1. Calculate the ratio of the tensile strain on an aluminum bar to that on a ste

Question

1. Calculate the ratio of the tensile strain on an aluminum bar to that on a steel bar if both bars have the same cross-sectional area and the same force is applied to each bar.

2.A rigid cube (each side is 0.2 m) is filled with water and frozen solid. When water freezes it expands about 9%. How much pressure is exerted on the sides of the cube?Hint: Imagine trying to squeeze the block of ice back into the original cube

3.The anterior cruciate ligament in a woman's knee is 2.5 cm long and has a cross-sectional area of 0.54 cm2. If a force of 2540 N is applied longitudinally, how much will the ligament stretch? The Young's modulus is

YACL = 0.1 109 N/m2.

Explanation / Answer

1) given that tensile stress is same

then Y*tensile strain = constant

Y1*s1 = Y2*s2

s1/s2 = Y2/Y1 = 210/69 = 3

2) initial volume is v = 0.2^3 = 8*10^-3 m^3

change in volume is 0.09*8*10^-3 = 0.00072 m^3

dv/v = 0.00072/(8*10^-3) = 0.09

bulk modulus is B = 2.15GPa

then chnage in pressure is dp = 2.15*10^9*0.09 = 19.35*10^7 Pa

3) stress = F/A = 2540/(0.54*10^-4) = 4.703*10^7 N/m^2

Y = stress/strain

strain = stress/Y = 4.703*10^7/(0.1*10^9) = 0.4703

e/l = 0.4703

e = 0.4703*0.025 =0.01175 m = 1.175 cm

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