Answer:
perpendicular to the direction of the greatest stress
Answer:
The answer is below
Explanation:
a) Given that the modulus of elasticity (E) = 317 GPa, to find the modulus of elasticity (in GPa) for the nonporous material (
), we use the formula:
![E_0=\frac{E}{1-1.9P+0.9P^2}\\\\where\ P=4.7\%=0.047,hence:\\\\ E_0=\frac{317}{1-1.9(0.047)+0.9(0.047)^2}\\\\E_0=347.3\ GPa](https://tex.z-dn.net/?f=E_0%3D%5Cfrac%7BE%7D%7B1-1.9P%2B0.9P%5E2%7D%5C%5C%5C%5Cwhere%5C%20P%3D4.7%5C%25%3D0.047%2Chence%3A%5C%5C%5C%5C%20E_0%3D%5Cfrac%7B317%7D%7B1-1.9%280.047%29%2B0.9%280.047%29%5E2%7D%5C%5C%5C%5CE_0%3D347.3%5C%20GPa)
b) If the porosity P = 11.1%, then the modulus of elasticity is:
![E=E_0(1-1.9P+0.9P^2)=347.3(1-1.9(0.111)+0.9(0.111)^2)=278\ GPa](https://tex.z-dn.net/?f=E%3DE_0%281-1.9P%2B0.9P%5E2%29%3D347.3%281-1.9%280.111%29%2B0.9%280.111%29%5E2%29%3D278%5C%20GPa)
Answer:
Average velocity is 3.93 cm/s
Root mean square velocity is 4.79 cm/s
Velocity peak to peak is 6.28 cm/s
Explanation:
Speed of 2 particles = 5.3 cm/s
Speed of 4 particles = 1.4 cm/s
Speed of 6 particles = 7.14 cm/s
Speed of 8 particles = 1.52 cm/s
Speed of 2 particles = 7.68 cm/s
![v_{avg}=\frac{2\times 5.3+4\times 1.4+6\times 7.14+8\times 1.52+2\times 7.68}{22}\\\Rightarrow v_{avg}=\frac{86.56}{22}\\\Rightarrow v_{avg}=3.93\ cm/s](https://tex.z-dn.net/?f=v_%7Bavg%7D%3D%5Cfrac%7B2%5Ctimes%205.3%2B4%5Ctimes%201.4%2B6%5Ctimes%207.14%2B8%5Ctimes%201.52%2B2%5Ctimes%207.68%7D%7B22%7D%5C%5C%5CRightarrow%20v_%7Bavg%7D%3D%5Cfrac%7B86.56%7D%7B22%7D%5C%5C%5CRightarrow%20v_%7Bavg%7D%3D3.93%5C%20cm%2Fs)
Average velocity is 3.93 cm/s
![v_{rms}=\sqrt{\frac{2\times 5.3^2+4\times 1.4^2+6\times 7.14^2+8\times 1.52^2+2\times 7.68^2}{22}}\\\Rightarrow v_{rms}=\sqrt{\frac{507.34}{22}}\\\Rightarrow v_{rms}=4.79\ cm/s](https://tex.z-dn.net/?f=v_%7Brms%7D%3D%5Csqrt%7B%5Cfrac%7B2%5Ctimes%205.3%5E2%2B4%5Ctimes%201.4%5E2%2B6%5Ctimes%207.14%5E2%2B8%5Ctimes%201.52%5E2%2B2%5Ctimes%207.68%5E2%7D%7B22%7D%7D%5C%5C%5CRightarrow%20v_%7Brms%7D%3D%5Csqrt%7B%5Cfrac%7B507.34%7D%7B22%7D%7D%5C%5C%5CRightarrow%20v_%7Brms%7D%3D4.79%5C%20cm%2Fs)
Root mean square velocity is 4.79 cm/s
![v_p=7.68-1.4=6.28\ cm/s](https://tex.z-dn.net/?f=v_p%3D7.68-1.4%3D6.28%5C%20cm%2Fs)
Velocity peak to peak is 6.28 cm/s