-/5 points M14 4.6.039 My Notes Ask Your Teacher A hanging wire made of an alloy
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Question
-/5 points M14 4.6.039 My Notes Ask Your Teacher A hanging wire made of an alloy of aluminum with diameter 0.13 cm is initially 2.9 m long. When a 46 kg mass is hung from it, the wire stretches an amount 1.59 cm. A mole of aluminum has a mass of 27 grams, and its density is 2.7 g/cm3 Based on these experimental measurements, what is Young's modulus for this alloy of aluminum? As you've done before, from the mass of one mole and the density you can find the length of the interatomic bond (diameter of one atom). This is 2.55 x 10-10 m for aluminum. As shown in the textbook, the micro quantity ks,, (the stiffness of one interatomic bond) can be related to the macro property Y N/m Additional Materials Section 4.6Explanation / Answer
r = d/2 = 0.065 cm = 0.00065 m
Area = pi * r^2
F = m* a
Stress = force / area
= 46 * 9.80 / (pi x * 0.00065^2)
= 339.63 * 10^6 N
Strain = extension / length
= 0.0159 / 2.9 = 5.48 * 10^-3
Young's modulus = stress / strain
= 339.63 * 10^6 N / 5.48 * 10^-3
= 61.97 * 10^9 Pa [1 Pa = 1 N/m^2 ]
Y = 61.97 * 10^9 N/m^2
the stiffness of one interatomic bond k_s,i = Y * d
= 61.97 * 10^9 N/m^2 * 2.55*10^-10 m
k_s,i = 15.802 N/m
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