The beam and the cable (with a frictionless pulley at D) support an 80 kg load at C. In a FBD of only the beam, there are how many unknowns? What are they?

The cdf of the amount of time a book on two-hour reserve is actually checked out can be represented by the function F(x) = P(X ≤ x), where X is the random variable representing the amount of time the book is checked out and x is a specific value of time.

If the cdf is given as f(x), we can find the probability that the book is checked out for a specific amount of time by evaluating the function at that value of x. For example, if we want to find the probability that the book is checked out for less than or equal to one hour, we would evaluate f(1) to get the probability.

Similarly, if we want to find the probability that the book is checked out for more than one hour but less than or equal to two hours, we would evaluate f(2) - f(1) to get the probability.

It is important to note that the cdf, F(x), gives the probability that the book is checked out for less than or equal to a specific amount of time, while the pdf, f(x), gives the probability density at a specific amount of time. The pdf can be found by taking the derivative of the cdf, F'(x) = f(x).

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Engineers apply their knowledge of mathematics and science to solve real-world problems, mathematicians develop and prove new mathematical theories and principles, and scientists use the scientific method to study the natural world and understand phenomena.

Engineers use their knowledge of mathematics and science to design and build practical solutions to real-world problems. They apply their knowledge of physics, chemistry, and mathematics to design, develop, test, and improve products, systems, and processes. They focus on the application of theories and principles to develop practical solutions that meet specific needs or goals.

Mathematicians, on the other hand, use their expertise in mathematics to study abstract concepts, develop new theories, and prove mathematical theorems. They focus on the development of mathematical theories and principles that can be applied to a wide range of fields, including engineering, physics, and computer science. Their work often involves developing new algorithms, models, and methods that can be used to solve complex problems.

Scientists use the scientific method to study the natural world, understand phenomena, and test hypotheses. They use a wide range of tools and techniques to gather data, analyze it, and draw conclusions. Their work often involves designing experiments, conducting observations, and developing models to explain natural phenomena. Scientists focus on understanding the underlying principles that govern the behavior of the natural world.

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The FOUR characteristics of the magnetic lines of force are:

To supply a load that operates at 6 V using four 3 V cells, we can connect the cells in series to increase the total voltage. We can connect two sets of two cells in series, and then connect these two sets in parallel.

This will give us a total voltage of 12 V (3 V + 3 V + 3 V + 3 V) and a current capacity that is equal to the capacity of each individual cell. We can then use a voltage regulator or a resistor to drop the voltage to 6 V, and connect the load RL in series with the voltage regulator or resistor. The circuit diagram will look like:

[3 V]---[3 V]--[3 V]---[3 V]--|

+---[RL]---(voltage regulator or resistor)---|

|

[ground]--------------------------------------------------------------------|

Note that the cells are connected in series in pairs, and the pairs are connected in parallel. The load is connected in series with the voltage regulator or resistor.

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Answer:

Door headers

Explanation:

A spade-type wood bit is used for drilling holes for wood. Electrical panels, wall studs, and concrete floors are all not made from wood. The best option for this question would be the door headers, because it consists of wood.

The interactions between the turbine and its surroundings include the flow of steam into and out of the turbine, as well as the transfer of heat (Q) and work (Wext) between the turbine and its surroundings. The sign of Q and Wext depend on the direction of these transfers.

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The displacement of end A with respect to the fixed support C is 0.00085 m

The displacement of end A with respect to the fixed support C can be determined using the principle of superposition, which states that the displacement of a point on a composite shaft is equal to the sum of the displacements caused by each individual load.

First, we need to determine the displacements caused by the 8 kN and 6 kN loads separately. We can use the equation for the displacement of a point on a shaft subjected to a concentrated load:

δ = PL/EA

Where P is the load, L is the length of the shaft section, E is the modulus of elasticity, and A is the cross-sectional area.

For the 8 kN load:

δ1 = (8 kN)(0.6 m) / (70 GPa)(0.0001 m²) = 0.000686 m

For the 6 kN load:

δ2 = (6 kN)(0.3 m) / (110 GPa)(0.0001 m²) = 0.000164 m

The total displacement of end A with respect to the fixed support C is the sum of these two displacements:

δ = δ1 + δ2 = 0.000686 m + 0.000164 m = 0.00085 m

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The diffraction pattern of a lattice is determined by the Bragg's law, which states that nλ = 2d sin θ, where n is the order of diffraction, λ is the wavelength of the incident beam, d is the lattice spacing, and θ is the angle of incidence. For a 2D triangular lattice with a lattice spacing of 0.15 nm in the x-direction, the diffraction pattern will have three lowest orders corresponding to n = 1, 2, and 3.

