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3 years ago

What is mantle convection?

1 answer:

8 0

Mantle convection is the slow creeping motion of Earth's solid silicate mantle caused by convection currents carrying heat from the interior of the Earth to the surface.

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What is the force per unit area at this point acting normal to the surface with unit nor- Side View √√ mal vector n = (1/ 2)ex +

Mumz [18]

Complete Question:

Given $\sigma = \left[\begin{array}{ccc}10&12&13\\12&11&15\\13&15&20\end{array}\right]$ at a point. What is the force per unit area at this point acting normal to the surface with $\b n = (1/ \sqrt{2} ) \b e_x + (1/ \sqrt{2}) \b e_z$ ? Are there any shear stresses acting on this surface?

Answer:

Force per unit area, $\sigma_n = 28 MPa$

There are shear stresses acting on the surface since $\tau \neq 0$

Explanation:

$\sigma = \left[\begin{array}{ccc}10&12&13\\12&11&15\\13&15&20\end{array}\right]$

equation of the normal, $\b n = (1/ \sqrt{2} ) \b e_x + (1/ \sqrt{2}) \b e_z$

$\b n = \left[\begin{array}{ccc}\frac{1}{\sqrt{2} }\\0\\\frac{1}{\sqrt{2} }\end{array}\right]$

Traction vector on n, $T_n = \sigma \b n$

$T_n = \left[\begin{array}{ccc}10&12&13\\12&11&15\\13&15&20\end{array}\right] \left[\begin{array}{ccc}\frac{1}{\sqrt{2} }\\0\\\frac{1}{\sqrt{2} }\end{array}\right]$

$T_n = \left[\begin{array}{ccc}\frac{23}{\sqrt{2} }\\0\\\frac{27}{\sqrt{33} }\end{array}\right]$

$T_n = \frac{23}{\sqrt{2} } \b e_x + \frac{27}{\sqrt{2} } \b e_y + \frac{33}{\sqrt{2} } \b e_z$

To get the Force per unit area acting normal to the surface, find the dot product of the traction vector and the normal.

$\sigma_n = T_n . \b n$

$\sigma \b n = (\frac{23}{\sqrt{2} } \b e_x + \frac{27}{\sqrt{2} } \b e_y + \frac{33}{\sqrt{2} } \b e_z) . ((1/ \sqrt{2} ) \b e_x + 0 \b e_y +(1/ \sqrt{2}) \b e_z)\\\\\sigma \b n = 28 MPa$

If the shear stress, $\tau$ , is calculated and it is not equal to zero, this means there are shear stresses.

$\tau = T_n - \sigma_n \b n$

$\tau = [\frac{23}{\sqrt{2} } \b e_x + \frac{27}{\sqrt{2} } \b e_y + \frac{33}{\sqrt{2} } \b e_z] - 28( (1/ \sqrt{2} ) \b e_x + (1/ \sqrt{2}) \b e_z)\\\\\tau = [\frac{23}{\sqrt{2} } \b e_x + \frac{27}{\sqrt{2} } \b e_y + \frac{33}{\sqrt{2} } \b e_z] - [ (28/ \sqrt{2} ) \b e_x + (28/ \sqrt{2}) \b e_z]\\\\\tau = \frac{-5}{\sqrt{2} } \b e_x + \frac{27}{\sqrt{2} } \b e_y + \frac{5}{\sqrt{2} } \b e_z$

$\tau = \sqrt{(-5/\sqrt{2})^2 + (27/\sqrt{2})^2 + (5/\sqrt{2})^2} \\\\ \tau = 19.74 MPa$

Since $\tau \neq 0$ , there are shear stresses acting on the surface.

3 0

3 years ago

____________ is the unit that measures the pressure or force that pushes the flow of electrons forward through a conductor.

velikii [3]

Volt is the unit that measures the pressure or force that pushes the flow of electrons forward through a conductor.

When there is a circuit having a cell / battery , that cell/battery forms an electric field due to difference in voltages , and set a voltage of value equals to the difference in the voltage of two end of that cell/ battery . Because of which a electric field got set up in the conductor , which pushes electron to move inside the conductor . Unit of voltage is volt .

VOLT - A unit of electrical pressure (or electromotive force) which causes current to flow in a circuit. One volt is the amount of pressure required to cause one ampere of current to flow against one ohm of resistance. VOLTAGE - That force which is generated to cause current to flow in an electrical circuit.

Voltage is the pressure from an electrical circuit's power source that pushes charged electrons (current) through a conducting loop, enabling them to do work such as illuminating a light. In brief, voltage = pressure, and it is measured in volts (V).

To learn more about voltage here

brainly.com/question/13521443?referrer=searchResults

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3 0

2 years ago

Read 2 more answers

How much protein would be consumed with a 3-ounce serving of

dalvyx [7]

Answer:

15kg

(i actually did this)

Explanation:

k12

hope this helped!

i hope you ace it!

6 0

3 years ago

A fugitive tries to hop on a freight train traveling at a constant speed of 5.0 m/s. Just as a box car passes him, the fugitive

Dima020 [189]

Answer:Given:

Initial speed of fugitive, v0 = 0 m/s

Final speed, vf = 6.1 m/s

acceleration, a = 1.4 m/s^2

Speed of train, v = 5.0 m/s

Solution:

t = (vf-v0)/a

t = (6.1-0)/1.4

t =4.36 s

Distance traveled by train, x_T =v*t

x_T =5*4.36 = 21.8 m

Distance travelled by fugitive, x_f = v0*t+1/2at^2

x_f = 0*4.36+1/2*1.4*4.36^2

x_f =13.31 m

5*t = v(t-4.36)+x_f

5*t=6.1*(t-4.36)+13.31

solve for t, we get

t = 12.08 s

The fugitive takes 12.08 s to catch up to the empty box car.

Distance traveled to reach the box car is

X_T = v*t

X_T = 5*12.08 s

X_T = 60.4 m

Explanation:

5 0

3 years ago

Why do organisms eat food? Be sure to explain your answer.

snow_tiger [21]

Answer:

organisms eat food because they will die if they don't, just like us humans. their bodies wont be able to run if they do not have a energy supply. the energy supply for every organism is food. this is why organisms eat food.

6 0

4 years ago

Read 2 more answers