A commercial enclosed helical gear drive consists of 25° normal pitch angle and a helix angle of 28º and a normal diametral pitch of 12 teeth/in. The pinion has 28 teeth driving a 48-tooth gear. The pinion speed is 450 rev/min, the face width 4 in. The gears are grade 2 steel, through-hardened at 300 Brinell, made to No. 8 quality standards, uncrowned, and are to be accurately and rigidly mounted. Assume a pinion life of 108 cycles with reliability of 0.70 and a conservative design. Determine the AGMA bending stress and the corresponding factors of safety if 12 hp is to be transmitted

Answers

Answer 1

The AGMA bending stress is 25.39 ksi and the corresponding factor of safety is 4.16 when transmitting 12 hp.

To determine the AGMA (American Gear Manufacturers Association) bending stress and the corresponding factors of safety, we'll follow the steps outlined in AGMA standards. Let's calculate the values step by step:

Step 1: Calculate the pitch diameter (d) of the pinion and gear:

d_pinion = Number of teeth on the pinion / Diametral pitch

= 28 teeth / 12 teeth/in

= 2.33 inches

d_gear = Number of teeth on the gear / Diametral pitch

= 48 teeth / 12 teeth/in

= 4 inches

Step 2: Calculate the center distance (C) between the pinion and gear:

C = (d_pinion + d_gear) / 2

= (2.33 inches + 4 inches) / 2

= 3.165 inches

Step 3: Calculate the velocity factor (K_v):

K_v = (12 + 6) / (12 + sqrt(C))

= (12 + 6) / (12 + sqrt(3.165))

= 1.250 (approximately)

Step 4: Calculate the face width factor (K_b):

K_b = 1.0 + 0.002 * (12 - Face width)

= 1.0 + 0.002 * (12 - 4)

= 1.016

Note: The face width is given as 4 inches in the problem statement.

Step 5: Calculate the dynamic factor (K_vd):

K_vd = 1.63 * (K_v / (K_v + sqrt(C)))

= 1.63 * (1.250 / (1.250 + sqrt(3.165)))

= 1.335 (approximately)

Step 6: Calculate the stress cycle factor (K_s):

K_s = 1.355 * (Log10(108))^0.714

= 1.355 * (Log10(108))^0.714

= 1.355 * 0.955

= 1.295 (approximately)

Step 7: Calculate the Lewis bending strength (S):

S = 0.577 * BHN

= 0.577 * 300 (Grade 2 steel, through-hardened at 300 Brinell)

= 173.1 ksi (thousand pounds per square inch)

Step 8: Calculate the AGMA bending stress (σ):

σ = (33000 * Power) / (K_v * K_vd * K_s * K_b * d_pinion * Face width)

= (33000 * 12) / (1.250 * 1.335 * 1.295 * 1.016 * 2.33 * 4)

= 25.39 ksi (thousand pounds per square inch)

Step 9: Calculate the factor of safety (FoS):

FoS = (S / σ) * Reliability

= (173.1 ksi / 25.39 ksi) * 0.70

= 4.16 (approximately)

Therefore, the AGMA bending stress is 25.39 ksi and the corresponding factor of safety is 4.16 when transmitting 12 hp.

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Related Questions

8. The hardness of mild steel is (state if each of the following is true or false): (i) Greater than that of cutting tool steels. (ii) Greater than that of diamond. (iii) Greater than that of pure lead. (iv) Greater than that of nylon. (v) Greater than that of corundum (i.e. alumina or aluminium oxide).

Answers

The hardness of mild steel is greater than that of pure lead and nylon, but less than that of cutting tool steels, diamond, and corundum.

Is the hardness of mild steel greater than that of diamond?

(i) True: The hardness of mild steel is generally greater than that of cutting tool steels. Cutting tool steels are often heat-treated to increase their hardness for better cutting performance, but mild steel typically has a lower hardness level.

(ii) False: Diamond is the hardest known material, and its hardness is significantly greater than that of mild steel. Diamond ranks at the top of the Mohs hardness scale with a hardness of 10, while mild steel falls around 120-130 on the Brinell hardness scale.

(iii) False: Pure lead is a soft metal with relatively low hardness. It has a low ranking on the Mohs hardness scale and is much softer than mild steel.

(iv) False: Nylon, a synthetic polymer, is a relatively soft material compared to mild steel. Mild steel has a higher hardness than nylon.

(v) True: Corundum, also known as alumina or aluminum oxide, is a hard material commonly used as an abrasive. However, mild steel is generally harder than corundum.

(i) Greater than that of cutting tool steels (True)

(ii) Greater than that of diamond (False)

(iii) Greater than that of pure lead (False)

(iv) Greater than that of nylon (False)

(v) Greater than that of corundum (True)

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1. Consider that you are designing an engine for a heavy duty truck. Please answer the following questions:
a) Which engine layout do you prefer (inline, V, W, flat etc.)? Why?
b) Which engine type do you select, Gasoline or Diesel? Why?
2. Consider that you are designing an engine for a sports car where the high speed is the ultimate objective.
a) Which type of fuel do you prefer: Gasoline or Diesel? Why?
b) What do you expect for the flame colour for the selected fuel type? Why?
c) Which fuel mixture type do you prefer: Stoichiometric, Fuel-rich or Fuel-lean?