The diffraction pattern for an isosceles triangle lattice with a height equal to its base will also have three lowest orders, but the angles of incidence will be different due to the different lattice spacing. The energy of the incident beam also affects the wavelength of the beam and therefore the diffraction pattern. A higher energy beam will have a shorter wavelength and will produce a different diffraction pattern than a lower energy beam.

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Answer: The optical microscope, also referred to as a light microscope, is a type of microscope that commonly uses visible light and a system of lenses to generate magnified images of small objects. Optical microscopes are the oldest design of microscope and were possibly invented in their present compound form in the 17th century. Basic optical microscopes can be very simple, although many complex designs aim to improve resolution and sample contrast.

The object is placed on a stage and may be directly viewed through one or two eyepieces on the microscope. In high-power microscopes, both eyepieces typically show the same image, but with a stereo microscope, slightly different images are used to create a 3-D effect. A camera is typically used to capture the image (micrograph).

The sample can be lit in a variety of ways. Transparent objects can be lit from below and solid objects can be lit with light coming through (bright field) or around (dark field) the objective lens. Polarised light may be used to determine crystal orientation of metallic objects. Phase-contrast imaging can be used to increase image contrast by highlighting small details of differing refractive index.

A range of objective lenses with different magnification are usually provided mounted on a turret, allowing them to be rotated into place and providing an ability to zoom-in. The maximum magnification power of optical microscopes is typically limited to around 1000x because of the limited resolving power of visible light. While larger magnifications are possible no additional details of the object are resolved.

Alternatives to optical microscopy which do not use visible light include scanning electron microscopy and transmission electron microscopy and scanning probe microscopy and as a result, can achieve much greater magnifications.

The necessary velocity, temperature, and density of the airflow in the wind-tunnel test section are 1250 m/s, 89.2 K, and 2.07 kg/m3, respectively.

To calculate the necessary velocity, temperature, and density of the airflow in the wind-tunnel test section such that the lift and drag coefficients are the same for the wind-tunnel model and the actual airplane in flight, we need to use the concept of dynamic similarity. Dynamic similarity occurs when the forces acting on two systems are proportional to each other. This is achieved when the Reynolds number and the Mach number are the same for both systems.

Reynolds number (Re) = (ρVd)/μ

Mach number (Ma) = V/a

Where ρ is the density, V is the velocity, d is the characteristic length, μ is the dynamic viscosity, and a is the speed of sound.

Since the wind-tunnel model is one-fifth the size of the actual airplane, the characteristic length (d) for the model will be one-fifth the characteristic length of the actual airplane.

dmodel = (1/5)dairplane

To achieve dynamic similarity, we need to have the same Reynolds number and Mach number for both systems.

Reairplane = Remodel

(ρairplaneVairplanedairplane)/μairplane = (ρmodelVmodeldmodel)/μmodel

Similarly, we need to have the same Mach number for both systems.

Maairplane = Mamodel

Vairplane/aairplane = Vmodel/amodel

Using the given values and the equations above, we can calculate the necessary velocity, temperature, and density of the airflow in the wind-tunnel test section.

ρmodel = (ρairplaneVairplanedairplaneμmodel)/(Vmodeldmodelμairplane)

Tmodel = (TairplaneVairplane^2)/(Vmodel^2)

Vmodel = (Vairplaneaairplane)/amodel

Plugging in the given values:

ρmodel = (0.414 kg/m3)(250 m/s)(10 km)(1.01x10^5 N/m2)/(Vmodel)(1/5)(10 km)(1.01x10^5 N/m2)

Tmodel = (223 K)(250 m/s)^2/(Vmodel^2)

Vmodel = (250 m/s)(√(287 J/kg-K)(223 K))/(√(287 J/kg-K)(Tmodel))

Solving for Vmodel, Tmodel, and ρmodel, we get:

Vmodel = 1250 m/s

Tmodel = 89.2 K

ρmodel = 2.07 kg/m3

Therefore, the necessary velocity, temperature, and density of the airflow in the wind-tunnel test section are 1250 m/s, 89.2 K, and 2.07 kg/m3, respectively.

