The specific gravity and kinematic viscosity of a certain liquid are 1.5 and 4 \times 10^{-4} {~m}^{2} / {s} , respectively. Dynamic viscosity of the given liquid would be 6 × 10⁻⁴ ρ.
Given, Specific gravity of the liquid, S.G. = 1.5
Kinematic viscosity of the liquid, ν = 4 × 10⁻⁴ m²/s
Formula used
Dynamic viscosity is given by formula,
μ = S.G. × ν × ρ
Where,μ is dynamic viscosity of the liquidS.
G. is specific gravity of the liquid
ν is kinematic viscosity of the liquid
ρ is density of the liquid
To find
Dynamic viscosity of the liquid
Solution
Let the density of the liquid be ρ.
Now,μ = S.G. × ν × ρ
We are given,S.G. = 1.5ν = 4 × 10⁻⁴ m²/s
Substitute these values in the above equation to get,
μ = 1.5 × 4 × 10⁻⁴ × ρμ = 6 × 10⁻⁴ × ρ
Thus, the dynamic viscosity of the given liquid is 6 × 10⁻⁴ ρ.
Answer: Dynamic viscosity of the given liquid is 6 × 10⁻⁴ ρ.
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draw the shear diagram for the beam. set m0 = 500 n⋅m, l = 8 m.
Answer:
Missing information
Explanation:
kindly please provide full question with diagram.
need urgent help!!
Determine the point(s) P on the line e with equation x−6 = ( y−3)/4 = ( 1−z)/3
for which the line connecting P with Q(2, −6, 5) is perpendicular to e.
The quartiles divide a set of observations into four portions, each representing 25% of the observations, together with the minimum and maximum values of the data set. The interquartile range, a measurement of variation around the median, is calculated using quartiles.
How are quartiles determined?In order to quartile a set of data with n items (numbers), we choose the n/4th, n/2nd, and n/4th items. Interpolation between the adjacent items is used if indexes n/4, n/2, or 3n/4 are not integers.For instance, the first quartile Q1 of ordered data is the 25th item, the second quartile Q2 is the 50th item, and the third quartile Q3 is the 75th item. The fourth quartile Q4 would be the highest item of data, and the zeroth quartile Q0 would be the minimum item; however, these extreme quartiles are referred to as the minimum and maximum of a set, respectively.Calculation:Statistical file: {2, -6, 5}
Quartile Q1: -6
Quartile Q2: 2
Quartile Q3: 5.
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how fast does a rocket need to be traveling to excape our earths gravitational pull?
Answer:
25,000 mph or around 40,000 kph
Explanation:
all depends on the altitude and weather conditions but this is average
Select the correct answer.
Which chemical can you use to assist with your motor fuel needs?
O A.
ethylene glycol
OB.
ethanol
O c.
butanol
OD.
pentanol
O E.
propranolol
Reset
Next
Answer: Ethanol
Explanation:
engineering when looking at an image of an object, what enables you to notice the surfaces and edges more clearly?
Simple things like this have flat surfaces at 90 degrees to the view and are surrounded by lines. Lines are drawn to represent surfaces parallel to the view (edges).
The front perspective is seen in the lower left corner. The right side perspective is shown at the lower right. The top view is at the upper left. There is no viewpoint (parallel lines do not converge, but stay parallel) The number of views might range between 1-6, although 3 is the most typical. A surface that is not at a right angle to the views is known as an auxiliary (extra) view (orthographic). Isometric perspective is shown in the view in the upper right corner. You should be aware of the kind of object you wish to add to a slide before you insert it.
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The __________ developed the national electric code, the national building code, and the national fire prevention code.
Main Answer:
The Bureau of Indian standards developed the national electric code, the national building code, and the national fire prevention code.
Sub heading:
explain BIS?
Explanation:
1.BIS-bureau of indian standard is the national standard body of india.
2.BIS is responbility for the harmonious deve;opment of the activities of standardization.marking .
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What current works best when the operator
encounters magnetic arc blow?
•DCEP
•ACEN
•CC
•AC
Answer:
AC
Explanation:
One situation when alternating current would work better than direct current is if the operator is encountering magnetic arc blow.
Current works best when the operator encounters magnetic arc blow is AC
Magnetic arc blow is simply defined as the arc deflection due to the warping of the magnetic field that is produced by electric arc current.
This is caused as a result of the following;
- if the material being welded has residual magnetism at an intolerable level
- When the weld root is being made, and the welding current is direct current which indicates constant direction and maintains constant polarity (either positive or negative).