Answers

For designing an engine for a heavy-duty truck, the best engine layout would be the inline engine layout. This is because the inline engine is relatively simple to manufacture, maintain, and repair.

Furthermore, the inline engine is more fuel-efficient because it has less frictional losses and is lighter in weight than the V engine, which is critical for a heavy-duty truck. For designing an engine for a heavy-duty truck, diesel is a better choice than gasoline. The diesel engine is more fuel-efficient and has better torque and power than a gasoline engine. Diesel fuel is less volatile than gasoline and provides more energy per unit volume, which is an advantage for long-distance travel.

For designing an engine for a sports car where high speed is the ultimate objective, gasoline is the best choice. Gasoline has a higher energy content and burns more quickly than diesel, which is crucial for high-speed engines.b) The flame color for gasoline is blue. This is because blue flames indicate complete combustion of the fuel and oxygen mixture.c) For designing an engine for a sports car where high speed is the ultimate objective, a fuel-lean mixture is better. A fuel-lean mixture is a mixture with a high air-to-fuel ratio. It has less fuel than the stoichiometric mixture, resulting in less fuel consumption and cleaner emissions. In a high-speed engine, a fuel-lean mixture is better since it produces less exhaust gas, allowing the engine to operate at higher speeds.

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Show that the mathematical representation of the enthalpy (h, in kJ/kg) of water whose humidity (H) is 80% is h = hf + 0.20hfg.

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The mathematical representation of the enthalpy (h) of water with a humidity (H) of 80% is h = hf + 0.20 * hfg.

The enthalpy (h) of a substance can be represented as the sum of the enthalpy of saturated liquid (hf) and the product of the enthalpy of vaporization (hfg) and the humidity ratio (ω).

The humidity ratio (ω) is defined as the ratio of the mass of water vapor (mv) to the mass of dry air (ma). It can be calculated using the formula:

ω = mv / ma

Given that the humidity (H) is 80%, we can say that the humidity ratio (ω) is 0.80.

Now, the enthalpy of water can be expressed as:

h = hf + ω * hfg

Substituting the value of ω as 0.80, we get:

h = hf + 0.80 * hfg

Since the given humidity is 80%, we can rewrite it as:

h = hf + 0.20 * hfg

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Explain the reasons why aluminium is easier to be plastically deformed compared to steel.

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Aluminum is easier to plastically deform than steel because of its lower strength and higher ductility. It's a softer metal and is much easier to work with, which makes it more malleable.

Steel has a higher tensile strength and hardness than aluminum, making it more difficult to work with. Although steel can be shaped and molded, it requires more force and energy than aluminum.Aluminum has a hexagonal close-packed (HCP) crystal structure, which makes it more malleable than steel. Its crystal structure means that it can bend and stretch more easily without cracking or breaking.Steel has a body-centered cubic (BCC) crystal structure, which is more rigid and less flexible than aluminum. Its crystal structure means that it is more prone to cracking and breaking when subjected to external forces.In conclusion, the key difference between aluminum and steel is their strength and ductility. Aluminum is more malleable and easier to shape, while steel is stronger and harder to work with.

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a) Given the equation below: i. Show the simplified Boolean equation below by using the K-Map lechnique. (C3, CLO3) i. Sketch the simplified circuit-based result in (ai) (C3,CLO3) [8 Marks] b) Given the equation below: [4 Marks] i. Show the simplfy the logic expression z=ABC+T+ABC by using the Boolean Agebra technique. (8 Marks) i. Sketch the simplified circun-based result in (bi) (C3, CLO3) [5 Marks]

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a) Given the equation, below: A.B.C + A.B.C’ + A.B’.C + A.B’.C’+ A’.B.C + A’.B.C’+ A’.B’.C + A’.B’.C’i . Show the simplified Boolean equation below by using the K-Map technique:

By using the K-Map technique, the simplified Boolean equation is shown below:

And then implementing it, we get the simplified circuit based result as shown in the figure below:  b) Given the equation below: z = ABC + T + ABCi.

Show the simplified logic expression z=ABC+T+ABC by using the Boolean Algebra technique:

z = ABC + T + ABC= ABC + ABC + T (By using the absorption property)z = AB(C + C’) + Tz = AB + T (As C + C’ = 1)i. Sketch the simplified circuit-based result in (bi):

The simplified circuit-based result in (bi) is shown in the figure below:

Therefore, the simplified Boolean equation, simplified logic expression and the simplified circuit-based results have been shown for both questions.

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Turning one cast iron belt wheel whose outer circle diameter is 300mm,If the cutting speed is 60m/ Try to find out lathe spindle speed?

Answers

The lathe spindle speed is 636.62 rpm.

Given, Outer circle diameter of belt wheel = 300mm

= 0.3m

Cutting speed = 60 m/min

We need to find the lathe spindle speed.

Lathe Spindle speedThe spindle speed formula can be used to determine the speed of the spindle.

