1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kakasveta [241]
3 years ago
9

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 +

(1/ 2)ez ? Are there any shear stresses acting on this surface?
Physics
1 answer:
Mumz [18]3 years ago
3 0

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.

You might be interested in
The force that pulls planets torwards the sun is called​
Studentka2010 [4]

Answer:

gravity

Explanation:

Gravity pulls the planets toward the Sun. Gravity pulls the moon toward Earth. Gravity pulls us toward the Earth. Gravity is a force. Inertia.

7 0
3 years ago
A car and a motorcycle start from rest at the same time on a straight track, but the motorcycle is 25.0 m behind the car. The ca
sergeinik [125]

Answer:

t = 8.45 sec

car distance d = 132.09  m

bike distance d = 157.08 m

Explanation:

GIVEN :

motorcycle is 25 m behind the car , therefore distance need to covered by bike to overtake car is 25+ d, when car reache distance d at time t

for car

by equation of motion

d  = ut + \frac{1}{2}at^2

u = 0 starting from rest

d = \frac{1}{2}at^2

t^2 = \frac{2d}{a}

for bike

d+25 = 0 + \frac{1}{2}*4.40t^2

t^2= \frac{d+25}{2.20}

equating time of both

\frac{2d}{a} = \frac{d+25}{2.20}

solving for d we get

d = 132 m

therefore t is= \sqrt{\frac{2d}{a}}

t =  \sqrt{\frac{2*132}{3.70}}

t = 8.45 sec

each travelled in time 8.45 sec as

for car

d = \frac{1}{2}*3.70 *8.45^2

d = 132.09  m

fro bike

d = \frac{1}{2}*4.40 *8.45^2

d = 157.08 m

7 0
3 years ago
Elements that give up electrons easily are called ________
valina [46]

Elements that give up electrons easily are called <u>metals.</u>

hope this helps!

5 0
3 years ago
I'm not sure what to do on this work sheet
Drupady [299]
#1 is 12 u just have to count that one was counting by 5's figure out the pattern on what its counting by and start at the bottom and count your way up till you get to the shaded line
7 0
3 years ago
Read 2 more answers
Three metal spoons are on a table. They are each at room temperature. If the three spoons touch.
hoa [83]
If the three spoon touch nothing happens because they are all at room Temperature
3 0
3 years ago
Read 2 more answers
Other questions:
  • Circle the statements that indicate a chemical property.
    15·1 answer
  • 1. What was the electromagnetic spectrum ?
    5·1 answer
  • When water molecules are disappearing into the air, there is a net _______?
    12·1 answer
  • In a game of egg-toss, you and a partner are throwing an egg back and forth trying not to break it. Given your knowledge of mome
    8·1 answer
  • "Which of the following statements about electrons is not true?
    13·1 answer
  • A fixed mass of an ideal gas is heated from 50°C to 80°C (a) at constant volume and (b) at constant pressure. For which case do
    13·1 answer
  • The diagram below illustrates the law of reflection.
    15·1 answer
  • For the following types of electromagnetic radiation, how do the wavelength, frequency, and photon energy change as one goes fro
    10·1 answer
  • Do Planets with more mass have more gravity than planets with less mass
    11·1 answer
  • a___of water a. of bread a. of soap a. of juice a. salt. a. sand a. of glass a. of corn fill in the blanks I follow him but righ
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!