Answer:
a. 58.8 N.
b. 6 * 10⁻³m³ or 6cm³.
Explanation:
a) Find the magnitude of the buoyant force.
Buoyant force is the force that a liquid applies into an object that is partially or totally submerged into it.
In this case, the buoyant force is given by the differente between the weight (in Newtons) of the rock in the air and the weight (in Newtons) of the rock while submerged in water.
Therefore:
Buoyant force: Fb= (9.00kg * 9.8m/s²) - (3.00kg * 9.8m/s²)= (88.2 N) - (29.4 N)= 58.8 N.
b) What is the volume of the rock? (water density = 1 000 kg/m³).
The Principle of Archimedes states the following: "A body immersed in a fluid experiences an upthrust equal to the weight of the fluid displaced".
This can be expressed in a mathematical equation in the following fashion:
\(Fb=dgv\), where d is the density of the liquid; g is the acceleration of gravity, and v is the volume of the part of the body that is submerged.
In this case, the rock is totally submerged, hence, v is the total volume is the rock.
Taking into account that we have all the needed variables of this equation, except for the volume, we can solve the equation for v and calculate it's value. This is the process:
\(Fb=dgv\\\\v=\frac{Fb}{dg} \\\\v=\frac{58.8 N}{(1 000 kg/m^{3} )(9.8m/s^{2} )}\\\\v=0.006m^{3}=6*10^{-3} m^{3}\)
Now, in order to give a more reaader friendly result, we may convert the volume from cubic meters to cubic certimeters by multiplying by 10³:
\(6*10^{-3} *10^{3} m^{3}=6cm^{3}\)
A crane lift must never exceed a maximum of ______ members per lift
Crane lift is a commonly used heavy equipment in construction sites, manufacturing industries, and logistics companies. A Cane lift must never exceed a maximum of four members per lift.
The maximum number of members allowed per lift is critical to avoid accidents. The maximum number of members allowed per crane lift varies depending on the crane’s capacity, size, design, and site conditions. The crane operator must always adhere to the safety guidelines and regulations, which specify the maximum weight, radius, height, and distance that a crane can lift without endangering workers or the public. Cranes lifts must never exceed a maximum of four members per lift, according to safety regulations. Crane lifts with a higher number of members can result in accidents, damage to materials, loss of property, or loss of life. Cranes are essential pieces of machinery for many industries, but they can be dangerous if not used correctly. Therefore, it is essential to follow safety guidelines and regulations when using cranes. The maximum number of members allowed per crane lift is four, and anything higher is a violation of safety guidelines.
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A 5% upgrade on a six-lane freeway (three lanes in each direction) is 1.25 mi long. On this segment of freeway, the directional peak-hour volume is 3800 vehicles with 2% large trucks and 4% buses (no recreational vehicles), the peak-hour factor is 0.90, and all drivers are regular users. The lanes are 12 ft wide, there are no lateral obstructions within 10 ft of the roadway, and the total ramp density is 1.0 ramps per mile. A bus strike will eliminate all bus traffic, but it is estimated that for each bus removed from the roadway, seven additional passenger vehicles will be added as travelers seek other means of travel. What are the density, volume-to-capacity ratio, and level of service of the upgrade segment before and after the bus strike?
Answer:
a) Density of the road segment
i) Before bus strike = 23.02 pc/mi/In
ii) after bus strike = 25.76 pc/mi/In
b) Volume to capacity ratio
i) Before bus strike = 0.69
ii) After bus strike = 0.78
C) level of service of the upgrade segment
i) Before bus strike = LOS C
ii) after bus strike = LOS D
Explanation:
a) Density of the road segment
i) before bus strike ( D1 )
D1 = 1662 / 72.18 = 23.02 pc/mi/In
ii) After bus strike ( D2 )
D1 = 1859 / 72.18 = 25.76 pc/mi/In
b) Volume to capacity ratio
i) Before bus strike ( v 1 )
V1 = 1662 / 2400 = 0.69
ii) After bus strike ( V2 )
V2 = 1859 / 2400 = 0.78
C) level of service of the upgrade segment ( Gotten from " LOS Criteria for basic freeway segments " )
i) Before bus strike = ( LOS C )
ii) After bus strike = LOS D
Attached below is the detailed solution to the question above
Find the value of P(-1.5≤Z≤2)
Answer:
0.9104
Explanation:
Suitable technology can tell you the probability.
