1. A 6-pole and three-phase induction motor has synchronous speed of (1000+X) RPM.

a) Find the no-load and full-load operating speed of motor for the cases given,

1. 2.5Hz electrical frequency of rotor for no-load condition. (30p)

2. 6.3Hz electrical frequency of rotor for full-load condition. (30p)

b) Find the speed regulation of motor by using parameters found above. (20p)

c) Determine the electrical frequency of rotor under full-load condition so that speed regulation would be equal to 5%? (Electrical frequency of rotor for no-load condition is still 2.5Hz.) (20p)

Answers

Answer 1

a. the electrical frequency of the rotor under full-load condition, for a speed regulation of 5%, would be approximately 2.381 Hz. b. the no-load operating speed of the motor is 50 RPM.

a) To find the no-load and full-load operating speeds of the motor, we can use the formula:

Speed (in RPM) = (120 * Frequency) / Number of Poles

Given:

Number of poles (P) = 6

1. For the no-load condition:

Electrical frequency of the rotor (f) = 2.5 Hz

Speed (no-load) = (120 * 2.5) / 6

              = 50 RPM

Therefore, the no-load operating speed of the motor is 50 RPM.

2. For the full-load condition:

Electrical frequency of the rotor (f) = 6.3 Hz

Speed (full-load) = (120 * 6.3) / 6

                 = 1260 RPM

Therefore, the full-load operating speed of the motor is 1260 RPM.

b) The speed regulation of the motor can be calculated using the formula:

Speed Regulation (%) = [(No-Load Speed - Full-Load Speed) / Full-Load Speed] * 100

Given:

No-Load Speed = 50 RPM

Full-Load Speed = 1260 RPM

Speed Regulation = [(50 - 1260) / 1260] * 100

                = -90.48%

Therefore, the speed regulation of the motor is approximately -90.48%.

c) To determine the electrical frequency of the rotor under full-load condition for a desired speed regulation of 5%, we can rearrange the formula for speed regulation:

Speed Regulation = [(No-Load Speed - Full-Load Speed) / Full-Load Speed] * 100

Rearranging the formula:

Full-Load Speed = No-Load Speed - (Speed Regulation/100) * Full-Load Speed

Given:

No-Load Speed = 50 RPM

Speed Regulation = 5%

Let's solve for the electrical frequency of the rotor at full-load:

Full-Load Speed = 50 - (5/100) * Full-Load Speed

(1 + 5/100) * Full-Load Speed = 50

1.05 * Full-Load Speed = 50

Full-Load Speed = 50 / 1.05

              = 47.62 RPM

Using the formula for speed:

Speed (full-load) = (120 * Electrical Frequency) / Number of Poles

47.62 = (120 * Electrical Frequency) / 6

Electrical Frequency = (47.62 * 6) / 120

                   = 2.381 Hz

Therefore, the electrical frequency of the rotor under full-load condition, for a speed regulation of 5%, would be approximately 2.381 Hz.

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Related Questions

Generally, the primary source of all water supply is said to be

Answers

The main sources of water are surface water, groundwater and rainwater.

When hermetic refrigerant motor-compressors are designed to operate continuously at currents greater than 156 percent of the rated-load current, the nameplate is marked with _______ current

Answers

The nameplate of a hermetic refrigerant motor-compressor that is designed to operate continuously at currents greater than 156% of the rated-load current is marked with branch-circuit selection current.

What is a hermetic refrigerant motor-compressor?

A hermetic refrigerant motor-compressor can be defined as a mechanical device that is designed and developed by combining a compressor and motor in a single outer-welded steel shell.

Basically, a hermetic refrigerant motor-compressor is used in the following areas:

Household refrigeratorsFreezersHeat pumpsAir coolersWater cooling equipment.Small refrigeration equipment.

According to HSE, the nameplate of a hermetic refrigerant motor-compressor that is designed to operate continuously at currents greater than 156% of the rated-load current is marked with branch-circuit selection current, so as to ensure safety for end users and technicians.

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When choosing a respirator for your job, you must conduct a
test.

