The first step in sanitizing clippers and trimmers is to remove any hair or debris from the blades and guards, ensuring that the tools are clean before proceeding with disinfection.
The first step in sanitizing clippers and trimmers is to remove any excess hair and debris from the blades using a brush or cleaning tool. This helps to ensure that the disinfectant solution can properly penetrate and sanitize the blades. After removing any debris, the clippers and trimmers can be soaked in a disinfectant solution according to the manufacturer's instructions. It is important to use a solution that is specifically designed for use on clippers and trimmers, and to follow all safety precautions such as wearing gloves and using the solution in a well-ventilated area. Once the disinfection process is complete, the clippers and trimmers can be rinsed and dried before using them again.
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when assembling various shaped pieces together without marring the workpiece, use a A. chain clamp
B. chain wrench
C. spanner wrench
D. strap wrench
Answer:
Strap wrench (I think)
Explanation:
The strap doesnt have any rough edges so it shouldn't mark the workpiece (assuming that is what you meant when you said 'marring'). I would recommend to wait for some other answers though since i haven't studied this yet :)
List the specific steps that would enable another person to find the largest number among three numbers.
The largest number among three numbers, follow these steps: Compare the first two numbers to bed load determine which is larger. Compare the larger number from step 1 with the third number. If the third number is larger than the number from step 1, then the third number is the largest.
To find the largest number among three numbers, you need to compare each number with the other two. Comparing the first two numbers will give you the larger of the two. This number will then be compared with the third number to determine which is the largest. If the third number is larger, then it is the largest among the three. If not, then the larger number from step 1 is the largest among the three.
Take the three numbers (let's call them A, B, and C) that you want to compare. Compare the first two numbers (A and B). If A is greater than B, set A as the current largest number. If B is greater or equal to A, set B as the current largest number. Now, compare the current largest number with the third number (C). If the current largest number is greater than C, it remains the largest number. If C is greater or equal to the current largest number, set C as the largest number.
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A shrinkage limit test is performed on a soil. The initial mass and volume of the soil are: V1=20.2cm^3 , while the final mass and volume are M2=24g and V2=14.3cm^3 . Note that in the initial state the soil is saturated, whereas in the final state the soil is completely dry.
Calculate:
a. the shrinkage limit SL of the soil.
b. the void ratio at the SL.
c. Gs of the soil solids.
d. the initial void ratio.
have a list sample_data = [1,2,3,4,5,6,7,8,9,10], and I want [1,4,9,16,25,36,49,64,81,100] from it. What should be the possible solution?
Select one:
To get [1,4,9,16,25,36,49,64,81,100] from [1,2,3,4,5,6,7,8,9,10], one should square each number in the list. This can be done by using a for loop with the range function or by using list comprehension.
The possible solution for getting [1,4,9,16,25,36,49,64,81,100] from the sample_data list [1,2,3,4,5,6,7,8,9,10] is to use the list comprehension to square each number in the list. This is shown below:sample_data = [1,2,3,4,5,6,7,8,9,10]squared_data = [num**2 for num in sample_data]print(squared_data)Output:[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]Alternatively, we can use a for loop to square each number in the sample_data list. This can be done as shown below:sample_data = [1,2,3,4,5,6,7,8,9,10]squared_data = []for num in sample_data:
squared_data.append(num**2)print(squared_data)Output:[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]In summary, to get [1,4,9,16,25,36,49,64,81,100] from the sample_data list [1,2,3,4,5,6,7,8,9,10], we can use list comprehension or a for loop with the append function to square each number in the sample_data list.
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An elevation is.... * 10 points a. A detailed description of requirements, composition and materials for a proposed building. b. A view of a building seen from one side, a flat representation of one façade. This is the most common view used to describe the external appearance of a building. c. The development of the last remaining lots in an existing developed area, the new development within an area already served by existing infrastructure and services, or the reuse of already developed, but vacant properties. d. The practice of creating structures and using processes that are environmentally responsible and resource-efficient throughout a building's life-cycle from siting to design, construction, operation, maintenance, renovation and deconstruction.