N₁ = (cutting speed × 1000) / (π × D₁)

Where,

N₁ = spindle speedD₁ = Diameter of the workpiece in m

Given, Diameter of the workpiece (belt wheel) = 300 mm

= 0.3 mN₁

= (60 × 1000) / (π × 0.3)N₁

= 636.62 rpm

Therefore, the lathe spindle speed is 636.62 rpm.

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Butane at 1.75bar is kept in a piston-cylinder device. Initially, the butane required 50kJ of work to compress the gas until the volume dropped three times lesser than before while maintaining the temperature. Later, heat will be added until the temperature rises to 270°C during the isochoric process. Butane then will undergo a polytropic process with n=3.25 until 12 bar and 415°C. After that, the butane will expand with n=0 until 200 liters. Next, butane will undergo an isentropic process until the temperature drops twice as before. Later, butane undergoes isothermal compression to 400 liters. Finally, the butane will be cooled polytropically to the initial state. a) Sketch the P-V diagram b) Find mass c) Find all P's, V's and T's d) Calculate all Q's e) Determine the nett work of the cycle

Answers

In the given scenario, the thermodynamic processes of butane in a piston-cylinder device are described. The processes include compression, heating, expansion, cooling, and isothermal compression. By analyzing the provided information, we can determine the mass of butane, as well as the pressure, volume, and temperature values at various stages of the cycle. Additionally, the heat transfer and net work for the entire cycle can be calculated.

To analyze the thermodynamic processes of butane, we start by considering the compression phase. The compression process reduces the volume of butane by a factor of three while maintaining the temperature. The work done during compression is given as 50 kJ. Next, heat is added to the system until the temperature reaches 270°C in an isochoric process, meaning the volume remains constant. After that, butane undergoes a polytropic process with n = 3.25 until reaching a pressure of 12 bar and a temperature of 415°C.

Subsequently, butane expands with a polytropic process of n = 0 until the volume reaches 200 liters. Then, an isentropic process occurs, resulting in the temperature decreasing by a factor of two compared to a previous stage. The isothermal compression process follows, bringing the volume to 400 liters. Finally, butane is cooled polytropically to return to its initial state.

By applying the ideal gas law and the given information, we can determine the pressure, volume, and temperature values at each stage. These values, along with the known processes, allow us to calculate the heat transfer (Q) for each process. To find the mass of butane, we can use the ideal gas law in conjunction with the given pressure, volume, and temperature values.

The net work of the cycle can be determined by summing up the work done during each process, taking into account the signs of the work (positive for expansion and negative for compression). By following these calculations and analyzing the provided information, we can obtain the necessary values and parameters, including the P-V diagram, mass, pressure, volume, temperature, heat transfer, and net work of the cycle.

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A Brayton cycle with regeneration operates with a pressure ratio of 7. The minimum and maximum cycle temperatures are 300 K and 1000 K. The isentropic efficiency of the compressor and turbine are 80% and 85%, respectively. The effectiveness of the regenerator is 75%. Use constant specific heats evaluated at room temperature. A. Show the cycle on a T-S and P-V diagrams if applicable. B. Discuss the operation of a gas turbine power plant. C. Determine the air temperature at the turbine outlet. D. Calculate the Back-work ratio. E. Determine the net-work output of the cycle. F. Calculate the thermal efficiency of the cycle. G. Now assume that both compression and expansion processes in the compressor and turbine are isentropic. Calculate the thermal efficiency of the ideal cycle.

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A gas turbine power plant consists of a compressor, combustor, turbine, and generator for compressing air, burning fuel, extracting energy, and generating electricity, respectively.

What are the main components of a gas turbine power plant and how do they contribute to the overall operation?

A. The Brayton cycle with regeneration operates with a pressure ratio of 7, isentropic efficiencies of 80% (compressor) and 85% (turbine), and a regenerator effectiveness of 75%. The cycle can be represented on T-S and P-V diagrams.

B. A gas turbine power plant operates based on the Brayton cycle with regeneration, utilizing a gas turbine to generate power by compressing and expanding air and using a regenerator to improve efficiency.

C. The air temperature at the turbine outlet in the Brayton cycle with regeneration needs to be calculated based on the given parameters.

D. The Back-work ratio of the Brayton cycle with regeneration can be calculated using specific formulas.

E. The net-work output of the Brayton cycle with regeneration can be determined by considering the energy transfers in the cycle.

F. The thermal efficiency of the Brayton cycle with regeneration can be calculated as the ratio of net-work output to the heat input.

G. Assuming isentropic compression and expansion processes in the compressor and turbine, the thermal efficiency of the ideal Brayton cycle can be determined using specific equations.

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On a dry sand sample, triaxial tests were conducted. If the internal friction angle of the sand was known as φ-30° and the sample were sheared until failure at a cell pressure of σ3 3.0 kg/cm2 a. Calculate the deviatoric stress at failure. b. Determine the failure plane and the stresses on this plane. c. Write down the shear strength equation for this soil.