Answers

Answer: A fit test. Either qualitative or quantitative.
You could use a fit test.


I hope this helps.

What are these tools called need help with it?

What are these tools called need help with it?

Answers

Answer:

those look like clamps

Explanation:

Which of the following are among the fastest growing occupations?

a. Computer specialists
b. Engineers
c. Systems analysts
d. All of the above

Answers

Employment growth is often used as a measure of economic expansion and a test for domestic economic health.

Installing and repairing computer hardware and software is typically a responsibility of a Computer specialist. They meet the needs of customers, review and troubleshoot equipment, carry out upgrades, as well as start debating the extent of client reparations or restitution.Engineers are professionals who invent, design, analyze, construct and test machinery, complex structures, frameworks, gadgets. These materials satisfy functional goals and demands while taking into account the limits placed by practicalities, regulatory oversight, safety, and costs.Analysts create diagrams that assist computer network designers and architects.In this, the system's architects, indicate the level systems and processes of an organization as well as design solutions to improve the organizational framework.

In this question all the choices were interlinked with each other therefore, the final answer is "Option d".

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We consider three different hash functions which produce outputs of lengths 64, 128 and 160 bit. After how many random inputs do we have a probability of ε = 0. 5 for a collision? After how many random inputs do we have a probability of ε = 0. 1 for a collision?

Answers

For ε = 0.1, approximately 2.147 random inputs are needed for a collision. The number of inputs required for the hash functions producing outputs of lengths 128 and 160 bits using the same formula.

To determine the number of random inputs needed to achieve a specific probability of collision, we can use the birthday paradox principle. The birthday paradox states that in a group of people, the probability of two individuals having the same birthday is higher than expected due to the large number of possible pairs.

The formula to calculate the approximate number of inputs required for a given probability of collision (ε) is:

n ≈ √(2 * log(1/(1 - ε)))

Let's calculate the number of inputs needed for ε = 0.5 and ε = 0.1 for each hash function:

For a hash function producing a 64-bit output:

n ≈ √(2 * log(1/(1 - 0.5)))

n ≈ √(2 * log(2))

n ≈ √(2 * 0.693)

n ≈ √(1.386)

n ≈ 1.177

For ε = 0.5, approximately 1.177 random inputs are required to have a probability of collision.

For ε = 0.1:

n ≈ √(2 * log(1/(1 - 0.1)))

n ≈ √(2 * log(10))

n ≈ √(2 * 2.303)

n ≈ √(4.606)

n ≈ 2.147

For ε = 0.1, approximately 2.147 random inputs are needed for a collision.

Similarly, we can calculate the number of inputs required for the hash functions producing outputs of lengths 128 and 160 bits using the same formula.

Please note that these calculations provide approximate values based on the birthday paradox principle. The actual probability of collision may vary depending on the specific characteristics of the hash functions and the nature of the inputs.

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Discuss the targeted design properties for resorbable polyurethanes for tissue repair and non-resorbable polyurethane permanent implants. How can the properties of the polyurethane be tailored to the application by modifying the structure?

Answers

The property is that polyurethanes have a good tear resistance as well as tensile strength.

What is polyurethanes?

Polyurethane is an umbrella word for a group of polymers formed via the condensation of polyisocyanates and polyalcohols. Despite its xenobiotic origins, polyurethane has been discovered to be biodegradable by naturally occurring microbes.

Polyurethanes are synthesized by reacting a polyol (an alcohol having more than two reactive hydroxyl groups per molecule) with a diisocyanate or a polymeric isocyanate in the presence of appropriate catalysts and additives

To manage cell fate and tissue healing, biodegradable polyurethane platforms have been used. Cell bonding, spreading, multiplication, and separation are all influenced by framework features such as compound, mechanical, and primary. These are not fully fixed as the science of biodegradable polyurethanes, platform manufacturing technologies, and surface change approaches.

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Constant practice would be most effective in learning a skill under which conditions?

Answers

Constant practice would be most effective in learning a skill under these conditions:

When the conditions under which the skill is executed do not changeWhen students are just starting to learn the skill.