Answer:
b. A view of a building seen from one side, a flat representation of one façade. This is the most common view used to describe the external appearance of a building.
Explanation:
An elevation is a three-dimensional, orthographic, architectural projection that reveals just a side of the building. It is represented with diagrams and shadows are used to create the effect of a three-dimensional image.
It reveals the position of the building from ground-depth and only the outer parts of the structure are illustrated. Elevations, building plans, and section drawings are always drawn together by the architects.
7 of 20
While driving off road, your travel path crosses a slope. Which of the following practices will help you
reduce the risk of rollover?
Slow down and maintain a controlled speed when driving on slopes. Excessive speed can increase the chances of losing control and rolling over. It's crucial to stay within a safe and manageable speed range.
How to explain the informationWhen encountering a slope, try to approach it at a right angle whenever possible. This helps to distribute the vehicle's weight more evenly across the wheels and reduces the risk of tipping over.
When driving uphill or downhill, aim to navigate the slope in a straight line. Avoid traversing diagonally across the slope, as it can shift the center of gravity and increase the chances of a rollover. Going straight minimizes the lateral forces acting on the vehicle.
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Problem 2.2 Simplify the following block diagramand obtain its overall transferfunction
Given block diagram in Figure 1. Figure 1 Block Diagram We have to simplify the given block diagram and obtain its overall transfer function.
The simplified block diagram is shown in Figure 2. Figure 2 Simplified Block Diagram From the simplified block diagram, we can write the overall transfer function of the given block diagram as follows:
\(\[H(s)=\frac{Y(s)}{R(s)}=\frac{G_1(s)\times G_2(s)\times G_3(s)}{1+G_1(s)\times G_2(s)\times G_3(s)\times H_1(s)}\].\)
\(where \[G_1(s)=\frac{2}{s+2}\] \[G_2(s)=e^{-5s}\] \[G_3(s)=\frac{1}{s+10}\] and \[H_1(s)=1\].\)
Substituting the given values, we get\(\[H(s)=\frac{\frac{2}{s+2}\times e^{-5s}\times \frac{1}{s+10}}{1+\frac{2}{s+2}\times e^{-5s}\times \frac{1}{s+10}\times 1}\] \[\Rightarrow H(s)=\frac{2e^{-5s}}{(s+2)(s+10)+2e^{-5s}}\] .\)
Therefore, the overall transfer function of the given block diagram is \(\[H(s)=\frac{2e^{-5s}}{(s+2)(s+10)+2e^{-5s}}\]\).
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Greek engineers had the unenviable task of moving largecolumns from the quarries to the city.One engineer,Chersiphron, tried several different techniques to do this. Onemethodwas to cut pivot holes into the ends of the stone andthen use oxen to pull the column. The 5-ft diameter columnweighs 14,000 lbs, andthe team of oxen generates a constantpull force of 2,000 lbs on the center of the cylinder,G. Knowingthat the column starts from rest and rolls without slipping,determine:(a) the velocity of its center,G,after it has moved7ft,and (b) the minimum static coefficient of friction that will keepit from slipping.
Answer:
yea
Explanation:
okkudjeheud email and delete the electronic version of this communication
Some analysts believe that the exclusion of some traditional partners from the "democratic camp" by the United States will deepen the gap between the two sides; the invitation of some countries or regions suspected of "democratic retrogression" will affect the "credibility" of the summit.
The exclusion of some traditional partners from the "democratic camp" by the United States will undoubtedly deepen the gap between the two sides.
About summit :
This move by the US is seen as a sign of its dissatisfaction with the policies and behavior of these countries. In addition, the invitation of some countries or regions suspected of "democratic retrogression" may lead to further erosion of the credibility of the summit in the eyes of the invited countries, as well as the international community. At the same time, it is worth noting that the United States must consider the consequences of such actions and the possible damage to its international image. If the US is seen as selectively choosing partners, it may undermine its overall influence in the world.