P(-1.5≤Z≤2) ≈ 0.9104
__
A phone app gives the probability as 0.9104426667829628.
Implement a Java method sumArray that is passed a double array a as its parameter and returns the sum of the values contained within the array a.
To implement a Java method sumArray that returns the sum of the values in a given double array, you can write the following code.
This method takes in a double array as its parameter and initializes a variable called "sum" to zero. It then iterates through the array using a for loop, adding each value in the array to the sum. Finally, it returns the total sum of the values in the array. The sumArray method starts by creating a variable called "sum" and setting it equal to zero. This variable will be used to keep track of the total sum of the array values. For each index in the array, the method adds the value at that index to the "sum" variable using the += operator. This will accumulate the sum of all the values in the array.
```java
public static double sumArray(double[] a) {
double sum = 0;
for (int i = 0; i < a.length; i++) {
sum += a[i];
}
return sum;
}
```
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rosbel or Janette lol baakkaaa
Answer:
t5g5gtttttttttttttttttttttttttttttttttttttttttttt
Explanation:gt555555555555555555555555555555555555555555555555
Answer:
dawbkjbjwwjhjfbfjewfaekfhawkjndwkja
Explanation: dum*as*
In a water purification system, a stream of water-and-acetone mixture (1.0 mol% acetone) is contacted with a stream of pure nitrogen to recover the acetone, using a counter-current multistage operation. The liquid solution is fed at 100 kmol/hr. The vapor-liquid distribution of acetone under the operating condition is characterized byequilibrium constant K of 1.5.
a)Determine the minimum flow rate of nitrogen that is needed to give 95% recovery of acetone. Determine the number of stages we need for the same recovery if we use a flow rate of nitrogen that is 1.5 times the minimum flow rate.
b) Repeat a) for the case where the entering gas is not pure nitrogen, but contains 0.02 mol% acetone.
a) To determine the minimum flow rate of nitrogen required for 95% recovery of acetone, we need to set up a material balance.
Since it is a counter-current operation, the equilibrium relation between the liquid and vapor phases can be expressed as:
K = y / x
where K is the equilibrium constant, y is the mole fraction of acetone in the vapor phase, and x is the mole fraction of acetone in the liquid phase.
Given that the feed stream contains 1.0 mol% acetone, the mole fraction of acetone in the liquid phase (x) is 0.01. We want to achieve 95% recovery, which means the mole fraction of acetone in the exiting liquid phase should be 0.95 * 0.01 = 0.0095.
Setting up the material balance equation for the liquid phase:
L1 * x1 + V1 * y1 = L2 * x2 + V2 * y2
Assuming V1 (vapor flow rate) is 100 kmol/hr (same as the liquid flow rate), we can solve for L1 (liquid flow rate) using the known values:
100 kmol/hr * 0.01 + 100 kmol/hr * y1 = L2 * 0.0095 + 100 kmol/hr * y2
Substituting the equilibrium relation (K = 1.5):
100 kmol/hr * 0.01 + 100 kmol/hr * (1.5 * 0.01) = L2 * 0.0095 + 100 kmol/hr * (1.5 * 0.0095)
Simplifying the equation:
1 + 1.5 = L2 * 0.0095 + 1.425
L2 * 0.0095 = 1.075
L2 = 1.075 / 0.0095 ≈ 113.16 kmol/hr
Therefore, the minimum flow rate of nitrogen required is approximately 113.16 kmol/hr.
If we use a flow rate of nitrogen that is 1.5 times the minimum flow rate, the flow rate would be 1.5 * 113.16 kmol/hr = 169.74 kmol/hr.