What is a skill acquisition plan?

A skill acquisition plan can be defined as a written plan that is used to outline the goals, objectives, materials, teaching methods, and data collection techniques for teaching trainees or employees, a specific skill or set of skills.

This ultimately implies that, skill acquisition plans include all of the following:

GoalsObjectivesMaterialsData collection

In conclusion, we can infer and logically deduce that constant practice would be most effective in learning a skill under these conditions:

When the conditions under which the skill is executed do not changeWhen students are just starting to learn the skill.

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Superheated steam from the boiler is delivered to a turbine at 650 C and 8.5 MPa. The turbine exhausts at 0.01 MPa. If the turbine is 75% efficient, determine: a. The actual work of the turbine. b. The actual outlet temperature and quality (if applicable) of the exhaust from the turbine. c. If the steam exhaust is condensed (in a condenser) to a saturated liquid, what is the work required by the pump to bring the liquid to the boiler pressure (8.5 MPa)

Answers

Superheated steam from the boiler is delivered to a turbine at 650 C and 8.5 MPa. The turbine exhausts at 0.01 MPa. Given that the turbine is 75% efficient, we need to determine the following: a. The actual work of the turbine.

b. The actual outlet temperature and quality (if applicable) of the exhaust from the turbine.c. If the steam exhaust is condensed (in a condenser) to a saturated liquid, what is the work required by the pump to bring the liquid to the boiler pressure (8.5 MPa).Solution:a) The turbine's actual work output (Wactual) = η (energy input)or Wactual = η (energy input) = η (h1 - h2)Here, η = 75% = 0.75. h1 = enthalpy of the steam entering the turbine = 3344.7 kJ/kg. h2 = enthalpy of the steam leaving the turbine = ?Using the steam tables, h2 = 2275 kJ/kg.Therefore,Wactual = 0.75 (3344.7 - 2275)kJ/kg = 706.7 kJ/kg.b) At turbine outlet, steam pressure P2 = 0.01 MPa.

The steam table shows that at this pressure the saturation temperature T2 is 45.8°C.Hence, the steam leaving the turbine is superheated since T2 > 45.8°C. Let us assume that the steam is superheated by ΔT. Therefore, the steam temperature leaving the turbine is:T2 + ΔT = 650°CT2 = 650 - ΔT°CAt 650°C, the superheated steam table gives us the enthalpy of superheated steam as 3454 kJ/kg.Therefore, the enthalpy of superheated steam at 650 - ΔT°C is: (3454 - Cp ΔT), where Cp is the specific heat capacity of superheated steam at constant pressure.Cp of superheated steam is not given, but its average value can be assumed as 2.1 kJ/kg K over the temperature range of 400 - 800°C.Therefore, h2 = 2275 kJ/kg + (3454 - 2.1 ΔT) kJ/kg2275 kJ/kg + 3454 kJ/kg - 2.1 ΔT kJ/kg = 5729 kJ/kg - 2.1 ΔT kJ/kgFor superheated steam, h2 = Cp T2.

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Should you prefer rooftop solar panels?

Answers

The rooftop solar is a form of solar energy that can be installed on the roof of a home or business. It is cost-effective, environmentally friendly, and provides many benefits to homeowners and businesses.

The rooftop solar has many advantages over other forms of solar energy. One of the main advantages is that it provides 100% clean electricity from renewable sources. In addition, it can be combined with other sources such as wind power and geothermal power for even more benefits.

There are also many uses for rooftop solar panels in homes and businesses. One example is using it to heat water for hot water systems or heating swimming pools.

For me Bluebird Solar Private Limited is the best website in India for rooftop solar panels in India.

High-mount stop lamps are typically attached to the exterior of the vehicle using:
A. nylon retainers.
B. visible screws.
C. rivets
D. self-locking nuts.

Answers

Answer:

Option A

Explanation:

Nylon retainers are knocking screws that have nylon coating on their thread which prevents them from loosening. It generally has two heads Hex Key an star screw. For high mount fixing, star screw is used as it is less prone to stripping. The nylon insert of a Nylock nuts enters into the screw and prevent it from loosening. It is useful in areas where there is high vibration.