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B/ Evaluate e^(πi/2)
You get a result immediately from Euler's formula:
e ^(i π/2) = cos(π/2) + i sin(π/2) = 0 + i * 1 = i
who is the strongest avenger i say hulk but who knows at this point
Answer:
or is the strongest evenger she hulk
Explanation:
?????????
Answer:
Thor!
Explanation:
In Thor: Ragnarok he beat the Hulk in order for Hulk to win thor had to be electrocuted and in Avengers: Endgame Thor is seen holding open the "Floodgates" and withstanding the radiation from a dying star, also the fact that Thor is a god means that he is all powerful and the rightful heir to the throne to Asgard, plus the fact that he has defeated Loki multiple times a feat that not even the Hulk has done.
Which is the maximum length for any opening on the surface of a 2G SMAW guided bend test specimen?
O 1/3 inch
O 1/4 inch
O 1/8 inch
O 1/2 inch
Answer:
1/8 is the maximum length for opening any on the surface of 2 gtam guided bend test specimen
FAULT LOCATION METHODS(input-output)
Fault location techniques are used in power systems for accurate pinpointing of the fault position.
This paper presents a comparative study between two fault location methods in distribution network with Distributed Generation (DG). Both methods are based on computing the impedance using fundamental voltage and current signals. The first method uses one-end information and the second uses both ends
If extension done in a stork position, during backward bending in a standing position of a special test for lumbar spine, produces pain in the lumbar or sacral regions of the spine, it may indicate _____.
mualem, y. 1976. a new model for predicting the hydraulic conductivity of unsaturated porous media, water resour. res., 12, 513–522.
The Mualem model is a physics-based mathematical model developed by Yakov Mualem in 1976, which is used to predict the hydraulic conductivity of unsaturated porous media. The hydraulic conductivity is the measure of how easily water can move through soil, and it is a crucial parameter for understanding water movement in soil.
The Mualem model is an empirical model that was developed based on the principle of soil-water retention curve. The soil-water retention curve is a measure of the relationship between the soil water potential and the soil water content, and it is an essential property of unsaturated porous media.
The Mualem model uses two empirical parameters, namely the residual water content and the shape parameter, to predict the hydraulic conductivity of unsaturated porous media. These parameters are related to the soil water retention curve, and they are obtained through experimental measurements.
The Mualem model has been widely used in various fields, such as hydrology, soil science, and geotechnical engineering, to predict the hydraulic conductivity of unsaturated porous media. It is a simple yet effective model that provides a good approximation of the hydraulic conductivity of unsaturated porous media, and it has been validated by numerous experimental studies.
In conclusion, the Mualem model is a physics-based mathematical model developed by Yakov Mualem in 1976, which is used to predict the hydraulic conductivity of unsaturated porous media. It is an empirical model that uses two parameters obtained from the soil-water retention curve to predict the hydraulic conductivity. The Mualem model is widely used in various fields and provides a good approximation of the hydraulic conductivity of unsaturated porous media.
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Consider these two sentences: "The boy was sick from eating so much ice cream," and, "That boy ate so much ice cream, it made him sick." These sentences have similar ------ but different syntax.
The given sentences have similar semantic meaning but different syntax.
Both sentences convey the same message that the boy got sick after consuming a large amount of ice cream. However, the first sentence emphasizes the result or consequence of eating too much ice cream, whereas the second sentence emphasizes the cause of the boy's sickness.
The syntax in the first sentence is subject-verb-object, while the second sentence follows a subject-object-verb structure. The second sentence uses the cause-effect relationship, where the cause (eating too much ice cream) is followed by the effect (getting sick), while the first sentence describes the effect first and then mentions the cause. In essence, the difference in syntax highlights a different perspective or emphasis on the same event.
In summary, both sentences are similar in meaning, but the syntax used changes the way the information is presented.
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Omg I just got 17/25 questions wrong using this on an Ag test , but got 100’s every time on health
Answer:
sorry im answering questions for the points cuz im built dfferent
Explanation:
Answer: That happens to me too sometimes. I hate when people give the wrong answers...like if u don't know the answer, then don't respond
while performing a running compression test how should running compression compare to static compression
Answer:
The idle speed of a running compression should be between 50-75 PSI and that is about half of the static compression.
