Answer:
a) L = 50.01 nm
b) 99.98%
Explanation:
Determine the necessary precipitate spacing and estimate the required percentage of precipitate phase
Given that the shear strength = G/100 by precipitation hardening
G = shear modulus
Radius of particles = 40 nm
attached below is the detailed solution
a) precipitate spacing ( L ) = √( 2π / f ) * R₁
= √ ( 2π / 0.00719956 ) * 1.693 nm
hence L = 50.01 nm
b) Determine The percentage of precipitate phase that is required
( precipitation strength / peak strength ) * 100
= ( 18.4583 / 18.4604 ) * 100
= 99.98%
5 . Which of the following is true about vehicles displaying a diamond-shaped sign that indicates a hazardous load
The following is true about vehicles displaying a diamond-shaped sign that indicates a hazardous load:
They must stop before a cross railroad track.
What is hazardous load?A hazardous load is any load determined by the Minister to be capable of posing a risk to health, safety, or property when transported on a public road. A hazardous load is defined as any load that has been prescribed by the Council in the Gazette as being capable of posing a risk to health, safety, and property when transported along the Regional Trunk Road Network.
A hazardous substance is any substance that is I listed, classified, or regulated in accordance with any environmental law; (ii) any petroleum product or by-product, asbestos-containing material, lead-based paint or plumbing, polychlorinated biphenyls, radioactive materials, or radon; or (iii) any other substance that is the subject of regulatory action by any governmental entity in accordance with any environmental law.
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Which action is effective in preventing the transmission of food borne viruses and bacteria
Freezing prevents bacteria from growing. If food is heated sufficiently, parasites, viruses, and most bacteria are killed.
Which best describes the similarities and differences between the Engineering and Technology pathway and the Science and Math pathway?
a) Both pathways require workers to use teamwork, leadership, and teaching skills while the Engineering and Technology pathway requires clerical skills.
b) Both pathways require workers to have observational skills while the Engineering and Technology pathway requires CAD knowledge.
c) Both pathways require workers to be creative, while the Science and Math pathway requires specialized knowledge in subject areas like physics or chemistry.
d) Both pathways require workers to have patience and persistence while the Science and Math pathway requires physical stamina, dexterity, and use of technical equipment.
Answer:
Both pathways require workers to be creative, while the Science and Math pathway requires specialized knowledge in subject areas like physics or chemistry.
Answer:
Right B is right?
Explanation:
In a single-family residence, a line-voltage thermostat is primarily used to control _____.
Answer:
In a single-family residence, a line-voltage thermostat is primarily used to control heating and cooling systems.
A single direct acting controller used to control space temperature and set up for 72°F setpoint with an 8°F throttling range assigned. The system pressure range is from 3 to 13 psig. Predict the following: (a) Controller PB setting when remote sensors with spans of 50°F, 150°F, and 200°F are used. (b) Controller pressure range. (c) Controller setpoint. (d) Controller output pressure at T = 72°F using the same sensors as in (a). (e) Controller output pressure at T = 76°F. (f) Predict the output pressure of the controller at T = 80°F when th
The controller PB is 0.22, the range of the controller pressure is between 3 to 13 psig, the controller setpoint is at 72°F, and the output pressure at that temperature is 3 psig while the controller output pressure at 76°F is 6 psig
What is Controller SystemsA controller system is a type of feedback system used to regulate the performance of an output device by comparing the output to a desired set point. It uses the difference between the two values (error) to continuously adjust a control input to reduce the error. In simple terms, the controller system monitors, adjusts, and regulates the operations of the output device to achieve a desired result. Common examples of controllers include thermostats, cruise control systems, and PID controllers.