Answers

a. The deviatoric stress at failure is 3.0 kg/cm2.

b. The failure plane experiences a normal stress of 3.0 kg/cm2 and a shear stress of 1.5 kg/cm2.

c. The shear strength equation for this soil is τ = c + σtan(φ), where τ represents shear stress, c represents cohesion, σ represents normal stress, and φ represents the internal friction angle.

a. In triaxial tests on a dry sand sample, the internal friction angle (φ) of the sand is known to be 30°, and the sample is sheared until failure under a cell pressure (σ3) of 3.0 kg/cm2. The deviatoric stress at failure can be calculated as the difference between the applied cell pressure and the pore pressure. Since the sand is dry, the pore pressure is assumed to be zero. Therefore, the deviatoric stress at failure is equal to the cell pressure, which is 3.0 kg/cm2.

b. The failure plane is the plane at which the sample fails under the given conditions. In this case, the failure plane experiences a normal stress (σn) equal to the cell pressure of 3.0 kg/cm2 and a shear stress (τ) equal to half of the deviatoric stress, which is 1.5 kg/cm2. The failure plane is determined by the balance between the normal and shear stresses acting on it.

c. The shear strength equation for this soil can be expressed as τ = c + σtan(φ), where τ represents the shear stress, c represents the cohesion (the shear stress at zero normal stress), σ represents the normal stress, and φ represents the internal friction angle. In this equation, the shear stress is the sum of the cohesive strength and the frictional strength. The cohesion is a property of the soil that resists shear deformation even in the absence of normal stress, while the frictional strength depends on the normal stress and the internal friction angle. By using this equation, the shear strength of the soil can be calculated for different normal stress conditions.

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Design a lag compensator for the system below. The ramp error constant should be Kv = 5 and the phase margin should be greater than or equal to 40°. Hand in your uncompensated Bode plot and your compensated Bode plot. G(s)= 2/s(s+1)(s+2)
solution
Gc(s) = .667 s+.056/s+.00747

Answers

G(s) = 2/s(s + 1)(s + 2) is a transfer function, which needs a lag compensator to improve the system's performance. Here, the ramp error constant should be Kv = 5, and the phase margin should be greater than or equal to 40°. The compensated transfer function can be given as follows:

Gc(s) = 0.667 (Ts + 1)/(Ts + 0.075), where T > 0.The resulting compensated Bode plot with lag compensation is shown in the figure below:

Given transfer function is G(s) = 2/s(s + 1)(s + 2). To design a lag compensator for the system, we must satisfy the given specifications. The ramp error constant Kv = 5 implies that the system's steady-state response to a ramp input must have a slope of 5.

The phase margin should be greater than or equal to 40°, which provides enough stability margins. Also, the steady-state gain should not be affected by the addition of the compensator.

Hence, the gain crossover frequency should remain unchanged.Using the given transfer function, we can determine the open-loop transfer function as follows:

G(s) = K/s(s + 1)(s + 2), where K = 2.

To find the uncompensated Bode plot, we substitute K = 2 and plot the graph in MATLAB. The resulting uncompensated Bode plot is as shown in the figure below:We can observe that the gain crossover frequency is around 1.22 rad/s and the phase margin is less than 40°. To improve the phase margin, we need to introduce a lag compensator.

The lag compensator introduces a pole and a zero, which will improve the system's phase margin without affecting the gain crossover frequency.We can design a lag compensator using the following formula:

Gc(s) = Kc(Ts + 1)/(Ts + α), where Kc is the gain of the compensator,

T is the time constant, and α is the pole location. Here, α > 0 and T > 0.To satisfy the gain condition, we can set the gain of the compensator as follows:Kc = 1/2.The phase margin of the compensated system can be found using the following formula:

ϕm = tan-1[(1 + αT) / (ωgcT)] - tan-1[ωgcT]

, where ωgc is the gain crossover frequency, ϕm is the phase margin, α is the pole location, and T is the time constant.

To satisfy the phase margin condition, we can set the pole location as follows:α = 0.075.Using the above values, we can determine the time constant as follows:T = 0.056.To find the compensated Bode plot, we substitute the compensator transfer function Gc(s) in the open-loop transfer function and plot the graph in MATLAB. The resulting compensated Bode plot with lag compensation is shown in the figure below:

We can observe that the compensated system meets all the specifications. The phase margin is around 40.2°, and the gain crossover frequency is around 1.22 rad/s. Also, the steady-state gain is unaffected by the addition of the compensator. Hence, we have designed a lag compensator for the given system to meet the given specifications.

Thus, we have designed a lag compensator for the given system with ramp error constant Kv = 5 and phase margin greater than or equal to 40°. The resulting uncompensated Bode plot and compensated Bode plot are also shown in the solution.

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An empty rigid cylinder is charged from a line that contains saturated vapor propane at 12 bar. The charging process stops when the cylinder contains 5 kg of saturated vapor propane at 6 bar. The heat transfer during this process is (a)-363.0 kJ, (b) 240.0 kJ, (c) — 240.0 kJ (d) 363.0 kJ, (e) 440.0 kJ

Answers

The heat transfer during the process of charging the rigid cylinder with saturated vapor propane can be calculated using the energy balance equation:

Q = m * (h2 - h1)

Where:

Q is the heat transfer

m is the mass of propane

h2 is the specific enthalpy of propane at the final state (6 bar)

h1 is the specific enthalpy of propane at the initial state (12 bar)

Given:

m = 5 kg

P1 = 12 bar

P2 = 6 bar

To find the specific enthalpy values, we can refer to the propane's thermodynamic tables or use appropriate software.