To determine the number of stages required for the same acetone recovery, we can use the concept of the Murphree efficiency. The Murphree efficiency (η) can be calculated as:
η = (L2 - L1) / (L2 - L2_actual)
For the given case, L2_actual is the flow rate of nitrogen that is 1.5 times the minimum flow rate, which is 169.74 kmol/hr. Substituting the known values:
η = (113.16 - L1) / (113.16 - 169.74)
Assuming a reasonable value for η (e.g., 0.8), we can solve for L1:
0.8 = (113.16 - L1) / (113.16 - 169.74)
0.8 * (113.16 - 169.74) = 113.16 - L1
L1 = 113.16 - (0.8 * (113.16 - 169.74))
L1 ≈ 135.41 kmol/hr
Therefore, if the flow rate of nitrogen is 1.5 times the minimum, the number of stages required for 95% recovery of acetone would be approximately 135.41 kmol/hr / 100 kmol/hr = 1.35 stages. Since we can't have fractional stages, we would need at least 2.
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Find y in terms of x, v, a, where v = x and a = x, if y = 4x^2. Express your answer in terms of some or all of the variables x, v, and a. Find y in terms of x, v, a, where v = x and a = x, if y = 4x^2. Express your answer in terms of some or all of the variables x, v, and a. Find y in terms of x, v, a, where v = x and a = x, if y = 3e^x. Express your answer in terms of some or all of the variables x, v, and a.
We can find the relationship between y, x, v, and a by taking the derivatives of y with respect to time (t).
Given v = x and a = x, we have:
v = dx/dt
a = dv/dt = d^2x/dt^2
Taking the derivative of y = 4x^2 with respect to time, we get:
dy/dt = d/dt (4x^2) = 8x(dx/dt) = 8xv
Taking the derivative of dy/dt with respect to time, we get:
d^2y/dt^2 = d/dt (8xv) = 8v(dx/dt) + 8x(dv/dt) = 8v^2 + 8xa
Substituting v = x and a = x, we get:
d^2y/dt^2 = 8x^2 + 8x^2 = 16x^2
Thus, we have found the relationship between y, x, v, and a as:
d^2y/dt^2 = 16x^2
Integrating this twice with respect to x, we get:
y = 4x^2 + C1x + C2
where C1 and C2 are constants of integration. To determine these constants, we need initial conditions or additional information about the problem.
For example, if we know that y = 0 when x = 0 and v = 1, then we can use these initial conditions to solve for C1 and C2:
y = 4x^2 + x
Alternatively, if we know that y = 0 when x = 0 and a = 1, then we can use these initial conditions to solve for C1 and C2:
y = 4x^2 + (1/2)x^2 = (9/2)x^2
For the case where y = 3e^x, we can follow the same procedure to find the relationship between y, x, v, and a:
dy/dt = d/dt (3e^x) = 3e^x(dx/dt) = 3ve^x
d^2y/dt^2 = d/dt (3ve^x) = 3v(dx/dt) + 3ve^x = 3x^2e^x + 3xe^x
Substituting v = x and a = x, we get:
d^2y/dt^2 = 6xe^x
Integrating this twice with respect to x, we get:
y = 3e^x + C1x^2 + C2x
where C1 and C2 are constants of integration. Again, we would need initial conditions or additional information to solve for these constants.
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tyuuyiopopiouyttrrtrffrlkl,k;;';'l.l
Answer:
Explanation:
do you have any other questions besides "tyuuyiopopiouyttrrtrffrlkl,k;;';'l.l"
Samantha is reviewing an engineer’s résumé for a design project involving equipment for an agricultural firm. What is it that she is looking for in his résumé?
The engineer must have humility.
The engineer must be a civil engineer.
The engineer must have the proper credentials.
The engineer must use materials from the US Green Building Council.
Answer:
i would say C
Explanation:
Answer:
c
Explanation:
ye
a 10-v zener diode is used to regulate the voltage across a variable load resistor.the input voltage varies between 13 v and 16 v and the load current varies between 10 ma and 85 ma. the minimum zener current is 15 ma. calculate the value of series resistance r.