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The maximum allowable power for the silicon chip when it is flush mounted in a substrate with an unheated starting length of 20 mm is 0.136 W.

To find the maximum allowable power for the silicon chip, we need to use the equation for heat transfer from a flat plate in parallel flow:

q'' = h(Ts - T∞)

Where q'' is the heat flux, h is the heat transfer coefficient, Ts is the surface temperature, and T∞ is the free stream temperature.

We can rearrange this equation to find the maximum allowable power:

q'' = h(Ts - T∞)Pmax = q''A = hA(Ts - T∞)

Where Pmax is the maximum allowable power and A is the area of the chip. We are given the values for u∞, T∞, Ts, and A, so we can plug these into the equation to find Pmax:

u∞ = 20 m/s

T∞ = 24°C

Ts = 80°CA

= (10 mm × 10 mm)

= 0.0001 m²

We also need to find the value for h, which we can do using the equation for the Nusselt number for a flat plate in parallel flow:

[tex]NuL = 0.664Re^{0.5}Pr^0.33[/tex]

Where NuL is the Nusselt number, Re is the Reynolds number, and Pr is the Prandtl number. We can rearrange this equation to find h:

h = (NuLk)/where k is the thermal conductivity and L is the length of the chip. We can find the values for Re and Pr using the equations:

Re = (u∞L)/νPr = (Cpμ)/k

Where ν is the kinematic viscosity, Cp is the specific heat capacity, and μ is the dynamic viscosity. We can find the values for these properties using the given values for u∞ and T∞ and looking up the properties of air at these conditions:

ν = 15.68 × 10^-6 m²/s

Cp = 1007 J/kg·Kμ

= 18.46 × 10^-6 kg/m·sk

= 0.02624 W/m·K

We can now plug these values into the equations to find Re, Pr, NuL, and h:

Re = (20 m/s × 0.01 m)/(15.68 × 10^-6 m²/s)

= 12755.1Pr =

(1007 J/kg·K × 18.46 × 10^-6 kg/m·s)/(0.02624 W/m·K)

= 0.708NuL

= 0.664(12755.1^0.5)(0.708^0.33)

= 59.58h

= (59.58 × 0.02624 W/m·K)/0.01 m

= 155.6 W/m²

We can now plug these values into the equation for Pmax to find the maximum allowable power:

Pmax = (155.6 W/m²·K)(0.0001 m²)(80°C - 24°C) = 0.874 W

We can use the equation for the Nusselt number for a flat plate with an unheated starting length:

NuL = 0.3387(ReLPr)^(1/3)

Where L is the length of the heated portion of the plate.

We can plug in the values for Re, Pr, and L to find NuL:

NuL = 0.3387(12755.1 × 0.01 m × 0.708)^(1/3)

= 9.23

We can now use this value for NuL to find a new value for h:

h = (9.23 × 0.02624 W/m·K)/0.01 m = 24.25 W/m²·

We can now plug this value for h into the equation for Pmax to find the maximum allowable power:

Pmax = (24.25 W/m²·K)(0.0001 m²)(80°C - 24°C)

= 0.136 W

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This statement is incorrect. All of the factors listed (humidity, surface finish, material, and temperature) can affect friction. For example, a rough surface finish will increase friction compared to a smooth surface, while increasing temperature can reduce friction.

There is no single factor that does not affect friction. All the factors, such as the nature of the surfaces in contact, the normal force between the surfaces, the roughness of the surfaces, the presence of lubricants or contaminants, and the temperature and humidity of the environment, can influence the frictional force between two surfaces.

A. The following code has memory leaks because it allocates memory dynamically for each row of the matrix using "new" keyword.

B. We need to free the memory that has been allocated using "delete" keyword.

A - The following code has memory leaks because it allocates memory dynamically for each row of the matrix using "new" keyword, but it does not free the allocated memory using "delete" keyword. This can lead to memory leakage in the program.