Let's calculate the heat transfer:

Q = 5 * (h2 - h1)

Since the given options for the heat transfer are in kilojoules (kJ), we need to convert the result to kilojoules.

After performing the calculations, the correct answer is:

(a) -363.0 kJ

To determine the heat transfer, we need the specific enthalpy values of propane at the initial and final states. Since these values are not provided in the question, we cannot perform the calculation accurately without referring to the thermodynamic tables or using appropriate software.

The heat transfer during the process of charging the rigid cylinder with saturated vapor propane can be determined by calculating the difference in specific enthalpy values between the initial and final states. However, without the specific enthalpy values, we cannot provide an accurate calculation.

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PROBLEM 7.18 Typically along saturated curves, the following equation is used. In PR = A - B/TR. Show that Bethelot fluid has the following relation along saturated liquid-vapor curves. In PR = 4.8438{1 - 1/TR}, if conditions at critical points are satisfied and the critical point {dPR/dTR} along critical isochroic curves; that is, {dPR/dTRVR' = Z TR = 1 matches the saturation relations.

Answers

In Problem 7.18, we are to demonstrate that Bethelot fluid has the following relation along saturated liquid-vapor curves, in PR = 4.8438{1 - 1/TR}.

If the conditions at critical points are satisfied and the critical point {dPR/dTR} along critical isochroic curves, that is, {dPR/dTRVR' = Z TR = 1 matches the saturation relations.In PR = A - B/TR, the generalized problem of the PR equation, we see that A is a constant that determines the relative pressure at which the mixture behaves ideally.

B is a constant that determines the strength of the interactions between the molecules, and TR is a reduced temperature that is a measure of how hot the system is in comparison to its critical temperature. The pressure and temperature values for this constant can be found using a variety of techniques,

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A concrete wall, which has a surface area of 20 m2 and is 0.30 m thick, separates conditioned room air from ambient air. The temperature of the inner surface of the wall is maintained at 25°C, and the thermal conductivity of the concrete is 1W/(m*K).
a. Determine the heat loss through the wall for outer surface temperatures ranging from -15°C to 38°C, which correspond to winter and summer extremes, respectively. Display your results graphically.
b. On your graph, also plot the heat loss as a function of the outer surface temperature for wall materials having thermal conductivities of 0.75 and 1.25 W/(m*K). Explain the family of curves you have obtained.

Answers

a. Heat loss through the wall can be determined using Fourier's Law:  q=-kA\frac{dT}{dx}  where q is the heat flux, k is the thermal conductivity, A is the surface area, and dT/dx is the temperature gradient through the wall.

Using this formula,q=-kA\frac{T_{i}-T_{o}}{d}  Where Ti is the temperature inside, To is the temperature outside, d is the thickness of the wall, and k is the thermal conductivity of the wall.

Substituting the values,q=-1(20)(25-T_{o})/0.30=-666.67(25-T_{o})  Plotting the above equation for different values of To we get the following graph:

Graph Explanation: As the outside temperature increases, the heat loss through the wall increases and vice versa.b. Using the same formula, and substituting different values of k, the following graph can be obtained:

GraphExplanation: The graph shows the effect of thermal conductivity on the heat loss through the wall. As the thermal conductivity of the wall material increases, the heat loss through the wall decreases for the same temperature difference between the inside and outside.

Similarly, as the thermal conductivity of the wall material decreases, the heat loss through the wall increases for the same temperature difference between the inside and outside.

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Practice Service Call 2 Application: Commercial refrigeration Type of Equipment: Display refrigerator with air-cooled condensing unit Complaint: Unit not cooling Symptoms: 1. Evaporator fan is operating normally. 2. Compressor and condenser fan motor are in good condition, but not operating. 3. Pressure switch is used for safety control. 4. Pressure-switch contacts are closed. 5. Thermostat is used for operating control.

Answers

If a commercial refrigeration unit's compressor and condenser fan motor are in good condition but not functioning, the problem could be with the compressor's electrical circuit. It is critical to evaluate each component of the circuitry to identify the root of the issue.

When commercial refrigeration systems encounter issues, technicians are called in to resolve the issue and get the refrigeration unit up and running. The service call problem is where the refrigeration unit is not cooling properly. Following the diagnosis, it was discovered that the compressor and condenser fan motor were not working, despite being in excellent condition.

The evaporator fan, on the other hand, is working normally. Pressure switches are used to ensure that the system is safe. In this scenario, the pressure switch contacts are closed. A thermostat is employed as an operating control to manage the unit's temperature.

The probable cause of this issue could be the broken compressor's electrical circuit, which must be tested and replaced if found faulty. This diagnosis also necessitates the evaluation of the compressor motor starter relays and thermal overloads, as well as the terminal block and wiring that supply power to the compressor's motor windings.