To calculate the value of the series resistance (R) in this circuit, we need to use the minimum zener current (Iz(min)) and the minimum input voltage (Vin(min)).Given that the minimum zener current (Iz(min)) is 15 mA, we know that the zener diode will regulate the voltage effectively when the load current is at least 15 mA.
Given that the minimum input voltage (Vin(min)) is 13 V, we need to find the voltage drop across the series resistance (R) when the load current is 15 mA.
Using Ohm's Law (V = I * R), we can calculate the voltage drop across R:
V = I * R
13 V = 15 mA * R
To find the value of R, we need to convert the load current from mA to A:
15 mA = 0.015 A
Now we can calculate R:
\(13 V = 0.015 A * RR = 13 V / 0.015 A\)
Calculating this, we get:
R = 866.67 ohms
Therefore, the value of the series resistance (R) is approximately 866.67 ohms.
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For the system below: 1. Write the equations of the of currents i1, 12, 13, 14 and is. 2- Obtain the transfer function E.(s)/E;(s) of the system 3- Obtain the output Cot) if e:(t) = 1.
The given value of e:(t) = 1 in the transfer function derived in step 2 and solve for C(t).C(t) = L^-1{[i4(s)*R4]/[Vi(s)]}*1, where L^-1 denotes the inverse Laplace transform.
Step 1: Write the equations of the currents i1, i2, i3, i4 and is in the given circuit diagram. Use Kirchhoff's Voltage Law (KVL) and Ohm's Law to write the equations in terms of voltage and resistance.i1 = (Vi - V1)/R1i2 = (V1 - V2)/R2i3 = (V1 - V3)/R3i4 = (V2 - V4)/R4is = V3/R5
Step 2: Find the transfer function E(s)/Ei(s) by using the Laplace transform. Replace the resistors R1, R2, R3, and R4 with their Laplace equivalents and solve for E(s)/Ei(s)E(s)/Ei(s) = [i4(s)*R4]/[Vi(s)]
Step 3: Find the output C(t) if e:(t) = 1 by using the inverse Laplace transform. Substitute the given value of e:(t) = 1 in the transfer function derived in step 2 and solve for C(t).C(t) = L^-1{[i4(s)*R4]/[Vi(s)]}*1, where L^-1 denotes the inverse Laplace transform.
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x − 3y − 8z = −10 2x + 5y + 6z = 13 3x + 2y − 2z = 3
Answer:
consistent; dependent; infinite
Explanation:
Subtract the first equation from the third equation.
3x + 2y − 2z = 3
− (x − 3y − 8z = −10)
2x + 5y + 6z = 13 Subtract.
Because the resulting equation is identical to the second equation, the system is consistent and dependent with infinitely many solutions.
What is a transition? A. An animation that happens on a single slide B. An outline format that uses roman numerals C. An image file imported to a title slide D. An effect that happens between slides Please select the best answer from the choices provided A B C D
Answer:
its c
Explanation:
What are the legal consequences of engineering solutions? Discuss with one real life examples. Please state the Code of Ethics and Engineers professional obligations in this case
Engineers play a crucial role in developing and implementing technological innovations to cater to the needs of society. However, if the engineering solutions do not comply with established codes of ethics and professional standards, the legal implications can be significant.
Engineers are expected to follow ethical standards to ensure that their engineering solutions meet safety, quality, and environmental criteria. The Code of Ethics of Engineers outlines the ethical principles, values, and practices that engineers should follow in their professional duties.
A violation of the Code of Ethics or a failure to comply with professional standards can lead to legal consequences. If an engineer's solution is not compliant with safety standards, the individual or company responsible for implementing that solution may face fines, penalties, or legal action. One real-life example of legal consequences resulting from engineering solutions is the Deepwater Horizon oil spill. In 2010, an explosion on the Deepwater Horizon oil rig caused a massive oil spill in the Gulf of Mexico, resulting in significant environmental and economic damage.