(a) Controller PB setting when remote sensors with spans of 50°F, 150°F, and 200°F are used:
This can be calculated as;
PB = (72°F - 50°F) / (200°F - 50°F) = 0.22
(b) Controller pressure range:
The range of the controller pressure is 3 - 13 psig
(c) Controller setpoint:
The controller set point is 72°F
(d)
The controller output pressure when T = 72°F while using the same sensors as in (a) is 3 psig
(e)
The controller output pressure at T = 76°F is 6.6 psig
(f) To predict the output pressure of the controller when T = 80°F with three remote sensors having spans of 50°F, 150°F, and 200°F are used will be 11.2 psig
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A bar of copper is subjected to a tensile load. The elastic modulus of the copper is 110 GPa, its yield strength is 240 MPa, its tensile strength is 400 MPa, and its Poisson's ratio is 0.340. If the original length of the rod is 250 mm and it has a round cross-section with an original diameter of 9.50 mm, what load (in N) would need to be applied in order for the rod's length to be 250.1 mm
Answer:
The answer is "3,118 N"
Explanation:
Using the hookes laws:
[tex]y=\frac{stress}{strain}=\frac{\frac{F}{A}}{\frac{\Delta L}{L}}[/tex]
So,
[tex]F=\frac{y \times \Delta L \times A}{L}\\\\[/tex]
[tex]=\frac{110 \times 10^{3} \times 0.1 \times \frac{\pi}{4} \times 9.5^2 }{250}\\\\=\frac{110 \times 10^{3} \times 0.1 \times \frac{3.14}{4} \times 90.25 }{250}\\\\=3,117.235 \ N\\\\=3,118 \ N\\\\[/tex]
Why is it so important that you need to know when calculate a bevel gear two (2) different numbers of gear teeth are to be know?
It is important to know the number of teeth on the two gears when calculating a bevel gear because the number of teeth determines the gear ratio, which in turn determines the torque and speed at which the gears will operate.
How to calculate the gear ratio?The gear ratio is calculated by dividing the number of teeth on the driving gear by the number of teeth on the driven gear.
If the number of teeth is not known, it would be impossible to accurately calculate the gear ratio and determine the performance of the gear set.
Additionally, the number of teeth also affects the meshing pattern and the contact ratio between gear teeth, which is also important to the gear's performance.
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Find the weight W needed to hold the wall shown in Fig. P2.76 upright. The wall is 10 m wide.
The weight needed to hold the wall is equal to 14.9285 N.
What is force equilibrium?The force equilibrium can be described as the addition of the forces about x, y, and z-axis will be equal to zero and the sum of the moment also equal to zero.
Given, the width of the wall, b = 10 m
The height of the water, d = 4 m
The height of the wall, l = 7m
The area of the wall, A = bd = 10(4) = 40 m²
The expression of the centroid of the wall, [tex]\displaystyle \bar x = \frac{d}{2}[/tex]
[tex]\displaystyle \bar x = \frac{4}{2} = 2 m[/tex]
The hydrostatic force, F = ρgAx
F = (1000) (9.81) (40) (2)
F = 784,000 N
The expression for the moment of inertia: [tex]\displaystyle I_C =\frac{bd^3}{12}[/tex]
[tex]I_c = 10\times 4/12 = 53.34 m^4[/tex]
The relation of the center of the pressure gate can be written as:
[tex]\displaystyle \bar h = \bar x +\frac{I_C}{A\bar x}[/tex]
[tex]\bar h = 2 + \frac{53.34}{40\times 2} = 2.667 \; m[/tex]
The moment about point: l × W - F(d - h) = 0
Substitute the values in the above equation:
7 × W - 78400 (4 - 2.667) = 0
7 W = 78400 (4 - 2.667)
W = 14.92 kN
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Tech A says that one approved way to clean dust off brakes is with compressed air. Tech B says that some auto parts may contain asbestos. Who is correct
Tech B is correct it's a verified fact that some auto parts may contain asbestos.
Do auto parts contain asbestos?
Asbestos has been used in a wide range of automotive products, including brakes, clutches, hood liners, gaskets, heat shields, and many others.
Drum and disc brakes were traditionally made with 35% to 60% asbestos. It is still legal in the United States to sell asbestos-containing auto parts, and many brake and clutch parts contain up to 35% asbestos.
Contaminated parts have been found in vehicles of all types, including cars, trucks, motorcycles, buses, trains, and military vehicles. Elevators and other types of transportation machinery also used asbestos brakes.
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find the capacitance reactance of a 0.1 micro frequency capacitor 50Hz and at 200Hz
Complete Question:
Find the capacitive reactance of a 0.1 microfarad capacitor with frequency 50Hz and at 200Hz.
