Answer:
A) max factored load ( pv = 1.4 * 18 ) = 25.2 kips
B) max load factored load = ( Pa = 18 + 2 ) = 20 kips
Explanation:
service dead load = 18 kips
service live load = 2 kips
A) Determine the maximum factored load and controlling AISC load combination
max factored load ( pv = 1.4 * 18 ) = 25.2 kips
DL = 18 kips
LL = 2 kips
B) Determine the max load and controlling AISC load combination
max load factored load = ( Pa = 18 + 2 ) = 20 kips
attached below
.Tech A says that unitized hubs have a wheel nut with a higher installation torque than
serviceable wheel bearings. Tech B says that unitized hubs have the proper bearing end
play designed into the assembly once they are torqued properly. Who is correct?
a. Tech A
b.
Tech B
C
Both a and b
D
Neither a and d
Tech A says that unitized hubs have a wheel nut with a higher installation torque than serviceable wheel bearings. Tech B says that unitized hubs have the proper bearing end play designed into the assembly once they are torqued properly is Option C: Both a and b
Describe a wheel bearing?When compared to manually adjusted, PreSet, or LMS hub assemblies, unitized hub assemblies often require a lot more assembly torque and special spindle nut systems.
Therefore, An essential component of the wheel assembly that connects the wheel to the axle is a wheel bearing. A metal ring is used to hold a group of steel balls (also known as ball bearings) or taper (also known as tapered bearings) together. It permits the wheel to spin easily and with little resistance.
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Both copper and stainless steel are being considered as a wall material for a liquid cooled rocket nozzle. The cooled exterior of the wall is maintained at 150°C, while the combustion gases within the nozzle are at 2750°C. The gas side heat transfer coefficient is known to be hᵢ = 2×10⁴ W/m²-K, and the radius of the nozzle is much larger than the wall thickness. Thermal limitations dictate that the temperature of copper must not exceed 540°C, while that of the steel must not exceed 980°C. What is the maximum wall thickness that could be employed for each of the two materials? For Cu, ρ = 8933 kg/m³, k = 378 W/m-K and for stainless steel, ρ = 7900 kg/m³, k = 23.2 W/m-K
a. The maximum thickness of the copper nozzle is 3.3 mm
b. The maximum thickness of the steel nozzle is 0.054 mm
The question has to do with heat transfer
What is heat transfer?Heat transfer is the movement of heat energy from one body to anotrher.
How to calculate the maximum wall thickness?Since the rate of heat loss by the gas equal rate of heat gain by the metal.
Rate of heat loss by gasThe rate of heat loss by gas is P = -hA(T - T') where
h = heat transfer coefficient of gas = 2 × 10⁴ W/m²-K, A = surface area of nozzle, T = maximum temperature of metal and T = Temperature of gas = 2750°CRate of heat gain by metalThe rate of heat gain by metal is given by P' = kA(T - T")/t where
k = thermal coefficient of metal, A = surface area of nozzle, T = maximum temperature of metal, T" = temperature of exterior wall of nozzle = 150°C and t = thickness of nozzle. Maximum thickness of nozzle.Since P = P', we have that
-hA(T - T') = kA(T - T")/t
Making t subject of the formula, we have
t = -k(T - T")/h(T - T')
a. Maximum thickness for copper nozzleGiven that for copper
T = 540°C and k = 378 W/m-KSubstituting the values of the variables into t, we have
t = -k(T - T")/h(T - T')
t = -378 W/m-K(540°C - 150°C)/[2 × 10⁴ W/m²-K(540°C - 2750°C)]
t = -378 W/m-K(390°C)/[2 × 10⁴ W/m²-K(-2210°C)]
t = 147420 W/m/4420 × 10⁴ W/m²
t = 147420 W/m/44200000 W/m²
t = 0.0033 m
t = 3.3 mm
So, the maximum thickness of the copper nozzle is 10.71 cm
b. Maximum thickness for steel nozzleGiven that for steel
T = 980°C and k = 23.2 W/m-KSubstituting the values of the variables into t, we have
t = -k(T - T")/h(T - T')
t = -23.2 W/m-K(980°C - 150°C)/[2 × 10⁴ W/m²-K(980°C - 2750°C)]
t = -23.2 W/m-K(830°C)/[2 × 10⁴ W/m²-K(-1770°C)]
t = 19256 W/m/3540 × 10⁴ W/m²
t = 19256 W/m/35400000 W/m²
t = 0.0000544 m
t = 0.0544 mm
t ≅ 0.054 mm
So, the maximum thickness of the steel nozzle is 0.054 mm
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One of the principles of supply chain strategy
The principle of supply chain strategy is Segregate customers on the basis of service needs of different groups and follow the supply chain to deliver goods and services to the consumers profitably.