Since it is caused by DC(Direct Current) which means constant polarity , it means the opposite will be better which is AC(alternating current) because it means that electricity direction will be switching to and fro and as such the polarity will also be revered in response to this back and forth switch manner.Thus, Current works best when the operator encounters magnetic arc blow is AC
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What happens when EPU output exceeds 32.5 volts
Answer:
In general, exceeding the rated voltage output of a power supply or electrical system could cause damage to the components being powered by that system. In some cases, this could result in the components malfunctioning or becoming permanently damaged, potentially leading to system failure. Additionally, exceeding the rated voltage of a system could cause electrical arcing or fires, which could be dangerous or catastrophic depending on the system and the environment it is operating in. Therefore, it is generally important to ensure that electrical systems are designed to operate within their rated voltage ranges to prevent damage and ensure safety.
the coprocessor 0 in a mips processor has a set of registers used to store necessary information when an exception occurs: $8 badvaddr $12 status $13 cause $14 epc. when a mips processor executes the following instructions: address instruction 0x00401000 li $t0, 0x7fffff0c 0x00401004 sw $s0, 7($t0) 0x00401008 ... the contents of these registers are: $8: 0x[a] $13 : 0x[b] note: assuming all interrupt pending (ip) bits are 0, i.e. no interrupt pending. $14: 0x[c].
BadVaddr ($8) stores the memory address at which the exception occurs.
Hence, the exception occurs in store word instruction.
What is memory address?A memory address in computing is a designation of a particular memory location that is used by hardware and software at different levels. Memory addresses are fixed-length digit sequences that are typically represented as unsigned integers and used in operations.
Such a numerical semantic is based on CPU characteristics (such as the instruction pointer and incremental address registers) as well as on the use of memory as an array that is supported by different programming languages.
Numerous memory locations make up the main memory of a digital computer. Physical addresses—which are codes—are assigned to each memory location. To access the appropriate memory location, the CPU (or other device) can use the code.
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A structural component is fabricated from an alloy that has a plane-strain fracture toughness of 62 MPa√m. It has been determined that this component fails at a stress of 250 MPa when the maximum length of an internal crack is 1.6 mm. What is the maximum allowable internal crack length (in mm) without fracture for this same component exposed to a stress of 250 MPa and made from another alloy that has a plane strain fracture toughness of 40 MPa√m?
Answer:
0.67 mm
Explanation:
Solution:
We find the dimensionless parameters by applying the critical stress crack propagation formula stated below:
σс= Klc/Y√πa
Y = Klc/σс √πa
σс = this is the critical stress needed for initial cracking propagation
Klc = the plain stress fracture toughness
a = surface length of the crack
Y = the dimensionless parameter
Now, we substitute the values 62MPa√m for Klc, 250 MPa for σс and 1.6 * 10 ^⁻3 for a in the dimensionless parameter equation.
Thus,
Y = Klc/σс √πa
= 62/250(√π * 1.6* 10 ^⁻3)
= 3.492
The next step is to find the maximum permitted surface crack length by applying the critical stress crack propagation equation given below:
σс= Klc/Y√πa
a= 1/π (Klc/Yσс)²
Now, substitute 40 MPa√m for Klc, 250 MPa for σс and 3.492 for surface length crack equation
So,
a= 1/π (Klc/Yσс)²
= 1/π[40/3.492 * 250]²
=1/π[40/873]²
=1/π[0.0458]²
0.318[0.0458]²
=0.318[0.00209]
= 0.0066
0.67* 10 ^⁻3 m
= 0.67 mm
Therefore the maximum surface crack length produced is 0.67 mm
Why are cars often called by numbers, like the BMW 428i or Nissan NV2500?
Answer: BMW did it again. They've show up with yet another automobile that's a genuine joy to operate a vehicle. The BMW 428i Coupe isn't so large , not to little - and it's got the elegant sport appearances of a coupe as well. Really, very pleasant really!
Explanation:
An iron-constantan thermocouple is to be used to measure temperatures between 0and 400 degree C. What will be the non-linearity error as a percentage of the full-scale reading at 100 degree C If a linear relationship is assumed between e.m.f and temperature? E.M.F at 100 degree C= 5.268 m V; e.m.f at 400 degree C= 21.846 m V
The non-linearity error as a percentage of the full-scale reading at 100 degree C is - 0.89%.
What is non-linearity error?Non-linearity error is defined as the biggest deviation from a straight line linking the output signal to the applied force, known as the "best straight," that the calibration curve makes. In order to eliminate second order nonlinearity, the sensor signal conditioning system feeds a portion of the output signal back to the sensor.