Answer:
I. Capacitive reactance = 31826.86 Ohms.
II. Capacitive reactance = 7956.72 Ohms.
Explanation:
Given the following data;
Capacitance = 0.1 uF = 0.0000001 Farad
Frequency = 50 Hz and 200 Hz
To find the capacitive reactance;
Mathematically, the capacitive reactance of an electronic circuit is given by the formula;
[tex] X_{c} = \frac {1}{2 \pi fc} [/tex]
Where;
Xc is capacitive reactance.f is the frequency.c is the capacitance.Substituting into the formula, we have;
I. At frequency, f = 50 Hz
[tex] X_{c} = \frac {1}{2 * 3.142 * 50 * 0.0000001} [/tex]
[tex] X_{c} = \frac {1}{314.2 * 0.0000001} [/tex]
[tex] X_{c} = \frac {1}{0.00003142} [/tex]
[tex]X_{c} = 31826.86[/tex]
II. At frequency, f = 200 Hz
[tex] X_{c} = \frac {1}{2 * 3.142 * 200 * 0.0000001} [/tex]
[tex] X_{c} = \frac {1}{1256.8 * 0.0000001} [/tex]
[tex] X_{c} = \frac {1}{0.00012568} [/tex]
[tex]X_{c} = 7956.72[/tex]
round your answers to the nearest hundredths if needed -25+5s=8
Answer:
s = 6.6
-25 + 5 × 6.6 = 8
Just let me know if you need any more help.
true or false : an attempt to pass a non-variable argument into a reference variable parameter will cause an error.
Answer: true
Explanation:
Tech A says that if you are unsure of what personal protective equipment (PPE) to use to perform a job, you should just use what is nearby. Tech B says that air tools are less likely to shock you than electrically powered tools. Who is correct
According to the question of personal protective equipment, tech B is correct.
What is personal protective equipment?
Personal Protective Equipment (PPE) is any equipment, clothing, or device designed for use on the body to protect the wearer from injury or infection. This can include items such as gloves, safety glasses, protective clothing, hard hats, respirators, and face masks. Proper use of PPE is important to help reduce the risk of exposure to hazardous materials and environments, as well as the spread of infection. PPE is most effective when used in combination with other safety measures, such as engineering controls, administrative controls, and good hygiene practices.
Air tools are powered by compressed air and are considered to be safer than electrically powered tools because they are not connected to an electrical source.
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when using the route command at a command prompt, which entry indicates the default route?
Regardless of whether a default static route is set up, the "default-information originate" command is used to advertise a default route into OSPF.
Static routing is the practice of using a manually specified routing entry rather than information from traffic generated by dynamic routing. Although it isn't always the case, network administrators frequently manually configure static routes in addition to adding entries to a routing table. In contrast to dynamic routing, static routes have been fixed and remain the same despite network configuration changes. Static and dynamic routing are not mutually exclusive. A router often combines both dynamic routing and static routing to maximize routing efficiency and provide fall backs in the case that dynamic routing information cannot be transmitted. As a last-resort gateway or in stub networks, static routing may also be used.
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Before you can take a lesson exam, you must:
A. Complete all required laboratory exercises.
OB. Listen to all of the audio in the lesson.
C. Review all materials in the course Library.
D. None of these.
You must listen to all of the lesson's audio before you can take the exam. This is the appropriate assertion.
What purpose does a laboratory exercise serve?Students will be able to build deeper and longer lasting knowledge and a deeper comprehension of the scientific method through carefully planned laboratory exercises that emphasize inquiry-based or problem-based learning with attention to active learning under appropriate supervision.
What advantages does audio learning offer?Supporters of this method of learning assert that learning by ear enables one to be adaptable when carrying out a variety of jobs. This is due to the fact that information can be processed without the need of hands or eyes by simply listening to audio recordings.
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Me in a good way what is 16÷ 4743
Answer:
0.00337339236
Answer:
Hey there! 16 divided by 4743 is approximately equal to 0.003366. This means that if you take 16 and divide it by 4743, the result will be a number that is very close to 0.003366. This division problem can be written as the fraction 16/4743, or as the decimal 0.003366.
________________________________________________________
What are some common mistakes to avoid when solving division problems?Some common mistakes to avoid when solving division problems include forgetting to carry the remainder, failing to check for divisibility, and mixing up the order of the dividend and the divisor. It is also important to pay attention to the units of measurement and to ensure that the units in the dividend and the divisor are compatible.
What are some strategies for solving division problems with large numbers?Some strategies for solving division problems with large numbers include using place value to break down the numbers into smaller units, using long division or a calculator to perform the division, and using estimation to check the reasonableness of the answer. It can also be helpful to use mental math techniques, such as rounding, to simplify the division problem. Other strategies might include using division to find the prime factorization of a number or to identify common factors or multiples.