What is supply chain?Supply chain is the group of activities performed by an organization to deliver goods and services to the consumer end.
Thus, one of the principle of supply chain strategy is separate the customers on the basis of service needs of different groups and follow the supply chain to deliver goods and services to the consumers so that they earn profit.
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what is road engineering
Explanation:
Road engineering is an engineering discipline branching from civil engineering that involves the planning, design, construction, operation, and maintenance of roads, bridges, and tunnels to ensure safe and effective transportation of people and goods. Road engineering became prominent towards the latter half of the 20th century after World War II. Standards of road engineering are continuously being improved. Road engineers must take into account future traffic flows, design of highway intersections/interchanges, geometric alignment and design, highway pavement materials and design, structural design of pavement thickness, and pavement maintenance.
What happens to the extension rate as the flow rate increases?
As the flow rate increases, the extension rate also increases. This is because the flow rate determines the amount of force applied to the material, which in turn causes the material to extend or stretch. Therefore, a higher flow rate will result in a higher extension rate.
When a material is subjected to a flow or shear stress, it begins to deform or stretch, which is referred to as extension. The rate at which this extension occurs depends on several factors, including the flow rate or the rate at which the stress is applied.
As the flow rate increases, the amount of force applied to the material increases, resulting in a higher extension rate. This is because the material experiences more stress, causing its molecules to rearrange and elongate, resulting in an increased extension rate. The extension rate may continue to increase with the flow rate up to a certain point, beyond which further increases in flow rate may not lead to significant increases in extension rate.
It's important to note that the relationship between flow rate and extension rate can vary depending on the material being tested, as well as other factors such as temperature, pressure, and the presence of impurities. Understanding the relationship between flow rate and extension rate is important in various fields, including materials science, engineering, and manufacturing, where the mechanical properties of materials are critical for their successful use.
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An object travels to the right with a speed of 149.5 m/s and then travels left at 164.8 m/s. What is the change in its velocity?
The change in the velocity of the object will be 314.30 meters per second.
What is the relative velocity?The movement of an object in relation to another observer is known as its relative velocity. It is the pace at which one object's relative location changes in relation to another object over time.
An object travels to the right with a speed of 149.5 m/s and then travels left at 164.8 m/s.
Then the velocity of the object is given as,
v = 149.50 - (-164.80)
v = 149.50 + 164.80
v = 314.3 m/s
The change in the velocity of the object will be 314.30 meters per second.
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Examine the pressure-measuring device shown in the figure below. (a) What is the gauge pressure reading in psi at point A? (b) What is the pressure difference between point A and B? (c) Which is higher, pressure at point A or at point B? (d) What is the absolute pressure in psi at point D? State any assumptions you made
Answer: 45
Explanation:just cuase I need to
A 150-lbm astronaut took his bathroom scale (a
spring scale) and a beam scale (compares masses) to the
moon where the local gravity is g ! 5.48 ft/s2
. Determine
how much he will weigh (a) on the spring scale and (b) on
the beam scale.
Given the following data:
Mass of astronaut = 150-lbm.