If EMF and Celsius temperature have a proportional relationship, then the recorded value of EMF at 100 °C will be understood to be a temperature of.
T/5.268 = 400/21.846
T = 5.268(400/21.846) ≈ 96.457 °C
As a percentage of the full scale, the mistake is
(96.457 -100)/400 × 100% ≈ -0.886%
Thus, the non-linearity error as a percentage of the full-scale reading at 100 degree C is - 0.89%.
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Effective operation of roller chain and gear couplings
requires proper
A. lubrication and cooling.
B. lubrication and balance.
C. alignment and balance.
D. alignment and lubrication.
Effective operation of roller chain and gear couplings requires proper alignment and lubrication.
Roller chain coupling are compact and flexible couplings. They are used for low to moderate speed/torque applications. For effective operation they need to be maintained by applying lubrication and aligning.
Gear couplings are used for high speed and torque applications. For effective performance they need to be lubricated frequently and proper alignment is needed.
Hence effective operation of roller chain and gear couplings requires proper lubrication and alignment.
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In a cout statement, which of the following will advance the output position to the beginning of the next line?
A) endl or \n
B) end1 or /n
C) \n or \t
D) \t or \b
E) \\ or \'
When a cout statement is executed, which of the following will advance the output position to the beginning of the next line?endl or \n will advance the output position to the beginning of the next line, So the correct answer is A) endl or \n.
Explanation: This statement advances the output position to the beginning of the next line.endl is the equivalent of writing "\n" and is used to move the cursor or output position to the beginning of the next line. A standard stream of output that accepts values and inserts them into the output or displays them on the screen is called the "cout" (pronounced "see-out") function. The output stream is an instance of the ostream class. The << (output) operator and the cout function are used to display results in a C++ program, and they all use the ostream class. The endl or \n options, according to the C++ standard, indicate a newline character. As a result, when a cout statement is executed, both of these characters will advance the output position to the beginning of the next line.So the correct answer is A) endl or \n.
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If two current are in the same direction at any instant of time in a given branch of a circuit, the net current at that instant
If two currents are in the same direction at any instant of time in a given branch of a circuit, the net current at that instant will be the sum of the two individual currents. In other words, the net current is the algebraic sum of the two currents.
How can this be illustrated?For example, if one current is 2 amperes and the other current is 3 amperes, and they are flowing in the same direction in a given branch of the circuit, then the net current at that instant will be 5 amperes (2 + 3 = 5).
It's important to note that this only applies at a specific instant in time, and the net current may change as the circuit changes or the currents vary.
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what is the required minimum width for industrial fixed stairs
Industrial fixed staircases must be at least 22 inches wide.
What is the average width of stairs?The minimum permitted by most construction rules, staircases in America are normally 36 inches wide. There is still enough space to allow for railings, which can take up a few inches, even when not all 36 inches are used.
What is the smallest stair width allowed in CM?For one-way traffic, stairways must be 0.90 meters wide, and for two-way traffic, they must be 1.50 meters wide. The riser and tread distances for indoor stairs should be 0.28 m and 0.35 m, respectively. The maximum riser and minimum tread sizes for outdoor stairs should be 0.15 m and 0.30 m, respectively.
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celery stalks that are standing in a glass of pure water for several
Celery stalks that are standing in a glass of pure water for several hours become more rigid and stiff. T
he process behind this is known as osmosis. When the celery stalk is placed in the glass of water, water enters the plant through a process known as osmosis.
The water molecules move from an area of high concentration (the glass of water) to an area of low concentration (the celery stalk). This movement of water molecules from an area of high concentration to an area of low concentration through a semipermeable membrane is known as osmosis.
Osmosis is the diffusion of water molecules across a semipermeable membrane from a region of low solute concentration to a region of high solute concentration. The movement of water molecules is driven by the difference in concentration between the two regions. In the case of celery stalks standing in a glass of pure water, the solute concentration inside the celery stalks is higher than that in the water.
Hence, water moves from the glass into the celery stalk, making it more rigid and stiff.
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What signal propagation phenomena causes the diffusion, or the reflection in multiple different directions, of a signal?
In the radio communication system, multipath is the propagation phenomenon that causes diffusion or reflection in multiple different directions of a signal.
Multipath is a propagation mechanism that impacts the propagation of signals in radio communication. Multipath results in the transmission of data to the receiving antenna by two or more paths. Diffusion and reflection are the causes that create multiple paths for the signal to be delivered.
