m/s² = 1479.51 N.
The distance the force is applied across is equal to the length of the bone, which is 36.0 cm.
The bone stiffness is equal to 1.87e11 Pa.
The cross-sectional area of the bone can be calculated using the following equation:
bone area = pi * (bone radius²
where:
bone area is the cross-sectional area of the bone, in square meters
pi is a mathematical constant with a value of approximately 3.14
bone radius is the radius of the bone, in meters
The radius of the bone is 2.0 cm, so the cross-sectional area of the bone is:
bone area = pi * (2.0 cm)² = 12.566370614359172 cm²
bone area = 12.566370614359172 cm² * (1 m / 100 cm)² = 0.0012566370614359172 m²
shortening = (1479.51 N * 0.36 m) / (1.87e11 Pa * 0.0012566370614359172 m²) = [tex]2.269 * 10^-^6 m[/tex]
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