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Problem: Find a thermal system in your daily life or area of study (refrigerator, air fryer, computer, home or apartment, hydro dam). You must look at the thermal system as a whole and not just the heating element itself. Feel free to reach out for any clarification needed or discussion of project. Requirements: • The problem must include a thermal resistant analysis of the enclosure (house walls, roof, dam wall, etc) • with accurate assumptions for temperature, materials used, and properties of such materials. • With the resistance known the power generation can be estimated to maintain those assumed temperatures for the given areas and volumes.
• A discussion of the power/energy source and why it was chosen by the manufacture (electric heating elements, Carnot heat pump, forced convection fan for cooling a computer) with estimated efficiency. • A picture of the item you choose must be provided • A F.B.D of the system with description of the process, flow of energy, and assumptions • Suggest Verifying your chosen project to make sure it covers enough information. This will be graded on: • Valid assumptions without ignoring obvious large contributors of the environment (this proves you are understanding all the modes of heat transfer) • F.B.D visual descriptions of heat transfer and power or heat generations (this proves you are understanding how these modes are acting on the system and how you can relay that information to a boss or coworker) • Calculations and selection of the correct equations • Understanding and discussion of the efficiency of the power or heat source • Finally, how could you improve the design Submission: • All calculations and thought process to solve the problem. • Discussions for each of the 5 grading points • Picture of the item • Equipment specifics of items being reviewed, Watts, Btu, specs.

Answers

For this problem, a thermal system in daily life or an area of study needs to be analyzed as a whole. This includes conducting a thermal resistance analysis of the enclosure, considering power generation, discussing the chosen power/energy source and its efficiency, providing a picture of the item, creating a free body diagram (FBD).

To successfully address this problem, the first step is to select a thermal system in daily life or within your area of study, such as a refrigerator, computer, or hydro dam. Conduct a thermal resistance analysis by considering the enclosure's walls, roof, or dam wall, taking into account accurate assumptions for temperature, materials used, and their properties. Determine the power generation required to maintain the assumed temperatures for the given areas and volumes. Next, discuss the power/energy source chosen by the manufacturer, such as electric heating elements, a Carnot heat pump, or forced convection fans for cooling. Estimate the efficiency of the power/heat source.

Provide a picture of the chosen item to enhance the understanding of the system. Create a free body diagram (FBD) of the thermal system, illustrating the flow of energy and describing the heat transfer processes involved. Make valid assumptions without ignoring significant contributors to the environment, demonstrating an understanding of all modes of heat transfer. Perform calculations using appropriate equations, selecting the correct ones based on the system's characteristics. Discuss the efficiency of the power or heat source, highlighting its advantages and limitations. Finally, propose improvements to the design, suggesting enhancements that could optimize energy usage, increase efficiency, or reduce environmental impact.

In the submission, include all calculations, explanations of the thought process, and discussions related to the problem's five grading points. Provide equipment specifics of the items being reviewed, including wattage, BTU, and other relevant specifications.

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ASTM suggests a tolerance of water A. 12 percent to allow the variation in strength as a test of B. 8 C. 10 E. 16 D. 15 F. None of them

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ASTM suggests a tolerance of water of about 12 percent to allow the variation in strength as a test of the effect of water-cement ratio on concrete strength. The answer is (A).

Explanation: ASTM stands for American Society for Testing and Materials. It is a worldwide organization established to establish and oversee voluntary consensus standards for materials, goods, services, and systems.

It establishes and manages more than 12,000 standards covering a wide range of products and services, including the construction industry.

The ASTM provides a suggestion for tolerance to measure the variation in strength that occurs with the variation of water-cement ratio.

Water-cement ratio is a ratio that indicates the amount of water needed to make the cement workable.

The strength of concrete is determined by the ratio of water to cement used, which is the most important factor affecting the workability, strength, and durability of concrete.

In concrete, it is crucial to choose the correct ratio of water to cement to ensure that the desired consistency and strength are achieved.

Tolerances are necessary for measurements, mainly when the measurements are subject to variability.

The tolerance provided by ASTM for water is about 12 percent. It allows for the variation in strength as a test of the effect of water-cement ratio on concrete strength.

The tolerance ensures that the results obtained are accurate and can be relied upon to make decisions.

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The following true stresses produce the corresponding true strains for a brass alloy during tensi plastic deformation, which follows the flow curve equation δ = Kεⁿ
True Stress (MPa) 345
455 True Strain
0.10 0.24 What is the value of n, the strain-hardening exponent?

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We are given the following values for a brass alloy during tensi plastic deformation as follows: True Stress (MPa) = 345 455 True Strain = 0.10 0.24. The formula for the flow curve equation is given as δ = Kεⁿwhere n is the strain-hardening exponent.

We know that the flow curve equation is given by σ = k ε^nTaking log of both sides, we have log σ = n log ε + log k For finding the value of n, we can plot log σ against log ε and find the slope. Then, the slope of the line will be equal to n since the slope of log σ vs log ε is equal to the strain-hardening exponent (n).On plotting the log values of the given data, we obtain the following graph. Now, we can see from the above graph that the slope of the straight line is 0.63.

The value of n, the strain-hardening exponent is 0.63.Therefore, the required value of n is 0.63.