Explanation:
The Running or Dynamic compression is used to determine how well the cylinder in an engine is absorbing air, reserving it for the proper length of time, and releasing it to the exhaust. The static or cranking compression test is used to check the sealing of the cylinder. Before performing the running compression test, the static compression test is first performed to rule out other issues like bent valves.
The standard value for the static compression is given by;
Compression ratio * 14.7 = Manufacturers Specification
The running compression should always be half of the static compression.
An AC sine wave has an RMS value of 100 V. What's the average of the waveform?
A. 90 V
B. 80 V
C. 102 V
D. 92.6 V
Just took the test and it ISN'T 92.6 V, my guess is 80 V but I dont know because it only says if I got it wrong.
What is wrong with the following code?
6
print (what is your name?)
Answer:
pakipic na lang po question nyo para masagot po
Explanation:
please po di ko masyado gets po e
it is simple the title name after all it is just asking your name
Suppose that 42\%42%42, percent of students of a high school play video games at least once a month. The computer programming club takes an SRS of 303030 students from the population of 792792792 students at the school and finds that 40\%40%40, percent of students sampled play video games at least once a month. The club plans to take more samples like this. Let \hat p p ^ p, with, hat, on top represent the proportion of a sample of 303030 students who play video games at least once a month. What are the mean and standard deviation of the sampling distribution of \hat p p ^ p, with, hat, on top? Choose 1 answer: Choose 1 answer: (Choice A) A \begin{aligned} \mu_{\hat p}&=0.42 \\\\ \sigma_{\hat p}&=\sqrt{\dfrac{0.42\left(0.58\right)}{30}} \end{aligned} μ p ^ σ p ^ =0.42 = 30 0.42(0.58) (Choice B) B \begin{aligned} \mu_{\hat p}&=(30)(0.42) \\\\ \sigma_{\hat p}&=\sqrt{30(0.42)(0.58)} \end{aligned} μ p ^ σ p ^ =(30)(0.42) = 30(0.42)(0.58) (Choice C) C \begin{aligned} \mu_{\hat p}&=(30)(0.4) \\\\ \sigma_{\hat p}&=\sqrt{30(0.4)(0.6)} \end{aligned} μ p ^ σ p ^ =(30)(0.4) = 30(0.4)(0.6) (Choice D) D \begin{aligned} \mu_{\hat p}&=0.4 \\\\ \sigma_{\hat p}&=\sqrt{\dfrac{0.4\left(0.6\right)}{30}} \end{aligned} μ p ^ σ p ^ =0.4 = 30 0.4(0.6)
Answer:
its A, first choice on khan
Explanation:
Các đặc điểm chính của đường dây dài siêu cao áp .
Answer:
Đường dây siêu cao áp 500kV: Những chuyện giờ mới kể ... Ngày 27/5/1994, hệ thống đường dây điện siêu cao áp 500kV Bắc - Nam chính thức đưa ... Tại thời điểm đó, các nước như Pháp, Úc, Mỹ khi xây dựng đường dây dài nhất ... và chế ra các máy kéo dây theo đặc thù công việc của từng đơn vị.
Explanation:
What are the things considered in the planning and design of social housing
Answer:
The things that you should consider in the planning and design of social housing are:
1. Physical requirements.
2. User Experience.
3. Time and Money.
4. Context/Setting.
5. Upkeep.
Hope this helps you!
Please mark me as a brainliest.
An adiabatic pump is to be used to compress saturated liquid water at 10 kPa to a pressure of 15 MPa in a reversible manner. 15 MPa P Pump Determine the work input using entropy data from the compressed liquid table. Use steam tables. (You must provide an answer before moving on to the next part.) The work input is kJ/kg. Determine the work input using inlet specific volume and pressure values. (You must provide an answer before moving on to the next part.) The work input is kJ/kg Determine the work input using average specific volume and pressure values. answer before moving on to the next part.) The work input is kJ/kg. Calculate the errors involved in parts b and c. The error involved in part b is 1% The error involved in part cis 1%.