Hence, option A is correct

What is the meaning of beauty and completeness? In relation to these what are the attributes a Muslim should adopt?

Answers

ᴄᴏᴍᴘʟᴇᴛᴇɴᴇꜱꜱ ᴍᴇᴀɴꜱ ᴛʜᴇ ꜱᴛᴀᴛᴇ ᴏꜰ ʙᴇɪɴɢ ᴄᴏᴍᴘʟᴇᴛᴇ ᴀɴᴅ ᴇɴᴛɪʀᴇ; ʜᴀᴠɪɴɢ ᴇᴠᴇʀʏᴛʜɪɴɢ ᴛʜᴀᴛ ɪꜱ ɴᴇᴇᴅᴇᴅ.

ʙᴇᴀᴜᴛʏ ᴍᴇᴀɴꜱ combination of qualities, such as shape, colour, or form, that pleases the aesthetic senses, especially the sight.

Select the correct answer.
Which country first initiated the slow city movement?
A. New Zealand
B. Italy
C. United States
D. China

Answers

Answer:

B. Italy

Explanation:

Hope this helps :)

The answer is B) Italy

Evidence shows that in manufacturing, ____ is positively correlated with hourly wage level a. retention b. productivity c. job satisfaction d. total profit.

Answers

Evidence shows that in manufacturing, productivity is positively correlated with hourly wage level.

Research has shown that there is a positive correlation between productivity and wages in the manufacturing industry. This is because when workers are paid higher wages, they tend to be more motivated to work harder and more efficiently, leading to increased productivity. In addition, higher wages may also attract more skilled workers, who can further contribute to increased productivity.

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Drawing 15.40:
Assuming an ideal drawing process, what is the smallest final diameter to which a
60-mm diameter rod can be drawn?

Answers

To calculate the smallest final diameter of a 60-mm diameter rod in an ideal drawing process, we will use the following steps:

1. Identify the initial diameter: The initial diameter of the rod is 60 mm.

2. Identify the drawing process terms: We are asked to calculate the smallest final diameter in an ideal drawing process.

3. Apply the ideal drawing process assumption: In an ideal drawing process, there is no limit to the amount of reduction that can be achieved. Therefore, the smallest final diameter can theoretically be reduced to an infinitesimally small value.

In conclusion, assuming an ideal drawing process, the smallest final diameter to which a 60-mm diameter rod can be drawn is theoretically infinitesimally small. However, in real-world applications, there will be practical limitations and material properties that would prevent such extreme reductions.

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Two stepped bar is supported at both ends.At the join point of two segments,the force F is applied(downwards).Calculate reactive forces R1 and R3 at the supports.What is value of absolute maximal stress?
Choose one answer nearest your result.

given= d1=10mm d2=20mm L1=20mm L2=10mm E=200GPa F=20kN

Two stepped bar is supported at both ends.At the join point of two segments,the force F is applied(downwards).Calculate

Answers

Answer:

F=200kN

Explanation:

1.Write an equation that shows the equivalency between meters and Gigameters.

Answers

Answer:

Explanation:

A gigameter is 1,000,000,000 meters

so, let us say m is the number of meters, g is the number of gigameters

the equation then is

\(g*10^9=m\)

Determine the support reactions of a beam with an articulated support

Determine the support reactions of a beam with an articulated support

Answers

An articulated support is a type of beam support that restrains a beam from moving in all directions except one rotational direction. Determining the support reactions of a beam with an articulated support can be done using the following steps:

Step 1: Draw a free-body diagram of the beam that indicates the forces acting on the beam.Step 2: Write down the equilibrium equations that relate the forces and moments acting on the beam to the support reactions. For a beam with an articulated support, there will be two unknown support reactions: the vertical reaction and the rotational reaction.

Step 3: Solve the equilibrium equations for the unknown support reactions.Step 4: Check the solution by verifying that the forces and moments acting on the beam are in equilibrium. This can be done by substituting the values of the support reactions into the equilibrium equations and verifying that they are satisfied.