Investigations revealed that several engineering solutions that were implemented on the rig were not in compliance with safety standards. Engineers had also failed to follow established procedures for ensuring safety and environmental protection. As a result, BP, the company responsible for the rig, faced significant legal consequences, including fines, penalties, and legal action by affected parties. Engineers involved in the project also faced legal consequences, including loss of license and potential criminal charges.
Engineers have a professional obligation to ensure that their solutions meet safety, quality, and environmental criteria. This means that they should adhere to established codes of ethics, follow established procedures for ensuring safety, and ensure that their solutions are in compliance with relevant laws and regulations. They also have a responsibility to report any violations or issues that could impact the safety or environmental impact of their solutions. Failure to meet these obligations can lead to legal consequences and impact public trust in the engineering profession.
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It is desired to obtain 500 VAR reactive power from 230 Vrms 50 Hz 1.5 KVAR reactor. What should be the angle of the AC to AC converter to be used? Calculate the THD of the current drawn from the mains (consider up to the 12th harmonic)?
Answer:
14.5° ; THD % = 3.873 × 100 = 387.3%.
Explanation:
Okay, in this question we are given the following parameters or data or information which is going to assist us in solving the question efficiently and they are;
(1). "500 VAR reactive power from 230 Vrms 50 Hz 1.5 KVAR reactor".
(2). Consideration of up to 12th harmonic.
So, let us delve right into the solution to the question above;
Step one: Calculate the Irms and Irms(12th) by using the formula for the equation below;
Irms = reactive power /Vrms = 500/230 = 2.174 A.
Irms(12th) = 1.5 × 10^3/ 12 × 230 = 0.543 A.
Step two: Calculate the THD.
Before the Calculation of the THD, there is the need to determine the value for the dissociation factor, h.
h = Irms(12th)/Irms = 0.543/ 2.174 = 0.25.
Thus, THD = [1/ (h)^2 - 1 ] ^1/2. = 3.873.
THD % = 3.873 × 100 = 387.3%.
Step four: angle AC - Ac converter
theta = sin^-1 (1.5 × 10^3/ 12 × 500) = 14.5°.
identifies potential new customers and preserves favorable business relationships with past customers
❎❎❎❎❎❎❎ sorry but that didn't help me that much
Select the four areas in which environmental engineers assist manufacturers with making decisions.
energy
pollution
money
time
development
creativity
Personally, I did the first 4, since pollution is a big factor, money and time can be helped with by making decision matrixes (usually done by the engineers to help the client) and energy, since that could also be decided using a decision matrix. Thank you for your help!
Answer:
In my opinion, Energy, Time, Money and Development
Answer:
Pollution, time, money, and energy.
Explanation:
Which of the following is a better thesis statement? Freedom is not free. American’s veterans pay a high price for our freedom. America’s veteran’s defend our freedom, but they sacrifice their personal ambitions and their lives, and many of them suffer physically and mentally from their experiences.
Answer:
C). America’s veterans defend our freedom, but they sacrifice their personal ambitions and their lives, and many of them suffer physically and mentally from their experiences.
Explanation:
A good thesis statement must provide the central idea or theme of the paper or the essay in a capsule form along with its theoretical base. The key characteristics of a thesis statement are its arguability, specificity, and intensity. As per these descriptions, the above statement correctly relates the main point('America's...freedom') very clearly and precisely. It also contains the arguability which can be supported through further evidences.
In your own words, describe the differences between en-
tering the workforce right after high school or working in a
skilled trade.
Answer:
if you are entering the workforce right after high school you are likely to get less pay and work maybe a little harder and also have to learn from the people at the job how to do the job compared to someone who is working in a skilled trade where they know what they are doing, are likely to get a higher pay, and dont need to be taught what to do.
Explanation:
Should prototyping be used on every systems development project? Why or why not?
Prototyping should not be used on every systems development project.
Below are the reasons why:
A prototype is a small-scale trial model of a product or software application created to test or demonstrate concepts and functionality.
Prototyping is a critical aspect of the development process since it helps businesses and developers determine if the application will perform as planned before investing significant time and money into full-scale development.