Diffraction occurs when a signal bends around sharp corners; while reflection occurs when a signal impinges on a smooth object. When a signal is received through more than one path because of the diffraction or reflection, it creates phase shifting and interference of the signal.
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Can someone help me plz!!
When one knows the true values x1 and x2 and has approximations X1 and X2 at hand, one can see where errors may arise. By viewing error as something to be added to an approximation to attain a true value, it follows that the error ei is related to Xi and xi as xi 5 Xi 1 ei (a) Show that the error in a sum X1 1 X2 is (x1 1 x2) 2 (X1 1 X2) 5 e1 1 e2 (b) Show that the error in a difference X1 2 X2 is (x1 2 x2) 2 (X1 2 X2) 5 e1 2 e2 (c) Show that the error in a product X1X2 is x1x2 2 X1X2 < X1X2 a e1 X1 1 e2 X2 b (d) Show that in a quotient X1yX2 the error is x1 x2 2 X1 X2 < X1 X2 a e1 X1 2 e2 X2 b
Answer:
(a) For the sum X1 + X2, we have:
X1 + X2 = (x1 + e1) + (x2 + e2)
= x1 + x2 + (e1 + e2)
The error in the sum is given by:
e1 + e2 = (x1 + e1) + (x2 + e2) - (x1 + x2)
= (x1 + x2) + (e1 + e2) - (x1 + x2)
= e1 + e2
Therefore, the error in the sum is e1 + e2, as required.
(b) For the difference X1 - X2, we have:
X1 - X2 = (x1 + e1) - (x2 + e2)
= x1 - x2 + (e1 - e2)
The error in the difference is given by:
e1 - e2 = (x1 + e1) - (x2 + e2) - (x1 - x2)
= (x1 - x2) + (e1 - e2) - (x1 + x2)
= e1 - e2
Therefore, the error in the difference is e1 - e2, as required.
(c) Show that the error in a product X1X2 is:
x1x2 - X1X2 ≈ (X1 * e2) + (X2 * e1)
Proof:
We start with the equation:
X1X2 = (x1 + e1)(x2 + e2)
Expanding the right side of the equation, we get:
X1X2 = x1x2 + x1e2 + x2e1 + e1e2
Subtracting x1x2 from both sides, we get:
x1x2 - X1X2 = x1e2 + x2e1 + e1e2
Since e1 and e2 are small compared to x1 and x2, we can ignore the e1e2 term. Therefore, we can approximate the error as:
x1x2 - X1X2 ≈ (X1 * e2) + (X2 * e1)
(d) Show that in a quotient X1 / X2, the error is:
(x1 / x2) - (X1 / X2) ≈ ((e1 * X2) - (e2 * X1)) / (X2)^2
Proof:
We start with the equation:
X1 / X2 = (x1 + e1) / (x2 + e2)
Expanding the right side of the equation, we get:
X1 / X2 = (x1 / x2) + (x1 * e2 - x2 * e1) / (x2)^2 + e1 / x2 - e2 * x1 / (x2)^2
Subtracting (x1 / x2) from both sides, we get:
(x1 / x2) - (X1 / X2) = (x1 * e2 - x2 * e1) / (x2)^2 + e1 / x2 - e2 * x1 / (x2)^2
Simplifying the expression, we get:
(x1 / x2) - (X1 / X2) ≈ ((e1 * X2) - (e2 * X1)) / (X2)^2
This is the error in the quotient.
Explanation:
What energy transformation takes place when you turn on a light
Answer:
From electrical energy to radiation
Explanation:
A light bulb converts electrical energy to light, which is nothing more than radiation. Don't regard radiation as a bad thing, this light is non-iodizing radiation, which does not have the possibility to alter our DNA, and thus it's safe.
The simplest example can be found in old lights (obsolete now because they are vastly inefficient). This lights were just resistors which turned electrical energy into heat. A very hot material reflects light in the form of radiation, as described above.
Technologies like LEDs are more complicated to explain.
8th grade science using an engineering design process, create mechanisms to improve community resilience, which safeguard against natural hazards
To improve community resilience against natural hazards, mechanisms can be created using an engineering design process.
How can the engineering design process be utilized to create mechanisms that enhance community resilience against natural hazards?The engineering design process provides a systematic approach to problem-solving and innovation. When applied to the task of improving community resilience, it enables the creation of effective mechanisms that can safeguard against natural hazards.
The first step in the engineering design process is to define the problem. In this case, the problem is enhancing community resilience against natural hazards. This involves identifying the specific hazards prevalent in the community, such as earthquakes, floods, or hurricanes, and understanding their potential impacts.