A child accidentally runs into the street in front of an approaching vehicle. The vehicle is traveling at 40 mi/h. Assuming the road is level, at what distance must the driver first see the child to stop just in time? a) 153.7 ft b) 300.3 ft c) 318.8 ft d) 146.7 ft
Assuming the road is level, the driver must see the child at 300.3 ft to stop just in time. Hence, option C) is the correct answer.
What is the distance needed to stop?The distance travelled between the moment the body decides to stop a moving vehicle and the moment the vehicle comes to a complete stop is known as the stopping distance. The stopping distance, indicated by the letter d, is dependent on a number of variables, including as the road's surface and the driver's reflexes.
What is the frictional stopping distance?The distance the car travels before coming to a halt is known as the stopping distance. It is depending on the vehicle's speed as well as the amount of road-to-wheel friction.
Briefing:Deceleration rate is considered 11.2 ft/s²
a = 11.2 ft/s²
= 1^2/2 = (40 mi/h×5280 ft/1 mi×1 h/3600 s)²/22×11.2=240.07 ft
Stopping distance would be:
= 240.07+ 60.23 ft = 300.3 ft
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Given that a fluid at rest is incapable of sustaining any shear stress, set up the relation between the surface traction on an arbitrarily oriented surface element and the pressure. From this, find the relation between the stress tensor and the pressure.
Answer:
Relation between the stress tensor and the pressure is attached below
Explanation:
Expressing the Relation between the surface traction on an arbitrarily oriented surface element
For an arbitrary element
net force can be represented as : P + dp/dx ( dx/2 ) - P + dp/dx ( dx/2 )
= dp/dx * dx
∴ The surface traction can be expressed as
= dp/dx * dxdydz + dp/dx * dxdydz
attached below is the remaining part of the solution
A BOD test is run using 30 mL of wastewater and 270 mL of dilution water. The initial DO of the mixture is 9.0 mg/L. On day 5 the DO in the bottle measured 4 mg/L. After 30 days, the DO in the bottle measured 2 mg/L, and after 50 days, the DO in the bottle still measured 2 mg/L. At the beginning of the test, we added a nitrification inhibitor so we can assume that nitrification is not occurring, so only the carbonaceous BOD is being measured.
a) What is the BODs of the wastewater?
b) What is the ultimate carbonaceous BOD?
c) How much BOD remains after 5 days?
d) Based on the data above, estimate the reaction rate constant k (1/day).
Answer:
Explanation:
From the given information:
The BOD of the wastewater can be determined by using the formula:
[tex]BOD _5 = \dfrac{DO_i-DO_f}{\dfrac{V_s}{V_b}}[/tex]
where;
[tex]BOD _5 =[/tex]biochemical oxygen demand = ???
[tex]DO_i=[/tex] initial dissolved oxygen = 9 mg/L
[tex]DO_f=[/tex] final dissolved oxygen = 4 mg/L
[tex]V_b =[/tex] sample of the bottle, which is normally 300 mL
[tex]V_s[/tex] = sample volume = 30 mL
[tex]BOD _5 = \dfrac{9-4}{\dfrac{30}{300}}[/tex]
[tex]BOD _5 = \dfrac{5}{\dfrac{1}{10}}[/tex]
[tex]BOD _5 = 5\times{\dfrac{10}{1}}[/tex]
[tex]\mathbf{BOD _5 = 50 \ mg/L}[/tex]
The ultimate Carbonaceous BOD is estimated from the formula:
[tex]y_t = L_o-L_t \\ \\ y_t = L_o-L_oe^{-kt} \\ \\ y_t = L_o (1-e^{-kt})[/tex]
Making [tex]L_o[/tex] the subject, we have:
[tex]L_o = \dfrac{y_t}{(1-e^{-kt}} \\ \\ L_o = \dfrac{50}{1 - e^{-0.25*5}}[/tex]
[tex]L_o[/tex] = 70 mg/L
c) The BOD left over after five days = [tex]L_oe^{-kt}[/tex]
= [tex]70 \times e^{-0.25 *5}[/tex]
= 20 mg/L
d) The reaction constant rate is estimated as follows:
Recall that:
[tex]\mathbf{BOD _5 = 50 \ mg/L}[/tex]
Since DO measure 2 mg/L;
After 30 days, [tex]BOD_{30} = (9-2) \times 10 = 70 \ mg/L[/tex]
Therefore, the reaction rate constant is:
[tex]\dfrac{50 \ mg/L}{70 \ mg/L} =\dfrac{1-e^{-k*5}}{1-e^{-k*30}} \\ \\ 50 (1-e^{-k*30}) = 70 (1-e^{-k*5}) \\ \\ K = 0.25 /day[/tex]
what was the main source of radio exposure for indie rock in the 1990s?