Acceleration due to gravity on Moon = 5.48 ft/s².
What is weight?Weight can be defined as the force acting on an object or a physical body due to the effect of gravity. Also, the weight of a physical object (body) is typically measured in Newton or ounces.
How to calculate the weight of this astronaut?Mathematically, the weight force on a physical body can be calculated by using this formula:
W = mg
Where:
W represents the weight.m represents the mass.g represents the acceleration due to gravity.Substituting the given parameters into the formula, we have;
Weight = 150 × 1/32.2 × 5.48
Weight = 25.5 lbf.
For the weight on beam scale.A beam scale is a measuring instrument that is designed and developed to compare the masses of a physical body and as such, it's not affected by the variations in acceleration due to gravity. Therefore, the beam scale would read 150-lbf as it read on earth.
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Would like some help with this question please ?
Answer:
D
Explanation:
Because the Boat D engine looks fast
A man weighs 145 lb on earth.Part ASpecify his mass in slugs.Express your answer to three significant figures and include the appropriate units.Part BSpecify his mass in kilograms.Express your answer to three significant figures and include the appropriate units.Part CSpecify his weight in newtons.Express your answer to three significant figures and include the appropriate units.Part DIf the man is on the moon, where the acceleration due to gravity is gm = 5.30 ft/s2, determine his weight in pounds.Express your answer to three significant figures and include the appropriate units.Part EDetermine his mass in kilograms.Express your answer to three significant figures and include the appropriate units.
Answer:
a) 4.51 lbf-s^2/ft
b) 65.8 kg
c) 645 N
d) 23.8 lb
e) 65.8 kg
Explanation:
Weight of the man on Earth = 145 lb
a) Mass in slug is...
32.174 pound = 1 slug
145 pound = \(x\) slug
\(x\) = 145/32.174 = 4.51 lbf-s^2/ft
b) Mass in kg is...
2.205 pounds = 1 kg
145 pounds = \(x\) kg
\(x\) = 145/2.205 = 65.8 kg
c) Weight in Newton = mg
where
m is mass in kg
g is acceleration due to gravity on Earth = 9.81 m/s^2
Weight in Newton = 65.8 x 9.81 = 645 N
d) If on the moon with acceleration due to gravity of 5.30 ft/s^2,
1 m/s^2 = 3.2808 ft/s^2
\(x\) m/s^2 = 5.30 ft/s^2
\(x\) = 5.30/3.2808 = 1.6155 m/s^2
weight in Newton = mg = 65.8 x 1.6155 = 106
weight in pounds = 106/4.448 = 23.8 lb
e) The mass of the man does not change on the moon. It will therefore have the same value as his mass here on Earth
mass on the moon = 65.8 kg
. You need to access customer records in a database as you're planning a marketing campaign. What language can you use to pull the records most relevant to the campaign? a. FTP b. SQL C. SMTP d. TLS
SQL can be used to access customer records in a database most relevant to the campaign.
SQLSQL (Structured Query Language) is a standardized programming language that's used to manage relational databases and perform various operations on the data in them.
SQL databases comprise a set of tables containing data in rows and columns.SQL can be used to access customer records in a database most relevant to the campaign.
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Answer:
The person above is totally correct.
When a magnet is quickly pushed into a coil of wire connected to a circuit _________.
Answer:
Work is needed to overcome a resistance to the push.
Write a program to play the Card Guessing Game. Your program must give the user the following choices: - Guess only the face value of the card. - Guess only the suit of the card. - Guess both the face value and the suit of the card. Before the start of the game, create a deck of cards. Before each guess, use the function random_shuffle to randomly shuffle the deck.
how am I going to do this, I have a friend that might be able to help I will check
Bejsickwnanciodkwbdjxiwnsnxbx
Answer:
is it a free point? or just a question if it is kindly respond
if one tries to solve eq.4.1-21 by the method of separation of variables without first recognizing that the solution can be written as the sum of a steady-state solution and a transient solution?