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You have received a model from another user and try to run it from its tool dialog box, but it displays a message that the tool has no parameters. How would you provide your own input data from the tool dialog box

Answers

Using the dialog box, the user needs to provide model parameters by entering manually or loading from a certain location in other to run the tool.

How to provide input data from the tool dialog box

In the dialog box , the modelbuilder should be opened and the Add variable option selected .

This wil allow one to write in inputs which the model can use.

Once , the variables have been added, save and exit.

Then run the model again in other to run using the just added parameters.

Also, If the tool expects input data from a specific location, you can use the "Browse" button to locate the data.

Therefore, models without parameters requires manual imputation in other to function properly.

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describe the pipe support

Answers

Answer:

A pipe support or pipe hanger is a designed element that transfer the load from a pipe to the supporting structures. ... The four main functions of a pipe support are to anchor, guide, absorb shock, and support a specified load. Pipe supports used in high or low temperature applications may contain insulation materials.

Name the manufacturing process that the worker is using to create the workpiece. The manufacturing process carried out by the blacksmith in the image is the process of​

Name the manufacturing process that the worker is using to create the workpiece. The manufacturing process

Answers

Answer:

Metamorphic manufacturing

Explanation:

I don't know what form of an answer you wanted but I hope this helps :)

You have a Linux system that has a 1000GB SSD, which has a 90GB partition containing an ext4 filesystem mounted to the / directory and a 4GB swap partition. Currently, this Linux system is only used by a few users for storing small files; however, the department manager wants to upgrade this system and use it to run a database application that will be used by 100 users. The database application and the associated data will take up over 200GB of hard disk space. In addition, these 100 users will store their personal files on the hard disk of the system. Each user must have a maximum of 5GB of storage space. The department manager has made it very clear that this system must not exhibit any downtime as a result of hard disk errors. How much hard disk space will you require, and what partitions would you need to ensure that the system will perform as needed? Where would these partitions be mounted? What quotas would you implement? What commands would you need to run and what entries to /etc/fstab would you need to create? Justify your answers.

Answers

Given the requirements and constraints, you will need to ensure that the system has sufficient hard disk space to accommodate the database application and the user data, while also ensuring that the system remains stable and free of hard disk errors. To do this, you will need to take the following steps:

Add Hard Disk Space: You will need to add enough hard disk space to accommodate the database application and user data. Given that the database application requires over 200GB of disk space, and each user requires 5GB of disk space, you will need a minimum of 200 + (100 x 5) = 700GB of hard disk space. If you have a spare 1000GB SSD available, you can use that.Create Partitions: You will need to create two partitions on the hard disk: one for the database application and another for the user data. Given that the database application requires over 200GB of disk space, you should create a partition with at least 200GB of disk space for the database application. Given that each user requires 5GB of disk space, you should create a partition with at least 100 x 5 = 500GB of disk space for the user data.Mount Partitions: You should mount the partition containing the database application to the /var/lib/mysql directory, and the partition containing the user data to the /home directory. This will ensure that the database application and user data are stored in separate partitions and do not interfere with each other.Implement Disk Quotas: To limit each user's disk usage to 5GB, you will need to implement disk quotas for the /home partition. You can do this by using the quota command, which allows you to set disk usage limits for individual users or groups of users.Update /etc/fstab: You will need to update the /etc/fstab file to specify the partitions that you have created and the mount points for those partitions. This will ensure that the partitions are mounted automatically when the system is started.

Here is an example of what the entries in /etc/fstab might look like:

/dev/sda1 /var/lib/mysql ext4 defaults 0 0

/dev/sda2 /home ext4 defaults,usrquota 0 0

To implement the disk quotas, you will need to run the following commands:

# touch /aquota.user

# chmod 600 /aquota.user

# mount -o remount /home

# quotacheck -avugm /home

# quotaon -avug

These steps should ensure that your Linux system meets the requirements and constraints set by the department manager, while also providing a stable and efficient system for the 100 users who will be using the database application.