B - To fix the problem, we need to free the memory that has been allocated using "delete" keyword. We can add a loop at the end of the function to iterate through each row of the matrix and delete the allocated memory using "delete" keyword. The correct code for the function buildMatrix would be:

void buildMatrix(int *matrix, int m, int n) {

int init = 10;

matrix = new int[m];

for(int i = 0; i < m; i++) {

matrix[i] = new int[n];

for(int j = 0; j < n; j++) {

matrix[i][j] = init;

init++;

}

}

// Free the allocated memory

for(int i = 0; i < m; i++) {

delete [] matrix[i];

}

delete [] matrix;

}

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The viscosity of the fluid at each temperature:

Ethanol production from sugarcane is comprised by the following steps: cleaning of sugarcane and extraction of sugars; juice treatment, concentration and sterilization; fermentation; distillation and dehydration.

We determine the questions, according to the numerical properties:

(a) To find P1, we need to use the formula for force applied to a cantilever beam with a point load at the end:
P1 = (3EI/s)L
Where E is the modulus of elasticity, I is the moment of inertia, s is the gap, and L is the length of the beam. Plugging in the given values, we get:
P1 = (3(30x10^6)(0.196)(12))/0.25 = 84.48 kips
After the pin is inserted and P1 is removed, the reaction forces at the supports are equal and opposite to the applied force, so RA = -P1/2 = -42.24 kips and RB = P1/2 = 42.24 kips.

(b) To find P2, we need to use the same formula but with the length of Pipe 2 instead of Pipe 1:
P2 = (3EI/s)L
P2 = (3(30x10^6)(0.196)(8))/0.25 = 56.32 kips
After the pin is inserted and P2 is removed, the reaction forces at the supports are equal and opposite to the applied force, so RA = -P2/2 = -28.16 kips and RB = P2/2 = 28.16 kips.

(c) The maximum shear stress in the pipes occurs at the supports and is equal to the reaction force divided by the cross-sectional area of the pipe. For Pipe 1, the maximum shear stress is RA/A = (-42.24 kips)/(π(2.5^2 - 2^2)) = -10.72 ksi. For Pipe 2, the maximum shear stress is RB/A = (28.16 kips)/(π(2.5^2 - 2^2)) = 7.15 ksi.

(d) To find the temperature increase required to close the gap, we need to use the formula for thermal expansion:
ΔL = αLΔT
Where ΔL is the change in length, α is the coefficient of thermal expansion, L is the original length, and ΔT is the temperature change. Rearranging the formula and plugging in the given values, we get:
ΔT = (s)/(αL) = (0.25)/(11.7x10^-6)(12) = 1785.47°F
After the pin is inserted, the reaction forces at the supports are equal and opposite to the thermal expansion force, so RA = -P1/2 = -42.24 kips and RB = P1/2 = 42.24 kips.

(e) When the structure cools back to the original ambient temperature, the reaction forces at the supports will be zero because there is no longer any thermal expansion force. So RA = 0 kips and RB = 0 kips.

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To disable the textbox if the radio button is not checked and enable the textbox if the radio button is checked, we can use the `checked` property of the radio button and the `disabled` property of the textbox. Here is the code:

```html
if (priceRadioButton.checked) {
 priceTextBox.disabled = false;
} else {
 priceTextBox.disabled = true;
}
```

This will check the `checked` property of the `priceRadioButton` and if it is `true`, it will set the `disabled` property of the `priceTextBox` to `false`, enabling the textbox. If the `checked` property of the `priceRadioButton` is `false`, it will set the `disabled` property of the `priceTextBox` to `true`, disabling the textbox.

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All Fluorescent Lights and Tubes Should Be Recycled or Disposed as Hazardous Waste. In California, when fluorescent lights and tubes are thrown away because they contain mercury.

Yet, the Resource Conservation and Recovery Act classifies the minuscule amounts of highly dangerous mercury present in these fluorescent bulbs, as well as high-intensity discharge (HID) lamps and neon light bulbs, as hazardous waste (RCRA).

Due of the materials they contain, used light bulbs and lamps may be considered hazardous waste. Due to the mercury presence in them, fluorescent lamps are frequently hazardous waste, and lead solder used in LED light bulbs could make them hazardous garbage as well.

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Power delivered to the runner is approximately 2.34 MW and the hydraulic efficiency of the Pelton wheel is approximately 88%.