Despite this, prototyping should not be used on every systems development project.
Why prototyping should not be used on every systems development project?
Not all systems development projects require prototyping.
Consider the following scenarios:
When creating minor modifications to current software, prototyping may not be needed at all.
When working on a project with a solid plan, a well-understood concept, and a well-known user interface, prototyping is not necessary.
The development team is already well-versed in the domain, so prototyping may not be needed.
The project does not require a considerable amount of time or money investment, so prototyping is not necessary.
In conclusion, prototyping should not be used on every systems development project.
Prototyping is essential to software development since it provides insight into potential problems and allows developers to address them before moving forward with full-scale development.
However, a prototype is not required in every situation, and it may be skipped in some circumstances.
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Discuss the philosophy and benefits of concurrent
engineering covering DFA/DFM
please do it in 30 minutes please urgently with
detailed solution... I'll give you up thumb
Concurrent engineering promotes cross-functional collaboration, early involvement of all stakeholders, and simultaneous consideration of design, manufacturing, and assembly aspects. This approach leads to several benefits.
Concurrent engineering promotes efficient product development by integrating design, manufacturing, and assembly considerations from the early stages. By involving manufacturing and assembly teams early on, potential design issues can be identified and resolved, resulting in improved product quality and reduced time to market. DFA focuses on simplifying assembly processes, reducing parts count, and improving ease of assembly, leading to lower production costs and improved product reliability. DFM aims to optimize the design for efficient and cost-effective manufacturing processes, reducing material waste and improving productivity. Concurrent engineering also enables better communication, shorter design iterations, and improved overall product performance.
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rank the following gases in order of decreasing rate of effusion. rank from the highest to lowest effusion rate. to rank items as equivalent, overlap them.
It means that the gas with the lowest molecular weight will have the highest effusion rate.
What has the highest rate of effusion?The given gases' effusion rates are listed in order from highest to lowest. The effusion rate of a hydrogen molecule is the highest, whereas that of a hydrocarbon is the lowest.
A gas will effuse faster when it is lighter and more slowly when it is heavier. Helium (He) will have the highest rate of effusion since it has the lowest molecular weight (atomic weight, in this example).
The following equation can be used to compare the rate of effusion for two gases: The effusion rates in this case are inversely related to the square root of the gas molecules' masses. A container contains an amalgam of neon and argon gas.
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Changing the color of a cell phone is
an example of a design
improvement
Answer:
Yes, yes it is
Explanation:
changing the color of a phone is indeed an improvment on what you are currently doing, and if you keep doing it little by little you are going to be a great engineer
convert the following decimal number to octal number and the to binary .58
Answer:
21/2 we get remainder 1
10/2 we get remainder 0
5/2 we get remainder 1
2/2 we get remainder 0
1. Now take the 1
The answer to the question is
(21)10=(10101)2
I need a detailed solution for the multi part question
Answer:
z=X=c+J=A
Explanation:
One situation that can make a measurement with a laser inaccurate is measuring to a: ________
One situation that can make a measurement with a laser inaccurate is measuring to a heavy reflective surface
What is reflective surface?Reflective surfaces or ground-primarily based totally albedo modification (GBAM) is a sun radiation control technique of improving the Earth's albedo (the cappotential to mirror the visible, infrared and ultraviolet wavelengths of the sun, lowering warmth switch to the floor). The IPCC defined this technique as "whitening roofs, adjustments in land use control (e.g., no-until farming), alternate of albedo at a bigger scale (masking glaciers or deserts with reflective sheeting and adjustments in ocean albedo)."
The maximum famous kind of reflective floor is a kind of roof referred to as the "cool roof". While cool roofs are commonly related to white roofs, they arrive in a lot of hues and substances and are to be had for each industrial and home buildings.
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2.3
What does NBT stand for?
Answer:
Named Binary Tag ( NBT)
Explanation:
The format is designed to store data in a tree structure made up of various tags
The meaning of the given word NBT is called; National Benchmark Test.
What is the meaning of NBT?The meaning of the given word NBT is called National Benchmark Test.