Answer: The main source of radio exposure for indie rock in the 1990s was college radio.
Explanation: College radio stations were especially important for indie rock bands, as they provided an alternative to the mainstream music played on commercial radio stations. College radio stations provided indie rock bands with a platform to reach a wider audience, and many of these bands gained a large following as a result. College radio stations also provided an outlet for independent labels to promote their music, which allowed indie rock to gain more exposure.
Need help with Part 1 – Additional Operations I MATLAB question
gove it to me. I'll do my best
The section is experiencing a positive bending moment about the z-axis, where Mz = 1.13 kN-m. What is the resulting stress at the top and bottom surfaces? And are they in tension or compression?
The resulting stress at the top and bottom surfaces is 837.5 N/m^2 and -837.5 N/m^2, respectively. The top surface is in compression and the bottom surface is in tension.
What is stress?
Stress in engineering is the amount of force per unit area placed on a material or structure. It can be physical, or it can be psychological. Stress can be positive or negative. Positive stress can cause a material to become stronger, while negative stress can cause it to become weaker or even fail. Stress can also refer to the amount of strain a material must endure before it yields or breaks. Stress is measured in terms of pounds per square inch (psi) or newtons per square meter (N/m2). Stress analysis is important in engineering as it helps to identify potential failure points in a design, or to determine how much a material can handle before it breaks. Stress analysis is used to ensure the safety and integrity of products, structures, and machines.
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Problem 9.10. Which of the following sets of values is closest to iL(0), vC(0).
Problem 9.10. Which of the following sets of values is closest to the energy stored in the capacitor and inductor (in J) at t=0-
Problem 9.10. What is the value of Vmax (integer answer required) in Volts
Problem 9.10. Which of the following is closest to the expression for vc(t) in Volts
In the cicuit of Figure P9.10, suppose ui"(1) = 10 V, R= 10 Ω, C = 0.4 mF, L = 0.25 (a) Compure 0), vo) i(0), and i1(0*)
(b) Compute the energy stored in the inductor and the capacitor at t = 0
(c) Using only energy considerations, compute the maximum value of ), t> 0 (d) Find the analytical expression for vt), and verify the maximum value of v) computed in part (c)
The energy of the magnetic and electric fields that have been stored can differ. A completely charged capacitor is linked in series with an inductor.
A passive-terminal electric device called an inductor, often referred to as a coil, choke, or reactor, stores electricity in a magnetic field when electric current passes through it. An insulated string twisted into a coil is typically included in an inductor. A passive digital component called an inductor can store electrical energy in the form of magnetic electricity. In essence, it uses a conductor that has been twisted into a coil; as electricity enters the coil from left to right, this will produce a magnetic field that rotates counter clockwise. The energy of the magnetic and electric fields that have been stored can differ.
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Which of the following is NOT a factor in the quality of digital video? a.- frame rate and resolution c. compression technique b. memory technology in your camera de color and bit depth
The choices that best describe the process of digitization are: Option A: binary-stored video. Option C converts analog video to digital video.
Information transformation into a digital format is referred to as digitization. Be aware that in this format, data is organized into discrete units of data called bits. As a result, the following options best represent the digitization process: Option A: binary-stored video. Option C converts analog video to digital video. This is due to the fact that digital video is a key technology for both video conferencing and video messaging in addition to being a key technology for digital television. This was demonstrated by its use in messaging apps for confidential conversations and for hosting virtual conferences for business meetings amongst personnel.
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Estimate properties and pipe diameter Determine the diameter of a steel pipe that is to carry 2000 gal/min of gasoline with a pressure drop of 5 psi per 100 ft of horizontal pipe. Pressure drop is a function of flow rate, length, diameter, and roughness. Either iterative methods OR equation solvers are necessary to solve implicit problems. Total head is the sum of the pressure, velocity, and elevation. What is the density of gasoline
Answer:
Diameter of pipe is 0.535 ft
Explanation:
see attachment, its works out 1st half
what's the difference between programming paradigms ?
Answer:
Programming paradigms are different approaches to programming. Each paradigm is concerned with the way code is written, structured, and organized. The main paradigms are procedural, object-oriented, functional, and logical. Each of these has its own set of rules and principles that guide how code is written and executed. Procedural programming focuses on implementing algorithms and breaking tasks down into smaller steps. Object-oriented programming focuses on breaking tasks down into objects and classes. Functional programming focuses on writing code that is easy to read and maintain. Logical programming focuses on using logic to solve problems.