Step-by-step explanation:

Calculate the coefficient of bucket using the bucket deflection angle:

cos(170°/2) = cos(85°) = 0.087

coefficient of bucket = 1 - 0.087 = 0.913

Calculate the mass flow rate:

mass flow rate = density x volumetric flow rate

= 1000 kg/m3 x 1 m3/s

= 1000 kg/s

Calculate the power delivered to the runner:

Power = mass flow rate x acceleration due to gravity x head x efficiency

= 1000 kg/s x 9.81 m/s2 x 270 m x 0.98 x 0.913

= 2341596.6 W

≈ 2.34 MW

Calculate the hydraulic efficiency:

Hydraulic efficiency = power output / power input

= 2.34 MW / (1000 kg/s x 9.81 m/s2 x 270 m x 0.98)

≈ 0.88 or 88%

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The pull force necessary on the rope to reduce the pressure of the liquid trapped inside a piston cylinder device to 76 kPa is 1.18 kN, expressed to three significant figures.

To determine the pull force necessary on the rope to reduce the pressure of the liquid trapped inside a piston cylinder device to 76 kPa, we can use the equation:

F = (P1 - P2) * A

where F is the force, P1 is the outside pressure, P2 is the pressure inside the piston, and A is the area of the piston.

Given that the outside pressure is 100 kPa, the pressure inside the piston is 76 kPa, and the diameter of the piston is 0.25 m, we can calculate the area of the piston as:

A = π * (d/2)2 = π * (0.25/2)2 = 0.0491 m2

Plugging in the values into the equation, we get:

F = (100 - 76) * 0.0491 = 1.18 kN

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Answer:

I need help also

Answer 1: The correct answer is B: CAD as it is used to describe 3D modeling programs that are used in fields that require precise and exact real-world measurements

CAD stands for Computer-Aided Design, which is used in fields such as construction, manufacturing, and engineering to create 2D or 3D models of products, buildings, and machines. These programs allow for precise measurements and calculations, making them essential in these industries where accuracy is critical.

Answer 2: The correct answer is A: To maintain safety and production quality. In the automotive industry, precise 3D modeling is necessary to ensure the safety of the vehicle and its occupants. The models must accurately represent every aspect of the car's design, from the smallest component to the overall structure. If the models are not precise, it could lead to production errors or safety hazards.

Answer 3: The correct answer is D: Wheel Physics. In the automotive industry, designers need to create 3D models of the vehicle that accurately represent the physics of its movement. This includes factors such as acceleration, braking, and steering, which are critical to the car's performance. Wheel physics is one such feature that would be helpful in this context.

Answer 4: The correct answer is A: CAD. CAD programs are commonly used in the construction industry to create 2D or 3D models of buildings and infrastructure. These programs allow designers to visualize the building's structure and layout, as well as its electrical, plumbing, and heating needs. This can help to identify potential design flaws, streamline construction processes, and ensure that the final product meets safety and quality standards.

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The application asks the user to input two integers before determining whether the second integer is less than the first. If so, the error "Second integer can't be less than the first" is printed.

printf ("Input two integers:") scanf ("%d%d", &number1, &number2) The sum of these two values is then added together using the + operator and kept in the sum variable. The total of numbers is displayed using the printf() function. "%d + %d =%d," number1, number2, and sum are printed.

first_int = int(input("Enter the first integer: "))

second_int = int(input("Enter the second integer: "))

if second_int < first_int:

"Second integer cannot be less than first," print

else:

 output_range = range(first_int, second_int+1, 10)

 for num in output_range:

   print(num, end=' ')

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In a Maxwell element, the stress and strain are directly proportional to each other. This means that as the stress increases, the strain also increases at the same rate.

Therefore, the strain time history for a Maxwell element will look exactly like the stress time history, just scaled by a factor of the modulus of elasticity. In a Kelvin element, the stress and strain are not directly proportional to each other. Instead, the strain will lag behind the stress, and will have a more gradual increase and decrease. This means that the strain time history for a Kelvin element will look similar to the stress time history, but with a smoother curve and less sharp peaks and valleys.

To draw the strain time history for each of these elements, simply plot the stress time history on the x-axis and the strain on the y-axis. For the Maxwell element, the strain will be equal to the stress divided by the modulus of elasticity. For the Kelvin element, the strain will be equal to the stress divided by the modulus of elasticity, but with a time delay factor added in. This time delay factor will cause the strain to lag behind the stress and have a more gradual increase and decrease.

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The ultimate tensile stress in MPa is 156.823 MPa and the shear stress in MPa is 155.146 MPa.

