The character Wolverine has had his bones replaced with a high-density, high-str

Question

The character Wolverine has had his bones replaced with a high-density, high-strength metal alloy called Adamantium, which has the following properties. A density of 7.90 g/cm3 A specific heat of .475 J/g K, and A coefficient of linear expansion of 13.5 x 10-6/C degree During a certain fight. Wolverine's core body temperature increases from 38.0 C to 40.0 C. Now let's model his left femur bones (thigh) as cylinder with a radius of 1.25 cm and a length of 49.5 cm What is the mass of his left humerus bone? degree m = grams Most people's bones are not perfectly symmetric. The mass of his right femur is 1920 grams. How much energy did the right bone have to absorb in order for its temperature to have increased by the given amount? Q = J By how much does the length of his bone increase? delta L = cm

Explanation / Answer

mass= volume x density

m = (pi x r^2 x L ) x density

m = pi x 1.25^2 x 49.5 x 7.90 = 1919.56 grams

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Q = mC deltaT

Q = 1920 x 475 x (40 - 38) = 1824000 J

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L = L0 ( 1 + alpha*deltaT)

L - L0 = L0*alpha*deltaT

L - L0 = 49.5*13.5x10^-6x2 = 1.336 x 10^-3 cm

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