Explanation:
Hope It Help You
Answer:
A programming paradigm is a style or approach to programming, characterized by the way in which the programmer writes the code. There are several different programming paradigms, including:
Explanation:
Imperative programming: This is the most traditional style of programming, in which the programmer writes code that specifies a series of steps to be carried out in order to solve a problem. Imperative programming languages include C, C++, and Java.
Object-oriented programming: In this style of programming, the programmer writes code in the form of objects, which are self-contained units that combine data and behavior. Object-oriented programming languages include Java, Python, and C#.
Functional programming: In functional programming, the programmer writes code in the form of functions, which are self-contained units that take input and produce output, without modifying any external state. Functional programming languages include Haskell, Lisp, and ML.
Logic programming: In this style of programming, the programmer writes code in the form of logical statements, and the language's runtime system is responsible for finding a solution that satisfies all of the statements. Logic programming languages include Prolog and Mercury.
Declarative programming: In declarative programming, the programmer specifies what the desired result should be, rather than how to achieve it. The language's runtime system is responsible for finding a way to produce the desired result. Declarative programming languages include SQL and regular expressions.
distinguish between the cis-acting regulatory elements referred to as promoters and enhancers.
Answer: ones on white chocolate and ones on a birthday cake
Explanation:
When operating near an uncontrolled airport, which frequency should the remote-pilot use to monitor air traffic
The frequency the remote-pilot should use to monitor air traffic near an uncontrolled airport is the Common Traffic Advisory Frequency (CTAF).
What is air traffic?
Air traffic is the movement of aircrafts such as planes and helicopters in a certain area. This may include both civilian and military aircrafts. Air traffic is managed by air traffic controllers who are responsible for ensuring the safety of aircrafts by providing directions and instructions on the ground and in the air. They also inform pilots about the current weather conditions and ensure the proper separation of aircrafts from each other. Air traffic controllers must constantly monitor the positions and movements of aircrafts in their airspace and keep track of all the data related to their flight paths.
The CTAF is a frequency used by pilots and air traffic control to exchange information about aircraft operating in the vicinity of an airport.
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Problem 6. Rods AC and BC are used to suspend the 200-kg mass. If each rod is made of a material for which the average normal stress can not exceed 150 MPa, determine the minimum required diameter of each rod to the nearest mm
The minimum required diameter should be 5 mm for each rod.
What is stress?In physics, stress describes the force acting on a material's unit area. A specific body can become deformed under stress. Strain is the term for the impact that stress has on the body. To restore an object to its original form and size, an opposing force known as a restoring force is produced inside the object. The symbol "σ" stands for stress, which is a tangible quantity. N/m2 is the stress unit in the SI system.
Strength is an object's capacity to withstand the applied stress to the fullest extent possible. Physics distinguishes between two types of stress: Tangential or Shearing Stress and Normal Stress based on the direction of the deforming forces that act on a body.
πd²[tex]_{min}[/tex]/4 = 1962/150
d[tex]_{min}[/tex] = [tex]$ \sqrt{\frac{4 \times 1962}{\Pi \times 150} }[/tex]
d[tex]_{min}[/tex] = 4.081
As, 4 < 4.081 < 5,
The minimum required diameter should be 5 mm for each rod.
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Show that the minimum cation-to-anion radius ratio for a coordination number of 6 is 0.414. [Hint: Use the NaCl rock salt crystal structure, and assume that anions and cations are just touching along cube edges and across face diagonals.
According to the question, the minimum cation-to-anion radius ratio is 8/1 = 0.414.
What is cation-to-anion radius ratio?
The cation-to-anion radius ratio is a measure of the relative sizes of cations and anions in a given compound. It is calculated by dividing the radius of the cation by the radius of the anion.
We will assume that the cation and anion are of equal size.
Let the radius of the cation and anion be r.
The distance between two adjacent cations/anions along a cube edge is 2r, so the length of the cube edge is 2r/2 = r.
The distance between two adjacent cations/anions across a cube face is sqrt(2)r, so the length of the cube face diagonal is sqrt(2)r/2 = r/sqrt(2).
The volume of the cube is (r/2)^3, so the total number of cations and anions inside the cube is (r/2)^3/(2r^3) = 1/8.
Therefore, the minimum cation-to-anion radius ratio is 8/1 = 0.414.
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