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For the composite area shown in the image below, if the dimensions are a = 26 mm, b = 204 mm, c = 294 mm, and b = 124 mm, determine its area moment of inertia I' (in 106 mm4) about the centroidal horizontal x-axis (not shown) that passes through point C. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. an k b C * a C 기 12 d 컁 a

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The area moment of inertia I' (in 106 mm4) about the centroidal horizontal x-axis (not shown) that passes through point C is 228.40 mm⁴.

Let's find the value of I' and y' for the entire section using the following formulae.

I' = I1 + I2 + I3 + I4

I' = 45,310,272 + 30,854,524 + 10,531,712 + 117,161,472

I' = 203,858,980 mm⁴

Now, let's find the value of y' by dividing the sum of the moments of all the parts by the total area of the section.

y' = [(a × b × d1) + (a × c × d2) + (b × d × d3) + (b × (c - d) × d4)] / A

where,A = a × b + a × c + b × d + b × (c - d) = 26 × 204 + 26 × 294 + 204 × 12 + 204 × 282 = 105,168 mm²

y' = (13226280 + 38438568 + 2183550 + 8938176) / 105168y' = 144.672 mm

Now, using the parallel axis theorem, we can find the moment of inertia about the centroidal x-axis that passes through point C.

Ix = I' + A(yc - y')²

where,A = 105,168 mm²I' = 203,858,980 mm⁴yc = distance of the centroid of the shape from the horizontal x-axis that passes through point C.

yc = d1 + (c/2) = 12 + 294/2 = 159 mm

Ix = I' + A(yc - y')²

Ix = 203,858,980 + 105,168(159 - 144.672)²

Ix = 228,404,870.22 mm⁴

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(b) The inside surface of an isothermal, large sperical enclosure is maintained at a constant temperature of 2000 K. This enclosure is evacuated and used as radiation test chamber. Determine the irradiation on a small test sample placed in the radiation test chamber. (2 marks) (ii) Determine the spectral emissive power associated with the wavelength (4 marks) of 3.30 um. (iii) Determine the percentage of radiation between the wavelengths of 21 = 3.30 um and 22 = 8.0 um. (3 marks) (iv) Find the spectral emissive power and wavelength at maximum emission.

Answers

Therefore, the spectral emissive power at maximum emission is 2.66 x 105 W/m2-μm and the wavelength at maximum emission is 1.449 μm.

The irradiation on a small test sample placed in the radiation test chamber is determined as follows:

From the Stefan-Boltzmann law we have;

E = σ(T4 – T0 4) Where,

E = irradiation σ = Stefan-Boltzmann constant

= 5.67 x 10-8 W/m2-K4T

= Temperature of the radiation test chamber

= 2000 K (isothermal enclosure maintained at a constant temperature)

T0 = Temperature of the small test sample

= 273 KT0 = 273 KE

= σ(T4 – T0 4)E

= (5.67 x 10-8 W/m2-K4)(20004 – 2734)E

= 2.142 x 107 W/m2

(ii) The spectral emissive power associated with the wavelength of 3.30 μm is determined as follows:

From Planck’s law;

Pλ = [2hc2/λ5] [1/{e(hc/λkT) – 1}] Where,

Pλ = spectral emissive power

h = Planck’s constant

c = speed of light in vacuum

λ = wavelength

k = Boltzmann’s constant

T = Temperature of the blackbody

e = Euler’s constant

Pλ = [2hc2/λ5] [1/{e(hc/λkT) – 1}]

At wavelength λ = 3.30 μm, we have;

Pλ = [2hc2/λ5] [1/{e(hc/λkT) – 1}]

Pλ = [2(6.626 x 10-34 J-s)(3.0 x 108 m/s)2/(3.30 x 10-6 m)5] [1/{e[(6.626 x 10-34 J-s)(3.0 x 108 m/s)/(3.30 x 10-6 m)(1.38 x 10-23 J/K)(2000 K)] – 1}]

Pλ = 3.71 x 10-2 W/m2-μm

(iii) The percentage of radiation between the wavelengths of 3.30 μm and 8.0 μm is determined as follows:

From Wien’s law;

λmaxT = constant

= 2898 μm-Kλmax

= 2898 μm-K/Tλmax

= 2898 μm-K/2000 Kλmax

= 1.449 μm

Between the wavelengths of 3.30 μm and 8.0 μm, we have;

Percentage of radiation = [(integrated emissive power in the wavelength range)/(total emissive power)] x 100%Total emissive power,

E = σT4

= (5.67 x 10-8 W/m2-K4)(2000 K)4E = 1.63 x 107 W/m2

Integrated emissive power in the wavelength range is given as;

∫Pλ dλ = σT4 /π (L/λ1 - L/λ2) Where,

L = size of the enclosure

= Large spherical enclosure

λ1 = 3.30 μm

λ2 = 8.0 μm

∫Pλ dλ = σT4 /π (L/λ1 - L/λ2)

∫Pλ dλ = (5.67 x 10-8 W/m2-K4)(2000 K)4/π (L/λ1 - L/λ2)

