"Temperature is the measure of the average kinetic energy of the particles in a substance, which is related to how hot or cold that substance is. Historically, two equivalent concepts of temperature have developed, the thermodynamic description and a microscopic explanation based on statistical physics"
1) B. Energy is the ability to do work
2) C. Energy is conserved, it just goes from one form to another.
3) Work = Force x displacement
= 300 x 100 = 30,000 Joules
4) leaning a brick because no displacement is taking place.
5) They change the amount/strength or direction of the force needed.
6) Less force is needed and applied over a longer distance.
7) Heat is the flow of thermal energy from one object to another.
Complete Question:
Given ![\sigma = \left[\begin{array}{ccc}10&12&13\\12&11&15\\13&15&20\end{array}\right]](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D10%2612%2613%5C%5C12%2611%2615%5C%5C13%2615%2620%5Cend%7Barray%7D%5Cright%5D)
at a point. What is the force per unit area at this point acting normal to the surface with
? Are there any shear stresses acting on this surface?
Answer:
Force per unit area, 
There are shear stresses acting on the surface since 
Explanation:
equation of the normal,
![\b n = \left[\begin{array}{ccc}\frac{1}{\sqrt{2} }\\0\\\frac{1}{\sqrt{2} }\end{array}\right]](https://tex.z-dn.net/?f=%5Cb%20n%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%5C%5C0%5C%5C%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%5Cend%7Barray%7D%5Cright%5D)
Traction vector on n, 
![T_n = \left[\begin{array}{ccc}10&12&13\\12&11&15\\13&15&20\end{array}\right] \left[\begin{array}{ccc}\frac{1}{\sqrt{2} }\\0\\\frac{1}{\sqrt{2} }\end{array}\right]](https://tex.z-dn.net/?f=T_n%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D10%2612%2613%5C%5C12%2611%2615%5C%5C13%2615%2620%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%5C%5C0%5C%5C%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%5Cend%7Barray%7D%5Cright%5D)
![T_n = \left[\begin{array}{ccc}\frac{23}{\sqrt{2} }\\0\\\frac{27}{\sqrt{33} }\end{array}\right]](https://tex.z-dn.net/?f=T_n%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B23%7D%7B%5Csqrt%7B2%7D%20%7D%5C%5C0%5C%5C%5Cfrac%7B27%7D%7B%5Csqrt%7B33%7D%20%7D%5Cend%7Barray%7D%5Cright%5D)
To get the Force per unit area acting normal to the surface, find the dot product of the traction vector and the normal.
If the shear stress, 
, is calculated and it is not equal to zero, this means there are shear stresses.
![\tau = [\frac{23}{\sqrt{2} } \b e_x + \frac{27}{\sqrt{2} } \b e_y + \frac{33}{\sqrt{2} } \b e_z] - 28( (1/ \sqrt{2} ) \b e_x + (1/ \sqrt{2}) \b e_z)\\\\\tau = [\frac{23}{\sqrt{2} } \b e_x + \frac{27}{\sqrt{2} } \b e_y + \frac{33}{\sqrt{2} } \b e_z] - [ (28/ \sqrt{2} ) \b e_x + (28/ \sqrt{2}) \b e_z]\\\\\tau = \frac{-5}{\sqrt{2} } \b e_x + \frac{27}{\sqrt{2} } \b e_y + \frac{5}{\sqrt{2} } \b e_z](https://tex.z-dn.net/?f=%5Ctau%20%3D%20%20%5B%5Cfrac%7B23%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_x%20%2B%20%5Cfrac%7B27%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_y%20%2B%20%5Cfrac%7B33%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_z%5D%20-%2028%28%20%281%2F%20%5Csqrt%7B2%7D%20%29%20%5Cb%20e_x%20%2B%20%281%2F%20%5Csqrt%7B2%7D%29%20%5Cb%20e_z%29%5C%5C%5C%5C%5Ctau%20%3D%20%20%5B%5Cfrac%7B23%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_x%20%2B%20%5Cfrac%7B27%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_y%20%2B%20%5Cfrac%7B33%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_z%5D%20-%20%5B%20%2828%2F%20%5Csqrt%7B2%7D%20%29%20%5Cb%20e_x%20%2B%20%2828%2F%20%5Csqrt%7B2%7D%29%20%5Cb%20e_z%5D%5C%5C%5C%5C%5Ctau%20%3D%20%20%5Cfrac%7B-5%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_x%20%2B%20%5Cfrac%7B27%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_y%20%2B%20%5Cfrac%7B5%7D%7B%5Csqrt%7B2%7D%20%7D%20%5Cb%20e_z)
Since , there are shear stresses acting on the surface.
The correct options are:
1 How tall are you?
2How far is it from your house to your school?
3How wide is your refrigerator?
All these measurements involve to measure a length. Instead, the other two options involve to measure different physical quantities; for instance, the question
4 How much does your sister weigh?
Involve to measure a weight (and so, a mass), while the question
5 How warm is it in San Diego?
requires to measure a temperature.