To determine the work input using entropy data from the compressed liquid table, we need to find the specific entropy of water at 10 kPa and 15 MPa, then calculate the change in entropy during the compression process.
From the compressed liquid table, we can find that the specific entropy of saturated liquid water at 10 kPa is 0.2888 kJ/kg-K. At 15 MPa, the specific entropy of saturated liquid water is 1.2960 kJ/kg-K.
The change in entropy during the compression process is ΔS = S2 - S1 = 1.2960 - 0.2888 = 1.0072 kJ/kg-K.
Using the definition of adiabatic work as dW = -TdS, where T is the temperature and dS is the change in entropy, we can calculate the work input per unit mass as:
dW = -TΔS
To find the temperature at each state, we can use the saturated liquid table again. At 10 kPa, the saturation temperature is 10.01°C, and at 15 MPa, the saturation temperature is 198.4°C.
Using these temperatures and the change in entropy calculated above, we get:
dW = - (198.4 + 273.15) * 1.0072 = -478.5 kJ/kg
Therefore, the work input using entropy data from the compressed liquid table is -478.5 kJ/kg.
To determine the work input using inlet specific volume and pressure values, we can use the equation for reversible adiabatic work:
dW = v(P2 - P1)
where v is the specific volume and P1 and P2 are the initial and final pressures, respectively.
Using the saturated liquid table, we find the specific volume of saturated liquid water at 10 kPa is 0.001043 m³/kg. At 15 MPa, we can use the compressed liquid table to find that the specific volume of saturated liquid water is approximately 0.001066 m³/kg.
Using these values in the equation above, we get:
dW = 0.001043 * (15 - 0.01) * 10⁶ = 154.7 kJ/kg
Therefore, the work input using inlet specific volume and pressure values is 154.7 kJ/kg.
To determine the work input using average specific volume and pressure values, we can use the average pressure and specific volume during the compression process:
Pavg = (P1 + P2) / 2 = (0.01 + 15) / 2 = 7.505 MPa
vavg = (v1 + v2) / 2 = (0.001043 + 0.001066) / 2 = 0.001055 m³/kg
Using these values, we can calculate the work input as:
dW = vavg * (P2 - P1)
dW = 0.001055 * (15 - 0.01) * 10⁶ = 155.7 kJ/kg
Therefore, the work input using average specific volume and pressure values is 155.7 kJ/kg.
To calculate the errors involved in parts b and c, we can use the formula:
error = |(actual value - approximate value) / actual value| * 100%
For part b, the actual value is -478.5 kJ/kg and the approximate value is 154.7 kJ/kg. Plugging in these values, we get:
error = |(-478.5 - 154.7) / -478.5| * 100% = 132.6%
Therefore, the error involved in part b is 132.6%.
For part c, the actual value is -478.5 kJ/kg and the approximate value is 155.7 kJ/kg. Plugging in these values, we get:
error = |(-478.5 - 155.7) / -478.5| * 100% = 132.5%
Therefore, the error involved in part c is 132.5%.
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calculate the mobility of the following linkage system. see below for additional information on the dof calculation.
The DOF of a mechanism is the number of independent parameters required to define the position and orientation of all of its links relative to a fixed reference frame.
To calculate the mobility of a linkage system, we need to determine the number of degrees of freedom (DOF) of the system. The DOF of a mechanism is the number of independent parameters required to define the position and orientation of all of its links relative to a fixed reference frame. The mobility is then calculated as the difference between the number of links and the DOF of the system.
To determine the DOF of the linkage system, we can use the Gruebler's equation, which is given by:
DOF = 3(n-1) - 2j - h
where n is the number of links, j is the number of joints, and h is the number of higher pairs. In this equation, the term 3(n-1) represents the number of degrees of freedom of an equivalent rigid body, which has n links and is constrained to move only in a planar motion.
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What is the reading of this Dial Caliper?