NBT ( national benchmark test ) is defined as a national test which must be written and passed by High school students that intend to go to the university ( i.e. passport to the university ).
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a wrench used to measure resistance while applying a twisting force using a common socket, and whose values are stated in inch-pounds or foot-pounds, is called a
A wrench used to measure resistance while applying a twisting force using a common socket, and whose values are stated in inch-pounds or foot-pounds, is called a; Torque wrench.
The features of the wrench are given as;
Measurement of resistance Applying a twisting force via a common socketValues are in inch pounds or foot poundsThe correct answer is Torque wrench because a torque wrench is simply a tool that is used to apply a particular torque to a fastener such as a bolt.
Finally, this torque wrench is modeled in form of a socket wrench with some special internal mechanisms and their values are measured in inch pounds or foot pounds.Read more about wrenches at; https://brainly.com/question/15755085
Most methods of transportation rely on some sort of infrastructure to drive, steer, navigate, or direct at some point or another in a journey. Which category of transportation system is least reliant on infrastructure?(1 point)
Answer:
Most methods of transportation rely on some sort of infrastructure to drive, steer, navigate, or direct at some point or another in a journey. Which category of transportation system is least reliant on infrastructure?(1 point). road
Explanation:
Average setup time on a certain production machine is 5.0 hr. Average batch size is 52 parts, and average operation cycle time is 4.2 min. The reliability of this machine is characterized by mean time between failures of 37 hr and a mean time to repair of 55 min.
(a) If availability is ignored, what is the average hourly production rate of the machine.
(b) Taking into account the availability of the machine, determine its average hourly production rate.
(c) Suppose that availability only applied during the actual run time of the machine and not the setup time. Determine the average hourly production rate of the machine under this scenario.
(a) The machine's average hourly production rate without considering availability is 6.02 parts/hr.
(b) The machine's average hourly production rate, taking into account availability, is 6.17 parts/hr.
(c) The machine's average hourly production rate when only available during run time is 5.71 parts/hr.
How to solve calculations on a production machine?(a) To calculate the average hourly production rate of the machine without considering availability, we need to first calculate the total time it takes to produce a batch of 52 parts.
Total time = (setup time) + (operation time per part x batch size)
Total time = 5.0 hr + (4.2 min/part x 52 parts)/60 min/hr
Total time = 5.0 hr + 3.64 hr
Total time = 8.64 hr
Average hourly production rate = Batch size / Total time
Average hourly production rate = 52 parts / 8.64 hr
Average hourly production rate = 6.02 parts/hr
Therefore, the average hourly production rate of the machine without considering availability is 6.02 parts/hr.
(b) To calculate the average hourly production rate of the machine taking into account availability, we need to first calculate the machine's availability using the mean time between failures (MTBF) and mean time to repair (MTTR) values.
Availability = MTBF / (MTBF + MTTR)
Availability = 37 hr / (37 hr + 0.92 hr)
Availability = 0.975 or 97.5%
Now we can calculate the total time that the machine is available for production:
Available time = Total time x Availability
Available time = 8.64 hr x 0.975
Available time = 8.42 hr
Average hourly production rate = Batch size / Available time
Average hourly production rate = 52 parts / 8.42 hr
Average hourly production rate = 6.17 parts/hr
Therefore, the average hourly production rate of the machine taking into account availability is 6.17 parts/hr.
(c) If availability only applies during the actual run time of the machine and not the setup time, we need to adjust the available time calculation:
Available time = (operation time per part x batch size) / 60 min/hr x Availability
Available time = (4.2 min/part x 52 parts) / 60 min/hr x 0.975
Available time = 4.11 hr
Total time = Available time + setup time
Total time = 4.11 hr + 5.0 hr
Total time = 9.11 hr
Average hourly production rate = Batch size / Total time
Average hourly production rate = 52 parts / 9.11 hr
Average hourly production rate = 5.71 parts/hr
Therefore, the average hourly production rate of the machine taking into account availability only during run time is 5.71 parts/hr.
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