If one tries to solve the equation 4.1-21 by the method of separation of variables without first recognizing that the solution can be written as the sum of a steady-state solution and a transient solution, the solution is incorrect.
Separation of Variables method is a method of solving linear and homogeneous partial differential equations that are classified as first-order. It's based on the concept of separating the variables by putting them on the opposite side of the equation sign before integration.
Both of these solutions are crucial in the method of separation of variables. The transient solution is necessary because it captures the behavior of the solution when it is not in a steady state, while the steady-state solution is required because it helps in obtaining the solution by assuming that the solution is in steady state.
If one tries to solve the equation 4.1-21 by the method of separation of variables without first recognizing that the solution can be written as the sum of a steady-state solution and a transient solution, then the solution obtained is incorrect.
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Which of the following choices accurately contrasts a categorical syllogism with a conditional syllogism?
An argument constructed as a categorical syllogism uses deductive reasoning whereas an argument constructed as a conditional syllogism uses inductive reasoning.
A categorical syllogism contains two premise statements and one conclusion whereas a conditional syllogism contains one premise statement and one conclusion.
A categorical syllogism argues that A and B are both members of C whereas a conditional syllogism argues that if A is true then B is also true.
An argument constructed as a categorical syllogism is valid whereas an argument constructed as a conditional syllogism is invalid.
Answer:
The correct option is - A categorical syllogism argues that A and B are both members of C whereas a conditional syllogism argues that if A is true then B is also true.
Explanation:
As,
Categorical syllogisms follow an "If A is part of C, then B is part of C" logic.
Conditional syllogisms follow an "If A is true, then B is true" pattern of logic.
So,
The correct option is - A categorical syllogism argues that A and B are both members of C whereas a conditional syllogism argues that if A is true then B is also true.
Cool air leaving the evaporator of an air conditioner has a relative humidity of 100%. This is because relative humidity level increases as _____.
This is because relative humidity level increases as dry-bulb temperature decreases. This temperature is measured using a specific thermometer.
Dry-bulb temperatureThe dry-bulb temperature refers to the air temperature, which can be estimated by using a thermometer exposed to the air.
The thermometer used to measure the dry-bulb temperature must be protected from radiation and moisture (i.e., the humidity of the air).
The dry bulb temperature can be considered as ambient temperature, whereas the wet-bulb temperature measures the humidity of the air.
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18. Determine the current and its direction for each network in Fig. 5.102. Before solving for I, redraw
each network with a single voltage source
Current is the rate at which electrons flow past a point in a complete electrical circuit. At its most basic, current = flow.
What is Current?An ampere (AM-pir), or amp, is the international unit used for measuring current. It expresses the quantity of electrons (sometimes called "electrical charge") flowing past a point in a circuit over a given time.
A current of 1 ampere means that 1 coulomb of electrons—that's 6.24 billion billion (6.24 x 1018) electrons—is moving past a single point in a circuit in 1 second.
The calculation is similar to measuring water flow: how many gallons pass a single point in a pipe in 1 minute (gallons per minute, or GPM).
Therefore, Current is the rate at which electrons flow past a point in a complete electrical circuit. At its most basic, current = flow.
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Please calculate the current for the circuit below
Answer:
The answer is "\(I = 0.0085106383 \ A\)"
Explanation:
Given:
\(R= 470 \ \Omega \\\\V= 4 \ v\)
Formula:
\(\to V=IR\\\\\to I = \frac{V}{R}\\\\\)
\(= \frac{4}{470}\\\\ = 0.0085106383 \ A\)
What should wheel bearing seals be checked for
Answer:
drugs
Explanation:
The voltage supplied by a wall socket varies with time, reversing its polarity with a constant frequency, as shown in the graph. (Figure 1)
What is the rms value Vrms of the voltage plotted in the graph?
Answer:
What is the rms value Vrms of the voltage plotted in the graph?
Express your answer in volts.