Answer:
45
Explanation:
bdgdsfggsfg
3. Suppose up to 300 cars per hour can travel between any two of the cities 1, 2, 3, and 4. Formulate a maximum flow problem that can be used to determine how many cars can be sent in the next two hours from city 1 to city 4. Give the network diagram and the LP formulation for your model.
Let $x ij$ represent the quantity of cars that will be delivered in the following two hours from city I to city j.
Create a maximum flow issue?Network Diagram:
LP Formulation:
Maximize Z = 150x14 + 150x24
Subject to:
x11 + x12 + x13 + x14 <= 300 (flow from city 1 to other cities)
x21 + x22 + x23 + x24 <= 300 (flow from city 2 to other cities)
x31 + x32 + x33 + x34 <= 300 (flow from city 3 to other cities)
x41 + x42 + x43 + x44 <= 300 (flow from city 4 to other cities)
x11 + x21 + x31 + x41 = 150 (flow into city 1)
x12 + x22 + x32 + x42 = 150 (flow into city 2)
x13 + x23 + x33 + x43 = 150 (flow into city 3)
x14 + x24 + x34 + x44 = 150 (flow into city 4)
xij >= 0 (all variables must be positive)
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a cube of material (1-inch sides) is compressed with a load of 150 tons, resulting in the onset of yielding: (a) determine the load required if the sides were constrained by forces of 50 tons and 100 tons, respectively (b) express the hydrostatic and deviatoric stress tensors for (a) (c) estimate what the material might be based on these findings and state what other information could be useful in determining the material being examined.
(a) The load required if the sides were constrained by forces of 50 tons and 100 tons, respectively, can be determined by considering the equilibrium of forces.
Since the cube is compressed uniformly, the load is distributed equally among all six faces. Therefore, if the sides were constrained by a force of 50 tons, the total load required would be 50 tons per face * 6 faces = 300 tons. Similarly, if the sides were constrained by a force of 100 tons, the total load required would be 100 tons per face * 6 faces = 600 tons.
(b) The stress tensor can be expressed in terms of hydrostatic stress and deviatoric stress.
The hydrostatic stress tensor, denoted as σ_hydro, is isotropic and acts equally in all directions. For a uniformly compressed cube, the hydrostatic stress is given by the formula:
σ_hydro = (load)/(area)
In this case, the area of each face of the cube is (1 inch)^2 = 1 square inch. Therefore, the hydrostatic stress is:
σ_hydro = (load)/(area) = (150 tons)/(1 square inch) = 150 tons/square inch
The deviatoric stress tensor, denoted as σ_dev, represents the stress that is not isotropic and acts differently in different directions. In this case, since the cube is compressed uniformly, there is no deviatoric stress.
(c) Based on these findings, it is difficult to determine the exact material being examined. The hydrostatic stress alone does not provide enough information to identify the material. Other information that could be useful in determining the material includes its mechanical properties such as elasticity, yield strength, and plastic behavior. Additionally, information about the material's composition, structure, and previous knowledge of similar materials could also help in identifying the material.
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(a) If the sides of a 1-inch cube of material are constrained by forces of 50 tons and 100 tons, the load required for yielding is 100 tons and 200 tons, respectively.
(b) For (a), the hydrostatic stress tensor is given by (P11+P22+P33)/3 while the deviatoric stress tensor is (σ11 - σ33) / 2.
(c) More information is needed to determine the identity of the material.
The following is a step-by-step explanation of the solution to the problem:
a) Yield stress is a measure of the maximum amount of stress that a material can withstand without deforming permanently. The load required for yielding a 1-inch cube of material with sides that are constrained by forces of 50 tons and 100 tons, respectively, can be determined as follows:
Since the load required for a 1-inch cube with no constraints is 150 tons, and since the material is isotropic, the required load for the case where the sides are constrained by 50 tons is 100 tons (i.e. 2/3 x 150 tons), and the required load for the case where the sides are constrained by 100 tons is 200 tons (i.e. 4/3 x 150 tons).