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A 550 kJ of heat quantity needed to increase water temperature from 32°C to 80°C. Calculate the mass
of the water when the specific heat capacity of water is 4200 J/kg °C.​

Answers

Answer:

  2.728 kg

Explanation:

The units help you keep the calculation straight.

  \(\dfrac{550\text{ kJ}}{(80^\circ\text{C}-32^\circ\text{C})(4.200\text{ kJ/kg\,$^\circ$C})}=\dfrac{550}{48\cdot4.2}\text{ kg}\approx\boxed{2.728\text{ kg}}\)

1. When jump starting a car, make sure it is in __________.

Answers

Answer:

Make sure both cars are in park or neutral with the parking brake engaged. This makes sure that all electrical functions (headlights, radios, etc.) are turned off.

When jump starting a car, make sure it is in the right distance of the cables to reach battery.

What is jump starting a car?Jump starting a car is commonly done from another car, and also it can be done from a jump battery.  If we have to jump start a car in a safe way, the following steps are more necessary,Take out your jumper cables.Before the cable was taking, Make sure cars are in the right distance to have the jumper cables reach each battery.Place both vehicles in Park or Neutral and shut off the ignition in both cars.When jump-starting a car, it was must to remember jumper cables typically have two clamps, one with the label “positive” in red and “negative” in black.Attach one of the red clips to the positive terminal of your battery. Attach the other red clip to the positive terminal of the other car. The similar way do for the negative terminals.

Thus, when jump-starting a car, always remember the cables are in the right position.

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What is another term to describe a systematic approach for developing training programs?

Answers

Another term to describe a systematic approach for developing training programs is Instructional Systems Design (ISD).

ISD is a process that involves analyzing training needs, designing instructional materials, developing and delivering the training, and evaluating its effectiveness. This approach ensures that training programs are effective, efficient, and meet the learning objectives of the participants.

ISD typically follows a step-by-step process, including conducting a needs assessment, setting specific objectives, designing the curriculum and instructional materials, implementing the training, and evaluating its outcomes.

By using ISD, organizations can develop high-quality and learner-centered training programs that align with the needs and goals of both the learners and the organization.

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Can space debris take out a whole state

Answers

Yes depends how big the debris is

For proper function hydraulics systems need a reservoir of which of the following?
A.) Compressible fluid
B.) Non-compressible fluid C.) Non-compressible air

Answers

A. Compressible fluid

Think of brake fluid on a vehicle, compressed as one applies the break= pressure to expand brake cylinders in the wheels which compress the pads on the wheel brake rotors.

Release brake and fluid relaxes back into the reservoir/accumulator.

A 2*8 inches wood member has a length =11 ft it's density is =30 Lb/ft^3 find the actual weight of this member in Lb

Answers

Answer:

359.046 Ib

Explanation:

density = m / v ---- ( 1 )

m = mass

v = volume = l * b * h

Given data :

density = 30 Ib / ft^3

l = 2 inches = 0.1667 ft

b = 8 inches = 0.6667 ft

h = 11 ft

v ( volume ) = 0.1667 * 0.6667 * 11 = 1.22 ft^3

back to equation 1

m = 30 * 1.22  = 36.6 Ib

Actual weight ( F ) = m * g

                              = 36.6 * 9.81 = 359.046 Ib.

Crude oil at 20 c fills the space between two concentric cylinders 250 mm high and with diameters of 150 mm and 156 mm. Find the torque is required to rotate the inner cylinder at 12 r min, the outer cylinder rernaining stationary

Answers

the torque is required to rotate the inner cylinder at 12 r min, the outer cylinder remaining stationary is 11.0807 N-m.

we have left out some other important details, such as the time required to reach that rpm, whether the beginning state is at rest, and the axis around which the cylinder is revolving. However, we'll suppose that it will be 60 seconds (time is necessary to convert rpm to angular acceleration)

rotation around the center axis

Angular acceleration = torque + MOI

Currently, angular acceleration equals 2 rpm/(t 60).