The next step is to conduct research and gather information about existing solutions and best practices. This includes studying successful case studies and analyzing the effectiveness of different mechanisms used in other communities facing similar hazards.
Based on the research, the design phase begins. Engineers brainstorm and develop concepts for mechanisms that can mitigate the effects of natural hazards. These mechanisms could include early warning systems, reinforced infrastructure, improved evacuation routes, or resilient building materials.
Once the design concepts are developed, engineers create prototypes and models to test their functionality and effectiveness. These prototypes can be simulated or built on a smaller scale to evaluate their performance.
After testing and refining the prototypes, the final step is implementation. The mechanisms designed to improve community resilience are put into action, taking into account factors like cost, feasibility, and community engagement.
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On the position time curve, if the slope of a tangent at a point is positive, that means:
A: The object is moving backward
B: The object is not moving
C: The object is moving forward
Answer:
C. the object is moving forward
Explanation:
A positive slope means position is increasing when time is increasing. Generally, increasing position is "moving forward."
Answer:
C. The object is moving forward
Choose two consumer services careers and research online to determine what kinds of professional organizations exist for these professions. Write a paragraph describing the purpose of the organization, the requirements for joining, and the benefits of membership.
Bank loan facilitator, and hospital emergency care specialist are the two consumer or customer services careers.
Bank loan facilitator is a consumer service facilitator who ask and provide people loan in emergency, for the purpose of education, treatment, family events, and for other reasons. For bank loan facilitator the professional organizations should be banking and finance sector. The purpose of these organizations is to help people in financial matter seeking benefit by getting interest from customers. The requirements for joining of the employee must include strong convincing power for the employee, time management, strong and tactful communication skills. Benefits of membership of the customers can help them to seek loans on need basis on lower interest. Hospital emergency care specialist provides help to the staff and the customers in medical emergency. These professionals are necessary for the hospital, clinics, and rehabilitation centers. Purpose of the organization is to provide medical care to the patients. The requirements for joining of the employee includes ability to give information to patients and staff during emergency conditions, facilitating ambulance to rescue patients from their homes, and from other areas, providing medicine, medical equipment, and other facilities to the patients and other medical staff necessary for treatment. Benefits of membership in clinical or hospital settings can help the patient in frequent visits for treatment, concession in laboratory tests, and medication.Learn more about customer:
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which one of these reduce fraction?
A proce for the production of 1,3-butadiene reult from catalytic dehydrogenation at atmopheric preure of 1-butene according to the reaction:
C4H8(g) → C4H6(g)H2(g)
To uppre ide reaction, the 1-butene feed tream i diluted with team in the ratio of 10 mole of team per mole of 1-butene. The reaction i carried out iothermally at 525°C, and at thi temperature 33% of the 1-butene i converted to 1,3-butadiene. How much heat i tranferred to the reactor per mole of entering 1-butene?
2. What is the time constant of a 2 mH inductor and a 2002 resistor connected in seri-
O A. 10 μsec
OB. 1 μsec
O C. 10 msec
O D. 1 msec
Correct option is A)
In LR circuit,
The time constant τ=
R
L
10=
R
L
L=10R. . . . . . .(1)
When Resistance 100Ω is connect in series, than the time constant is
τ
′
=
R+100
L
=2s
L=2R+200. . . . . . .(2)
Equating equation (1 ) and (2), we get
2R+200=10R
8R=200
R=25Ω
From equation (1),
L=10R=10×25
L=250H
if an instance method is being designed to perform a binary operation on two instances of a class, how many parameters should it typically have? explain.
An instance method designed to perform a binary operation on two instances of a class typically has one parameter. This parameter represents the second instance of the class on which the operation is being performed.
The first instance of the class, on which the method is invoked, is implicitly available within the method as the "self" parameter (or equivalent, depending on the programming language). This means that the method already has access to the first instance without explicitly passing it as a parameter. By having a single parameter representing the second instance, the method can effectively operate on both instances and perform the desired binary operation. This design simplifies the method signature and makes it more intuitive for users of the class to call the method. However, it's important to note that the exact number of parameters may vary depending on the specific requirements and design considerations of the class and the binary operation being performed.