Vrms = ? V
2.
When a lamp is connected to a wall plug, theresulting circuit can be represented by a simplified AC circuit, asshown in the figure. (Part B figure) Here the lamp has been replaced by a resistor with an equivalentresistance Part B figure) Here the lamp has been replaced bya resistor with an equivalent resistance R = 120 . What is the rms value Irms of the current flowing through the circuit?
Express your answer in amperes.
Irms = ? A
3.
What is the average power Pavg dissipated in the resistor?
Express your answer in watts.
Pavg = ? W
Compute the corresponding angular measurements in the centesimal system for the
following angles which are in the Sexagesimal system
i. 125˚
ii. 12˚
The sexagesimal system angles for 125 is 2.18 and for 12 is 0.209
What is the sexagesimal system?
We know that 180 = π
Therefore,
(i) 125 = 125 * π / 180
= 125 * 22/ 7 * 180
= 2750 / 1260
= 2.18
(ii) 180 = π
12 = 12* π /180
= 12* 22/ 7 * 180
= 264/ 1260
= 0.209
Therefore, The sexagesimal system angle for 125 is 2.18 and for 12 is 0.209.
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_____ datum reference(s) may be necessary to obtain the desired level of control with an orientation tolerance.
A. No
B. One
C. Two
D. One or two
The answer is D, one or two datum references may be necessary to obtain the desired level of control with an orientation tolerance.
Datum references are used to establish a reference point or plane on a part, and orientation tolerances specify the allowable variation in orientation of features relative to those datum references. The number of datum references required depends on the complexity of the part and the orientation tolerances specified. In some cases, a single datum reference may be sufficient, while in others, two or more may be necessary to achieve the desired level of control. Ultimately, the number of datum references needed should be determined by the engineer or designer based on the specific requirements of the part and its intended function.
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A student borrows $60,000 for business school at 6.5% stated annual interest with equal monthly payments over 10 years. Consider this as a loan with no payments or interest during school so that the problem structure is equivalent to a standard loan received one period before the first payment. How much is the monthly payment?
Answer:
$681.29
Explanation:
The amortization formula seems to apply. The monthly payment on a loan of P at rate r for t years is ...
A = P(r/10)/(1 -(1 +r/12)^(-12t))
For the given loan parameters, the monthly payment is ...
A = $60,000(0.065/12)/(1 -(1 +0.065/12)^(-12·10)) ≈ $681.29
The monthly payment is $681.29.
Use the following transfer functions to find the steady-state response yss(t) to the given input function f(t). A. T(s) = Y(s)/F(s) = 10/(10s + 1)(4s + 1), f(t) = 10 sin 0. 2 t b. T(s) = Y(s)/F(s) = 1/2s^2 + 20s + 200, f(t) = 16 sin 5t
Using the following transfer functions to find the steady-state response yss(t) to the given input function f(t) the steady-state response to the input f(t) = 16 sin 5t.
(a) First, we need to find the Laplace transform of the input function f(t):
F(s) = L{f(t)} = L{10 sin 0.2t} = 10/(s^2 + 0.04)
Then, we can find the steady-state response by evaluating the transfer function at s = jω (where j = sqrt(-1) and ω is the frequency of the input signal):
T(jω) = Y(jω)/F(jω) = 10/[(10jω + 1)(4jω + 1)]
|T(jω)| = |Y(jω)/F(jω)| = 10/|10jω + 1||4jω + 1|
Phase angle of T(jω) = phase angle of 10 - phase angle of (10jω + 1) - phase angle of (4jω + 1)
At steady state, the output will have the same frequency as the input (ω = 0.2), so we can substitute ω = 0.2 in the above expressions to get:
|T(j0.2)| = 10/|2j + 1||0.8j + 1| ≈ 0.267
Phase angle of T(j0.2) = phase angle of 10 - phase angle of (2j + 1) - phase angle of (0.8j + 1) ≈ -2.06 radians
Finally, we can find the steady-state response by taking the inverse Laplace transform of T(j0.2):
yss(t) = L^-1{T(j0.2)} = 0.267 cos(0.2t - 2.06)
Therefore, the steady-state response to the input f(t) = 10 sin 0.2t is yss(t) = 0.267 cos(0.2t - 2.06).