In order to avoid getting an extremely high figure, we estimated that the diameter of the cylinder was 600 mm rather than 600 meters: angular acceleration= 1.047 rad/s² MOI for cylinder across center dia= 1/4MR²+ 1/12ML²

MOI= 10.5833 kg-m

Now, the product of these two is torque.

11.0807 N-m of torque

Various MOI equations can be used to compute for different axes of rotation.

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The complete question is:

Crude oil at 20 c fills the space between two concentric cylinders 250 mm high and with diameters of 150 mm and 156 mm. Find the torque is required to rotate the inner cylinder at 12 r min, the outer cylinder remaining stationary.

For this problem, you will write a module that holds sets over a type a. Our goal is to
represent the set as a sorted list with NO repeated elements. Therefore, the type a will
always be of the classes:
• Eq: so that == and /= are defined for elements of type a
• Ord: so that we can compare using <, etc.
• Enum: So that we can make lists of the form [x..y] where x and y are elements of type
a.
• Bounded: so that minBound::a and maxBound::a are the smallest and largest elements
of a.
(Note that this means we can form [minBound..maxBound]::[a], a list of all the elements of
a.)
So our declaration of the Set type is:
data Set a = Set [a]
deriving (Show, Eq, Ord)
I also have 2 functions that let you go back and forth between sets and lists, primarily for
testing purposes. You need to import Data.List for these to work, so I’m giving the syntax
for that below:
import qualified Data.List as L
list2set :: Ord a => [a] -> Set a
list2set = Set . L.nub . L.sort
set2list :: Set a -> [a]
set2list (Set xs) = xs
The temptation in implementing the set operations below is the overrely on list2set which
results in code that is simple, clear, and slow!! For example, for the union operation we could
define:
unionS_slow :: (Ord a) => Set a -> Set a -> Set a
unionS_slow (Set xs) (Set ys) = list2set (xs ++ ys)
The problem is that this will result in worst case O(n 2 ) running time (where n is the max
of the length of the 2 sets) and this is much too slow. To speed things up, we need to take
advantage of the fact that the lists are sorted and have no repeat elements. So a much better
implementation of union is the following, which has a O(n) running time:
unionS :: (Ord a) => Set a -> Set a -> Set a
unionS (Set xs) (Set ys) = Set $ merge xs ys
where
merge [] ys = ys
merge xs [] = xs
merge (x:xs) (y:ys)
| x | x>y = y:merge (x:xs) ys
| otherwise = x:merge xs ys
Note that on any of these problems, I will be looking for (at worst) an O(n) running time,
so be careful about using list2set! In particular, you don’t want to use those for intersectS or
diffS.
(a) Write two functions:
singS :: a -> Set a
emptyS :: Set a
which (respectively) create a single element set of the input and an empty set.
(b) Write the function:
addToS :: (Ord a) => a -> Set a -> Set a
so that the first input will be added to the set in the appropriate location.
(c) Write the function:
intersectS :: (Ord a) => Set a -> Set a -> Set a
so that intersectS s1 s2 returns a set representing the intersection of s1 and s2.
(d) Write the function:
diffS :: (Ord a) => Set a -> Set a -> Set a
So that diffS s1 s2 returns a set representing the set-difference of s1 and s2, which is
precisely the elements contained in s1 that are not in s2.
(e) Write the function:
subseteq :: (Ord a) => Set a -> Set a -> Bool
So that subseteq s1 s2 returns true whenever s1 is a subset of s2.
(f) Now, put all these in a module named sets, and test your functions. I would like you to
submit either a haskell script or a set of instructions you run at the command prompt
after loading your module that indicate success of each of your functions.