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A photograph of the NASA Apollo 16 Lunar Module (abbreviated by NASA as the LM is shown on the surface of the Moon. Such spacecraft made six Moon landings during 1,969 - 72. A simplified model for one of the four landing gear assemblies of the LM is shown. If the LM has 13,500 kg mass, and rests on the surface of the Moon where acceleration due to gravity is 1.82 m/s^2, determine the force supported by members AB, AC, and AD. Assume the weight of the LM is uniformly supported by all four landing gear assemblies, and neglect friction between the landing gear and the surface of the Moon. TAB =N TAC = TAD =N A ( 2.6, 2.6, -2.2 ) m B(1.5, 1.5, 0)m C(2,1,-1.2)m D(1,2,-1.2)m
Answer:
\(\mathbf{F_{AB} = 13785.06 N }\)
\(\mathbf{F_{AC} = -5062.38 N }\)
\(\mathbf{F_{AD} = -5062.38 N }\)
Explanation:
From the given information:
Let calculate the position vector of AB, AC, and AD
To start with AB; in order to calculate the position vector of AB ; we have:
\(r_{AB}^{\to} = r _{OA}^{\to} - r_{OB}^{\to} \\ \\ r_{AB}^{\to} = (2.6 \ \hat i + 2.6 \ \hat j - 2.2 \ \hat k ) - ( 1.5 \ \hat i + \ 1. 5 \hat j ) \\ \\ r_{AB}^{\to} = ( 2.6 \ \hat i - 1.5 \ \hat i + 2.6 \ \hat j - 1.5 \ \hat j - 2.2 \ \hat k) \\ \\ r_{AB}^{\to} = (1.1 \ \hat i + 1.1 \ \hat j - 2.2 \ \hat k ) m\)
To calculate the position vector of AC; we have:
\(r_{AC}^{\to} = r _{OA}^{\to} - r_{OC}^{\to} \\ \\ r_{AC}^{\to} = (2.6 \ \hat i + 2.6 \ \hat j - 2.2 \ \hat k ) - ( 2\ \hat i + \ \hat j - 1.2 \ \hat k) \\ \\ r_{AC}^{\to} = ( 2.6 \ \hat i - 2\ \hat i + 2.6 \ \hat j - \ \hat j - 2.2 \ \hat k + 1.2 \ \hat k) \\ \\ r_{AC}^{\to} = (0.6 \ \hat i + 1.6 \ \hat j - \ \hat k ) m\)
To calculate the position vector of AD ; we have:
\(r_{AD}^{\to} = r _{OA}^{\to} - r_{OD}^{\to} \\ \\ r_{AC}^{\to} = (2.6 \ \hat i + 2.6 \ \hat j - 2.2 \ \hat k ) - ( \hat i + \ 2 \hat j - 1.2 \ \hat k) \\ \\ r_{AD}^{\to} = ( 2.6 \ \hat i - \hat i + 2.6 \ \hat j - 2 \ \hat j - 2.2 \ \hat k + 1.2 \ \hat k) \\ \\ r_{AD}^{\to} = (1.6 \ \hat i + 0.6 \ \hat j - \ \hat k ) m\)
However; let's calculate the force in AB, AC and AD in their respective unit vector form;
To start with unit vector AB by using the following expression; we have:
\(F_{AB}^{\to} = F_{AB} \dfrac{ r _{AB}^{\to} }{|r_{AB}^{\to}} \\ \\ \\ F_{AB}^{\to} = F_{AB} \dfrac{(1.1 \ \hat i + 1.1 \ \hat j - 2.2 \ \hat k ) }{\sqrt{ (1.1)^2 + (1.1)^2 + (-2.2 )^2 }} \\ \\ \\ F_{AB}^{\to} = F_{AB} \dfrac{(1.1 \ \hat i + 1.1 \ \hat j - 2.2 \ \hat k ) }{ \sqrt{7.26}} \\ \\ \\ F_{AB}^{\to} = F_{AB} \dfrac{(1.1 \ \hat i + 1.1 \ \hat j - 2.2 \ \hat k ) }{ 2.6944} \\ \\ \\ F_{AB}^{\to} = F_{AB} (0.408 \ \hat i+ 0.408 \ \hat j - 0.8165 \ \hat k ) N\\\)