(b) First, we need to find the Laplace transform of the input function f(t):
F(s) = L{f(t)} = L{16 sin 5t} = 16/(s^2 + 25)
Then, we can find the steady-state response by evaluating the transfer function at s = jω (where j = sqrt(-1) and ω is the frequency of the input signal):
T(jω) = Y(jω)/F(jω) = 1/(2jω^2 + 20jω + 200)
|T(jω)| = |Y(jω)/F(jω)| = 1/|2jω^2 + 20jω + 200|
Phase angle of T(jω) = phase angle of 1 - phase angle of (2jω^2 + 20jω + 200)
At steady state, the output will have the same frequency as the input (ω = 5), so we can substitute ω = 5 in the above expressions to get:
|T(j5)| = 1/|2(-25)j + 20j + 200| ≈ 0.0126
Phase angle of T(j5) = phase angle of 1 - phase angle of (2(-25)j + 20j + 200) ≈ -1.46 radians
Finally, we can find the steady-state response by taking the inverse Laplace transform of T(j5):
yss(t) = L^-1{T(j5)} = 0.0126 cos(5t - 1.46)
Therefore, the steady-state response to the input f(t) = 16 sin 5t.
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a list of numbers has n elements, indexed from 1 to n. the following algorithm is intended to display the number of elements in the list that have a value greater than 100. the algorithm uses the variables count and position. steps 3 and 4 are missing. step 1 set count to 0 and position to 1. step 2 if the value of the element at index position is greater than 100, increase the value of count by 1. step 3 (missing step) step 4 (missing step) step 5 display the value of count. which of the following could be used to replace steps 3 and 4 so that the algorithm works as intended?
To complete the algorithm, the missing steps 3 and 4 should iterate through the list until the end is reached. This can be achieved with a loop. Here is a possible solution:
Step 3: while position is less than or equal to n, repeat steps 4 and 5.
Step 4: increase the value of position by 1.
Step 5: if the value of the element at index position is greater than 100, increase the value of count by 1.
This revised algorithm will go through each element in the list and count the number of elements with a value greater than 100. The loop in steps 3-5 ensures that all elements are considered.
It is worth noting that there are other ways to implement this algorithm, such as using a for loop or a foreach loop, but the core logic remains the same: iterate through the list and count the elements that meet a certain condition.To complete the algorithm that counts the number of elements in a list with values greater than 100, you can replace steps 3 and 4 with the following:
Step 3: Increase the value of position by 1.
Step 4: If position is less than or equal to n, go back to step 2.
So, the complete algorithm is as follows:
1. Set count to 0 and position to 1.
2. If the value of the element at index position is greater than 100, increase the value of count by 1.
3. Increase the value of position by 1.
4. If position is less than or equal to n, go back to step 2.
5. Display the value of count.
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A satellite at a distance of 36,000 km from an earth station radiates a power of 10 W from an
antenna with a gain of 25 dB. What is the received power if the effective aperture area of the
receiving antenna is 20 m2?
The received power if the effective aperture area of the receiving antenna is 20 m2 is 177.77 m2.
What is Power?In physics, power is referred to as the rate of energy conversion or transfer over time. The unit of power in the SI system, often known as the International System of Units, is the Watt (W). A single joule per second is one watt.
Power was formerly referred to as activity in some research. A scalar quantity is power. As power is always a function of labor done, it follows that if a person's output varies during the day depending on the time of day, so will his power.
A measure of the pace at which energy is transferred, power is a physical quantity. As a result, it can be described as the pace of job completion relative to time.
