Explanation:
stresses within itself or other factors. since 1000m is above the ground, it would rely on gravity, such as; " what goes up must come down," the gravity is present because it is above ground level, example, a mud slide on a small island, needs h2o to become heavier to collapse...
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.
Answer:
87.1 mph
Explanation:
We are given that
Mass,m=60 kg
Power,P=340 W
Speed,v=5 m/s
Area,
Drag coefficient,
Coefficient of rolling resistance,
Friction force,
Where 
Let speed of cyclist=v'
Drag force,
Density of air,
Power,P=
1 m=0.00062137 miles
1 hour=3600 s
Density of powder 1 = 0.5 g / 45 cm^3 = 1/90 g/cm^3
Density of powder 2 = 1.3 g / 65 cm^3 = 1/50 g/cm^3
Therefore the densities of the two powders are different, hence chemical reaction has occurred.
(note: none of the other choices make sense. In fact, a different density does not necessarily indicate a chemical change, see paragraph below).
Density of powders are not definitive unless they are each of the same size and texture. For example, granular sugar, rock sugar, and icing sugar all have different densities. I would conclude that this experiment does not lend to a reliable answer.