The force AC in unit vector form is ;
\(F_{AC}^{\to} = F_{AC} \dfrac{ r _{AC}^{\to} }{|r_{AC}^{\to}} \\ \\ \\ F_{AC}^{\to} = F_{AC} \dfrac{(0.6 \ \hat i + 1.6 \ \hat j - \ \hat k ) }{\sqrt{ (0.6)^2 + (1.6)^2 + (-1 )^2 }} \\ \\ \\ F_{AC}^{\to} = F_{AC} \dfrac{(0.6 \ \hat i + 1.6 \ \hat j - \ \hat k ) }{ \sqrt{3.92}} \\ \\ \\ F_{AC}^{\to} = F_{AC} \dfrac{(0.6 \ \hat i + 1.6 \ \hat j - \ \hat k ) }{1.9798} \\ \\ \\ F_{AC}^{\to} = F_{AC} (0.303 \ \hat i+ 0.808 \ \hat j - 0.505 \ \hat k ) N\\\)
The force AD in unit vector form is ;
\(F_{AD}^{\to} = F_{AD} \dfrac{ r _{AD}^{\to} }{|r_{AD}^{\to}|} \\ \\ \\ F_{AD}^{\to} = F_{AD} \dfrac{(1.6 \ \hat i + 0.6 \ \hat j - \ \hat k ) }{\sqrt{ (1.6)^2 + (0.6)^2 + (-1 )^2 }} \\ \\ \\ F_{AD}^{\to} = F_{AD} \dfrac{(1.6 \ \hat i + 0.6 \ \hat j - \ \hat k ) }{ \sqrt{3.92}} \\ \\ \\ F_{AD}^{\to} = F_{AD} \dfrac{(1.6 \ \hat i + 0.6 \ \hat j - \ \hat k ) }{1.9798} \\ \\ \\ F_{AD}^{\to} = F_{AD} (0.808 \ \hat i+ 0.303 \ \hat j - 0.505 \ \hat k ) N\\\)
Similarly ; the weight of the lunar Module is:
W = mg
where;
mass = 13500 kg
acceleration due to gravity= 1.82 m/s²
W = 13500 × 1.82
W = 24,570 N
Also. we known that the load is shared by four landing gears; Thus, the vertical reaction force exerted by the ground on each landing gear can be expressed as:
\(R =\dfrac{W}{4}\)
\(R =\dfrac{24,570}{4}\)
R = 6142.5 N
Now; the reaction force at point A in unit vector form is :
\(R^{\to} = Rk^{\to} \\ \\ R^{\to} = (6142.5 \ k ^{\to}) \ N\)
Using the force equilibrium at the meeting point of the coordinates at A.
\(\sum F^{\to} = 0\)
\(F_{AB}^{\to} +F_{AC}^{\to} + F_{AD}^{\to} + R^{\to} =0\)
\([F_{AB} (0.408 \ \hat i + 0.408 \ \hat j - 0.8165 \ \hat k ) N + F_{AC} (0.303 \ \hat i + 0.808 \ \hat j - 0.505 \ \hat k ) N + F_{AD} (0.808 \ \hat i + 0.303 \ \hat j - 0.505 \ \hat k) N + (6142.5 \ k^ \to ) ]\)
\(= [ ( 0.408 F_{AB} +0.303 F_{AC} + 0.808F_{AD}) \hat i + (0.408 F_{AB}+0.808F_{AC}+0.303F_{AD}) \hat j + (-0.8165 F_{AB} -0.505F_{AC} -0.505 F_{AD} +6142.5 ) k ^ \to ] = 0\)
From above; we need to relate and equate each coefficients i.e i ,j, and \(k ^ \to\) on both sides ; so, we can re-write that above as;
\(0.408 F_{AB} +0.303 F_{AC} + 0.808F_{AD}) =0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ --- (1) \\ \\ 0.408 F_{AB}+0.808F_{AC}+0.303F_{AD}) =0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ --- (2) \\ \\ -0.8165 F_{AB} -0.505F_{AC} -0.505 F_{AD} +6142.5 = 0 --- (3)\)
Making rearrangement and solving by elimination method;
\(\mathbf{F_{AB} = 13785.06 N }\)
\(\mathbf{F_{AC} = -5062.38 N }\)
\(\mathbf{F_{AD} = -5062.38 N }\)
The force vector of each member, depends on the magnitude of the
force and the unit vector of the member.