Therefore, The received power if the effective aperture area of the receiving antenna is 20 m2 is 177.77 m2.
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When should a bimetal thermometer be calibrated?
Bimetal thermometers should be calibrated at least once a year or whenever readings are suspect.
Calibrating Bimetal Thermometers for Accurate ReadingsA bimetal thermometer should be calibrated at least once a year, or whenever readings are suspect. This is important because bimetal thermometers are made up of two strips of different metals that contract and expand in response to changes in temperature. Over time, the bimetallic strips can become misaligned, resulting in inaccurate temperature readings.
To ensure accuracy, bimetal thermometers need to be calibrated by a professional. During the calibration process, the thermometer is compared to a reference thermometer and adjusted accordingly to bring it back to its original accuracy.
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engineering controls can be utilized as one element of hazard control
Engineering controls are an essential element of hazard control in the workplace, providing a means of minimizing or eliminating hazards at their source.
Engineering controls are a type of hazard control that reduces or eliminates the hazard at its source. Engineering controls are used to minimize or eliminate hazards that pose a significant risk of harm or danger to individuals, such as chemical or noise exposure.
These measures are frequently a vital component of an effective occupational health and safety program in the workplace. Examples of engineering controls include the use of ventilation to control fumes, dust, and other airborne hazards, as well as the use of sound barriers to reduce noise levels. In addition, the use of machine guards, interlocks, and other safety devices on equipment and machinery is considered a form of engineering control to safeguard workers from contact with hazardous moving parts.
Other types of engineering controls include changes in the manufacturing process or the substitution of less harmful materials to eliminate the hazard. Engineering controls are an essential element of hazard control in the workplace, providing a means of minimizing or eliminating hazards at their source. These controls, when combined with other forms of hazard control, such as administrative and personal protective equipment, provide a comprehensive approach to worker safety and health.
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Three single-phase loads in parallel are supplied from a 1400V (RMS), 60 Hz supply. The loads are as follows: Load 1: Inductive load: 125 kVA, 0.28 power factor Load 2: Capacitive load: 10 kW, 40 kVAR Load 3: Resistive load: 15 kW Find the total kW, kVAR, kVA, and supply power factor. (5 points) Find the capacitive correction (in kVARs) required to improve the power factor to 0.8 and calculate the supply current with this correction in place. (10 points) What is the least current that can service these three loads and how much compensation would it require
Answer:
The answer is below
Explanation:
\(\theta_1=cos^{-1}0.28=73.74^o\ lagging\\\\S_1=125\angle 73.74^o=35\ kW+j120\ kVAR\\\\S_2=10\ kW-j40\ kVAR\\\\S_3=15\ kW\)
Total power = P = 35 kW + 10 kW + 15 kW = 60 kW
Total kVAR = 120 kVAR - 40 kVAR = 80 kVAR
\(Total\ apparent \ power =S= S_1+S_2+S_3=(35+j120)+(10-j40)+(15)\\\\S=60\ kW+j80\ kVAR=100\angle 53.13^o\\\\Current(I)=\frac{S^*}{V^*} \frac{100000\angle -53.13^o}{1400\angle0}=71.43\angle-53.13^o\\ \\Power\ factor (PF)=cos(53.13)=0.6\ lagging\\\\The \ new\ power\ factor\ is\ to \ be\ 0.8[cos^{-1}0.8=36.87^o], hence\ since\ the\ total\ \\real\ power(P)= 60\ kW, the\ capacitor\ kVAR(Q_c)\ is:\\\\Q_c=60tan(53.13)-60tan(36.87)=80-45=35\ kVAR\\\\\)
\(C=\frac{Q_c}{wV^2} =\frac{35000\ VAR}{2\pi*60\ Hz*1400\ V}=47.38\ \mu f\)
New current (I') = \(\frac{S'^*}{V^*}=\frac{60000-j45000}{1400}=53.57\angle-36.87^o\)
Current reduce from 71.43 A to 53.57 A