The ultimate tensile stress can be found by dividing the tensile peak load by the cross-sectional area of the specimen. The cross-sectional area of a circular specimen is given by πr^2. The stress in MPa can be found by dividing the stress in N/m^2 by 10^6.

a) The ultimate tensile stress in MPa is:

Ultimate tensile stress = (Tensile peak load) / (Cross-sectional area)

= (4281 N) / (π(2.95 mm)^2)

= (4281 N) / (27.298 mm^2)

= 156.823 N/mm^2

= 156.823 MPa

b) The shear stress in MPa is:

Shear stress = (Shear force) / (Cross-sectional area)

= (4100 N) / (π(2.9 mm)^2)

= (4100 N) / (26.423 mm^2)

= 155.146 N/mm^2

= 155.146 MPa

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The two fields of study of workshop technology and workshop practice are linked but different. The study of the different instruments, apparatus, devices, and methods employed in industrial workshops.

Workshop technology is a subset of technology that deals with various manufacturing procedures used to create equipment or machine parts. The module unit's goal is to give the student the information, abilities, and attitudes necessary to carry out fundamental workshop duties.

The foundation of the actual industrial setting is the workshop, which supports the development and improvement of the pertinent technical hand skills needed by the technician working in the various engineering industries and workshops.

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The maximum shear stress that develops under uniaxial tension when the material reaches its uniaxial tensile yield strength is 52.8 MPa.

This is lower than the octahedral shear stress at this point (81.1 MPa), which indicates that the material is more likely to fail under the state of stress given in the question than under uniaxial tension.

According to the maximum distortion energy theory, the uniaxial tensile yield strength of the material can be determined using the following equation:

σy = √[(σ1-σ2)^2 + (σ2-σ3)^2 + (σ3-σ1)^2]/√2

Where σ1, σ2, and σ3 are the principal stresses.

In this case, the principal stresses are:

σ1 = 40 MPa
σ2 = 50 MPa
σ3 = -60 MPa

Plugging these values into the equation gives:

σy = √[(40-50)^2 + (50-(-60))^2 + (-60-40)^2]/√2

σy = √[100 + 12100 + 10000]/√2

σy = √[22200]/√2

σy = 105.5 MPa

Therefore, the uniaxial tensile yield strength of the material is 105.5 MPa.

The octahedral shear stress at this point can be determined using the following equation:

τoct = √[(σ1-σ2)^2 + (σ2-σ3)^2 + (σ3-σ1)^2]/3

Plugging in the same principal stresses gives:

τoct = √[(40-50)^2 + (50-(-60))^2 + (-60-40)^2]/3

τoct = √[100 + 12100 + 10000]/3

τoct = √[22200]/3

τoct = 81.1 MPa

Therefore, the octahedral shear stress at this point is 81.1 MPa.

To compare this octahedral shear stress with the maximum shear stress that develops under uniaxial tension when the material reaches its uniaxial tensile yield strength, we can use the following equation:

τmax = σy/2

Plugging in the uniaxial tensile yield strength gives:

τmax = 105.5/2

τmax = 52.8 MPa

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Answer:

  see bold numbers below

Explanation:

Given the attached series-parallel circuit, you want to know ...

The circuit impedance is the sum of the series resistance and the parallel combination of the 1Ω resistor and the 3 mH inductor. For ω = 333, the inductor's impedance is Xl = jωL = j(333)(.003)Ω = j0.999Ω.

The total impedance is the sum ...

  Ztot = 10 + 1/(1/1 +1/j0.999) = 10.51∠2.73°

The total current in the circuit is ...

  Is = Vs/Ztot = 10∠45°/10.51∠2.73° = 0.9513∠42.27°

The branch currents are in reverse proportion to the branch impedance

  Ir = Is(Xl/(1+Xl)) = 0.6724∠87.30°

  Il = Is(1/(1+Xl)) = 0.6730∠-2.70°

Expressed as a sine function, these have the magnitude and phase angle indicated by the phasor:

  Is(t) = 0.9513·sin(333t +42.27°)

  Ir(t) = 0.6724·sin(333t +87.30°)

  Il(t) = 0.6730·sin(333t -2.70°)

At t=0, each of these current values is the magnitude of the current multiplied by the sine of the phase angle. In effect, it is the imaginary part of the current when it is expressed in complex form.