Thus, the load required for yielding with constraints of 50 tons and 100 tons, respectively, is 100 tons and 200 tons.
b) To calculate the hydrostatic stress tensor, we need to calculate the sum of the three diagonal stresses and divide by 3.
In our example, this means that the hydrostatic stress tensor is (50+100+150)/3 = 100 tons.
The deviatoric stress tensor, on the other hand, is given by the formula (σ11 - σ33) / 2.
The values of the diagonal stresses for this particular example are P11 = P22 = 50 tons and P33 = 150 tons.
Therefore, the deviatoric stress tensor is (50 - 150) / 2 = -50 tons.
c) Based on the given data, it is impossible to determine the identity of the material. We need additional information such as the deformation and failure properties, the density, and other parameters to identify the material.
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Help I need fast is it true or false
Answer:
False
Explanation:
It can only survive outside of the body for six days
The solid homogeneous cylinder is released from rest on the ramp. If θ= 40° , µs= 0.30 and µk= 0.20. Determine the magnitudes of the acceleration of the mass (W= 8lb) center G and the friction force exerted by the ramp on the cylinder.
Answer:
A) 13.80 ft/s^2
B) 1.714 Ib
Explanation:
Magnitude of acceleration center G
mass = W / g = 8 / 32.2 = 0.2484 Ib.s^2/ft
calculate the acceleration along x direction
A = ra
r = radius
a = angular acceleration
A = 6 in \(\frac{1 ft}{12 in}\) * a
a= 2A
equation of the plane along the x-direction
w sin∅ - F = ma
8* sin40 - F = 0.2484 * a
hence F = 5.1423 - 0.2484 a
next find the moment of inertia along the z axis
I = 1/2 mr^2
= 1/2 * 0.2484 * (6/12)^2 = 0.03105 Ib.ft.s^2
Applying moment balance equation
F * r = inertia * a
(5.1423 - 0.2484 a)*0.5 = 0.03105 * 2A
2.57115 = 0.1863 A hence
A = 13.80 ft/s^2 ( acceleration of the cylinder )
B) Calculate the friction force exerted by the ramp on the cylinder
F = 5.1423 - 0.2484 A
= 5.1423 - 0.2484 ( 13.80 )
= 1.714 Ib
The magnitudes of the acceleration and the friction force are;
Acceleration = 13.8 ft/s²
Friction Force = 1.714 lb
The image of the solid homogeneous cylinder is missing and so i have attached it.
From the image we see that;
Weight; W = 8 lbRadius; r = 6 in = 0.5 ftWe are given;
Angle of incline; θ = 40°Coefficient of static friction; µ_s = 0.30 coefficient of kinetic friction; µ_k = 0.20We know that formula for weight is; W = mg
Thus; m = W/g
where g is acceleration due to gravity = 32.2 ft/s²
m = 8/32.2
mass; m = 0.2484 lb.s²/ft
Now, to get the acceleration along the x-axis, we will use the formula;
a = rα
where α is angular acceleration. Thus;
a = 0.5α
α = 2a ----- (eq 1)
Now, resolving forces along the x-direction gives;
W*sinθ - F = ma
Plugging in the relevant values;
8*sin 40 - F = 0.2484a
F = 8*sin 40 - 0.2484a -----(eq 2)
Now, moment of inertia of the cylinder along the z-axis is gotten from;
I = ¹/₂mr²
I = ¹/₂ × 0.2484 × 0.5²
I = 0.03105 lb.ft/s²
Taking equilibrium of moments we have;
F*r = I*α
Thus;
(8*sin 40 - 0.2484a)0.5 = 0.03105α
⇒ 2.57115 - 0.1242a = 0.03105α
⇒ 0.03105α + 0.1242a = 2.57115
From eq 1, α = 2a. Thus;
0.03105(2a) + 0.1242a = 2.57115
0.1863a = 2.57115
a = 2.57115/0.1863
a = 13.8 ft/s²
Formula for the friction force exerted by the ramp on the cylinder is;F = 8*sin 40 - 0.2484a
F = 5.1423 - 0.2484(13.8)
F = 1.714 lb
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