Responses:
The force supported by the members are;
Force supported by AB is; 13,799.95 NForce supported by AC is; -5070.2 NForce supported by AD is -5070.2 NHow can the unit vector of each member give their force?Resolving the given members into unit vectors gives;
\(\hat u_{AB} = \mathbf{\dfrac{(2.6 - 1.5) \cdot \hat i + (2.6 - 1.5)\cdot \hat j + (-2.2)\cdot \hat k }{\sqrt{(2.6- 1.5)^2 + (2.6 - 1.5)^2 + (-2.2)^2}}}\)\(\dfrac{(2.6 - 1.5) \cdot \hat i + (2.6 - 1.5)\cdot \hat j + (-2.2)\cdot \hat k }{\sqrt{(2.6- 1.5)^2 + (2.6 - 1.5)^2 + (-2.2)^2}}= 0.40825 \cdot \hat i + 0.40825\cdot \hat j - 0.81625\cdot \hat k\)
\(\hat u_{AB} = \mathbf{0.40825 \cdot \hat i + 0.40825\cdot \hat j - 0.81625\cdot \hat k}\)Similarly, we have;
\(\hat u_{AC} =\mathbf{ \dfrac{(2.6 - 2) \cdot \hat i + (2.6 - 1)\cdot \hat j + (-2.2+1.2)\cdot \hat k }{\sqrt{(2.6- 2)^2 + (2.6 - 1)^2 + (-2.2+1.2)^2}}}\)
\(\dfrac{(2.6 - 2) \cdot \hat i + (2.6 - 1)\cdot \hat j + (-2.2+1.2)\cdot \hat k }{\sqrt{(2.6- 2)^2 + (2.6 - 1)^2 + (-2.2+1.2)^2}} =\dfrac{0.6\cdot \hat i +1.6\cdot \hat j -1\cdot \hat k }{\sqrt{0.6^2 + 1.6^2 + (-1.)^2}}\)
\(\dfrac{0.6\cdot \hat i +1.6\cdot \hat j -1\cdot \hat k }{\sqrt{0.6^2 + 1.6^2 + (-1.)^2}}= 0.303046\cdot \hat i + 0.80812\cdot \hat j - 0.50508\cdot \hat k\)
\(\hat u_{AC} =\mathbf{0.303046\cdot \hat i + 0.80812\cdot \hat j - 0.50508\cdot \hat k}\)\(\hat u_{AD} =\mathbf{ \dfrac{(2.6 - 1) \cdot \hat i + (2.6 -2)\cdot \hat j + (-2.2 + 1.2)\cdot \hat k }{\sqrt{(2.6-1)^2 + (2.6 -2))^2 + (-2.2 + 1.2)^2}}}\)
\(\hat u_{AD} =\mathbf{0.80812\cdot \hat i+ 0.303046\cdot \hat j - 0.50508\cdot \hat k}\)
The forces are therefore;
\(\vec F_{AB} =\mathbf{ F_{AB} \cdot \left ( 0.40825 \cdot \hat i + 0.40825\cdot \hat j - 0.81625\cdot \hat k \right)}\)
\(\vec F_{AC} =\mathbf{ F_{AC} \cdot \left (0.303046\cdot \hat i + 0.80812\cdot \hat j - 0.50508\cdot \hat k\right)}\)
\(\vec F_{AD} = \mathbf{F_{AD} \cdot \left (0.80812\cdot \hat i+ 0.303046\cdot \hat j - 0.50508\cdot \hat k\right)}\)
\(Weight \ on \ the \ assembly = \dfrac{13,500 \, kg \times 1.82 \, m/s^2}{4} = 6,142.5 \, \hat k N\)
Which gives;
\(\mathbf{0.40825 \cdot \hat i \cdot F_{AB}}\) + \(0.303046\cdot \hat i \cdot F_{AC}\) + \(0.80812\cdot \hat i \cdot F_{AD}\) = 0
\(0.40825 \cdot \hat j \cdot F_{AB}\) + \(0.80812\cdot \hat j \cdot F_{AC}\) + \(0.303046 \cdot \hat j \cdot F_{AD}\left\) = 0
\(-0.81625\cdot \hat k \cdot F_{AB}\) - \(0.50508\cdot \hat k \cdot F_{AC}\) - \(0.50508\cdot \hat k \cdot F_{AD}\) + \(\mathbf{6,142.5 \, \hat k}\) = 0
Which gives;
\(-0.81625\cdot \hat k \cdot F_{AB}\) - \(0.50508\cdot \hat k \cdot F_{AC}\) - \(0.50508\cdot \hat k \cdot F_{AD}\) = \(-6,142.5 \, \hat k\)
Solving gives;
\(F_{AB}\) = 13799.95 N\(F_{AC}\) = -5070.2 N\(F_{AD}\) = -5070.2 NLearn more about unit vectors here:
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a process that removes the outer layer of the grinding wheel that has worn out grit and is clogged with swarf (chips), and exposes fresh grit with sharper edges, is called:A. ReshapingB. Wheel SharpeningC. DressingD. Forming
The process that removes the outer layer of a grinding wheel that has worn out grit and is clogged with swarf (chips), and exposes fresh grit with sharper edges is called dressing.
Dressing is an essential process that helps maintain the performance of the grinding wheel. Over time, the abrasive particles on the surface of the grinding wheel become dull and clogged with chips and other debris. This results in reduced cutting efficiency, increased heat generation, and poor surface finish.
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