  Is(0) = 0.9513·sin(42.27°) = 0.6399 A

  Ir(0) = 0.6724·sin(87.30°) = 0.6716 A

  Il(0) = 0.6730·sin(-2.70°) = -.0317 A

__

Additional comment

Solving these problems is immensely aided by a calculator that easily handles complex numbers. The one shown in the attachments does not thread polar conversions over a list, but otherwise works nicely for this problem. Angle mode is set to degrees. The value of x is 0.999i.

The value of arr that could be used to show that the method does not work as intended is:

int[][] arr = {{1, 2, 3}, {4, 5, 6}, {7, 8, 0}};

This value of arr can be used to show that the method does not work as intended because the method is supposed to return true if 0 is found in its two-dimensional array parameter arr. However, in this case, the method will throw an ArrayIndexOutOfBoundsException.

This is because the for loop that iterates over the rows of the array is using the <= operator instead of the < operator. This means that the loop will try to access an index that is one greater than the last valid index of the array, causing an ArrayIndexOutOfBoundsException.

To fix this issue, the for loop that iterates over the rows of the array should use the < operator instead of the <= operator:

for (int row = 0; row < arr.length; row++)

With this change, the method will correctly return true if 0 is found in its two-dimensional array parameter arr and false otherwise.

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The normal stresses in members (1), (2), and (3) after brass post (2) is heated by 20°F are 79.63 ksi, 13.74

The problem can be approached by assuming that the structure is in static equilibrium, which means that the sum of all forces acting on it is zero, and that the deformations of the posts are small enough to be considered elastic.

a) Equilibrium equations:

The forces acting on the structure are the weight of the block (80 kips) and the reactions at the supports. Since the block is supported equally by the three posts, each post will carry a third of the weight (80/3 kips). The equilibrium equations can be written as follows:

[tex]∑F_x = 0: R_1 - R_3 = 0[/tex]

[tex]∑F_y = 0: R_1 + R_2 + R_3 - 80/3 = 0[/tex]

Compatibility equation:

Since the three posts have the same original length, the deformations of each post under load should be the same. This can be expressed as:

[tex]ΔL_1 = ΔL_2 = ΔL_3[/tex]

where ΔL_i is the elongation of post i.

Assuming that the posts deform only in the axial direction, the elongation can be expressed as:

[tex]ΔL_i = PL_i/(AE_i)[/tex]

where P is the load carried by the post, L_i is the original length of the post, A is the cross-sectional area of the post, E_i is the modulus of elasticity of the post material, and α_i is the coefficient of thermal expansion of the post material.

Since the posts have the same original length and cross-sectional area, the compatibility equation can be simplified as:

[tex]PL_1/(AE_1) = PL_2/(AE_2) = PL_3/(AE_3)[/tex]

Solving for the unknown reactions and normal stresses in the posts, we obtain:

[tex]R_1 = R_3 = 80/6 = 13.33 kips[/tex]

[tex]R_2 = 80/3 - 13.33 = 20 kips[/tex]

[tex]σ_1 = R_1/A = 13.33/S[/tex]

[tex]σ_2 = R_2/A = 20/S[/tex]

[tex]σ_3 = R_3/A = 13.33/S[/tex]

b) To determine the normal stresses in the posts after brass post (2) is heated by 20°F, we need to take into account the thermal expansion of the posts. The new length of post 2 can be expressed as:

[tex]L_2' = L_2(1 + α_2ΔT)[/tex]

where L_2 is the original length of post 2, α_2 is the coefficient of thermal expansion of brass, and ΔT is the temperature increase (20°F in this case).

The new elongation of post 2 can be expressed as:

[tex]ΔL_2' = PL_2'/(AE_2)[/tex]

Substituting L_2' and solving for P, we obtain:

[tex]P = (A*E_2/[(1 + α_2ΔT)*L_2])ΔL_2'[/tex]

Substituting P into the equilibrium equations and solving for the unknown reactions, we obtain:

[tex]R_1 = R_3 = 79.63 kips[/tex]

[tex]R_2 = 80/3 - R_1 - R_3 = 13.74 kips[/tex]

Substituting the new reactions into the normal stress equations, we obtain:

σ_1 = σ_3 = 79.63/S

σ_2 = 13.74/S

Therefore, the normal stresses in members (1), (2), and (3) after brass post (2) is heated by 20°F are 79.63 ksi, 13.74

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