Answers

In Haskell, a module named 'Set's is created with functions for set operations. The functions include 'singS' to create a set with a single element, 'emptyS' to create an empty set, 'addToS' to add an element to a set, 'intersectS' to find the intersection of two sets, 'diffS' to find the difference between two sets, and 'subseteq' to check if one set is a subset of another. The module provides a convenient way to work with sets in Haskell.

a) Two functions `singS` and `emptyS` are to be written as follows in Haskell:

singS :: a -> Set a
singS x = Set [x]
emptyS :: Set a
emptyS = Set []

Here, `singS` takes an input of type `a` and returns a `Set` containing only that input element while `emptyS` returns an empty `Set`.

b) The function `addToS` is to be written as follows:

addToS :: (Ord a) => a -> Set a -> Set a
addToS x (Set []) = Set [x]
addToS x (Set xs)
 | x == head xs = Set xs
 | x < head xs = Set (x:xs)
 | otherwise = Set $ head xs : set
 where Set set = addToS x (Set (tail xs))This function takes an input of type `a` and a `Set a` and returns the `Set` with the input element added to it.

c) The function `intersectS` is to be written as follows:

intersectS :: (Ord a) => Set a -> Set a -> Set a
intersectS (Set []) _ = Set []
intersectS _ (Set []) = Set []
intersectS (Set xs) (Set ys) = Set $ intersect xs ys

Here, the `intersect` function from `Data.List` is used to calculate the intersection of two sets and returns the resulting `Set`.

d) The function `diffS` is to be written as follows:

diffS :: (Ord a) => Set a -> Set a -> Set a
diffS (Set []) _ = Set []
diffS xs (Set []) = xs
diffS (Set xs) (Set ys) = diff (Set xs) ys
 where
   diff xs (Set []) = xs
   diff (Set []) _ = Set []
   diff (Set (x:xs)) (Set (y:ys))
     | x == y = diff (Set xs) (Set ys)
     | x < y = diff (Set xs) (Set (y:ys))
     | otherwise = diff (Set (x:xs)) (Set ys)

Here, `diffS` function takes two `Set` and returns a `Set` which is the difference between the two input `Set`s.

e) The function `subseteq` is to be written as follows:

subseteq :: (Ord a) => Set a -> Set a -> Bool
subseteq (Set xs) (Set ys) = all (`elem` ys) xs

This function checks whether all the elements of the first input `Set` are in the second input `Set`. If yes, it returns `True`, otherwise `False`.

f) The functions will be grouped into a module named `Sets`.

The `Sets.hs` file will look as follows:

```module Sets whereimport qualified Data.List as Ldata Set a = Set [a]deriving (Show, Eq, Ord)singS :: a -> Set a
singS x = Set [x]
emptyS :: Set a
emptyS = Set []addToS :: (Ord a) => a -> Set a -> Set a
addToS x (Set []) = Set [x]
addToS x (Set xs)
 | x == head xs = Set xs
 | x < head xs = Set (x:xs)
 | otherwise = Set $ head xs : set
 where Set set = addToS x (Set (tail xs))intersectS :: (Ord a) => Set a -> Set a -> Set a
intersectS (Set []) _ = Set []
intersectS _ (Set []) = Set []
intersectS (Set xs) (Set ys) = Set $ intersect xs ysdiffS :: (Ord a) => Set a -> Set a -> Set a
diffS (Set []) _ = Set []
diffS xs (Set []) = xs
diffS (Set xs) (Set ys) = diff (Set xs) ys
 where
   diff xs (Set []) = xs
   diff (Set []) _ = Set []
   diff (Set (x:xs)) (Set (y:ys))
     | x == y = diff (Set xs) (Set ys)
     | x < y = diff (Set xs) (Set (y:ys))
     | otherwise = diff (Set (x:xs)) (Set ys)subseteq :: (Ord a) => Set a -> Set a -> Bool
subseteq (Set xs) (Set ys) = all (`elem` ys) xs```To test the functions, open the terminal and run the following command:

```ghci
:l Sets.hs```

After this, the following commands can be run to check the functions:

`singS 1` will output `Set [1]``emptyS` will output `Set []``addToS 1 (Set [2, 3, 4])` will output `Set [1,2,3,4]``intersectS (Set [1,2,3]) (Set [2,3,4])` will output `Set [2,3]``diffS (Set [1,2,3]) (Set [2,3,4])` will output `Set [1]``subseteq (Set [1,2]) (Set [1,2,3])` will output `True` and `subseteq (Set [1,2,3]) (Set [1,2])` will output `False`.

Learn more about Haskell at:

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