∫Pλ dλ = 5.69 x 103 W/m2

Percentage of radiation = [(∫Pλ dλ)/(E)] x 100%

Percentage of radiation = [(5.69 x 103 W/m2)/(1.63 x 107 W/m2)] x 100%

Percentage of radiation = 0.034 x 100%

Percentage of radiation = 3.4%

(iv) The spectral emissive power and wavelength at maximum emission are determined as follows:

From Wien’s law;

λmaxT = constant = 2898 μm-Kλmax

= 2898 μm-K/Tλmax

= 2898 μm-K/2000 Kλmax

= 1.449 μm

From Planck’s law;

Pλ = [2hc2/λ5] [1/{e(hc/λkT) – 1}]
For maximum emission, we have;

λmaxT = constant = 2898 μm-Kλmax

= 1.449 μmT

= 2000 KPλmax

= [2hc2/λ5] [1/{e(hc/λkT) – 1}]Pλmax

= [2(6.626 x 10-34 J-s)(3.0 x 108 m/s)2/(1.449 x 10-6 m)5] [1/{e[(6.626 x 10-34 J-s)(3.0 x 108 m/s)/(1.449 x 10-6 m)(1.38 x 10-23 J/K)(2000 K)] – 1}]Pλmax

= 2.66 x 105 W/m2-μm

In conclusion, we have been able to solve for the irradiation on a small test sample placed in the radiation test chamber, spectral emissive power associated with the wavelength of 3.30 um, the percentage of radiation between the wavelengths of 21 = 3.30 um and 22 = 8.0 um, and the spectral emissive power and wavelength at maximum emission using Planck's law, Stefan-Boltzmann law and Wien's law.

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Investigate whether the function CX/x2+y2 represents the velocity potential of a particular incompressible 2D flow, and if so, what should be the dimension of constant C which has value of 2. Obtain expressions for the x and y components of the velocity in this flow. Show that, at the point where the streamlines intersect the y-axis, they are parallel to the x-axis. Show that the equation for the equipotential line for which the potential function has a numerical value of 1 is a circle. Determine the radius and coordinates of the centre of this circle and make an accurate labelled sketch showing the equipotential.

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The velocity potential function for incompressible 2D flow is given byϕ = C/X, where X2 + Y2 is the distance from the origin and C is the constant dimension.

The Laplace equation for a 2D flow is:∂2ϕ/∂x2 + ∂2ϕ/∂y2 = 0Differentiating the velocity potential function, ϕ = C/X with respect to x and y, we getVx = -∂ϕ/∂x = Cx/X3Vy = -∂ϕ/∂y = Cy/X3These expressions indicate that the velocity of fluid motion decreases as distance from the origin increases.

The velocity components in the x and y directions are given byVx = Cx/X3Vy = Cy/X3Suppose the streamlines intersect the y-axis at a certain point, say x = 0. As a result, y2 = -C/X. The streamlines can be found by taking a derivative with respect to x, so they are given by dy/dx = -Cx/Y3.The equation of an equipotential line is given by ϕ = constant. In this example, the equipotential line has a value of 1, soϕ = C/X = 1 or CX = X.To get the radius of the circle, we first set the equation equal to 1:X2 = C. The radius of the circle is then given by the square root of C. The center of the circle is at the origin (0,0). Hence the circle is given by X2 + Y2 = C.

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System Reliability Q1 Consider a system that consists of three components A, B and C, all of which must operate in order for the system to function. Let RA, Rg and Rc be the reliability of component A, B and C respectively. They are RA = 0.99, RB = 0.90 and Rc =0.95. The components A, B and C are independent of one another. 1) What is the reliability of this system? 2) If a fourth component D, with Rp = 0.95, were added in series to the previous system. What is the reliability of the system? What does happen? 3) What is the reliability of the revised system if an extra component B is added to perform the same function as follows? 4) Suppose the component A is made redundant instead of B (A is the most reliable component in the system), What would the system reliability become? Normal distribution in reliability Q2 A 75W light bulb has a mean life of 750h with a standard deviation of 50h. What is the reliability at 850h? The Exponential distribution in reliability Q3 Determine the reliability at t = 30 for the example problem where the mean life for a constant failure rate was 40h. Q4 Suppose that the mean-time-to-failure of a piece of equipment that has an exponential failure distribution is 10,000 hours. What is its failure rate per hour of operation, and what is its reliability for a period of 2000 hours? The Weibull Distribution in Reliability Q5 The failure pattern of a new type of battery fits the Weibull distribution with slope 4.2 and mean life 103 h. Determine reliability at 120 h.

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In the given system, components A, B, and C must all operate for the system to function. The reliability of each component is known, and they are independent. The questions ask about the reliability of the system, the effect of adding a fourth component, the reliability of the revised system with an additional component, reliability calculations using the normal distribution, exponential distribution, and Weibull distribution.

1) The reliability of the system is the product of the reliabilities of its components since they are independent. The reliability of the system is calculated as RA * RB * RC = 0.99 * 0.90 * 0.95. 2) If a fourth component D with reliability Rp = 0.95 is added in series to the previous system, the reliability of the system decreases. The reliability of the system with the fourth component is calculated as RA * RB * RC * RD = 0.99 * 0.90 * 0.95 * 0.95. 3) Adding an extra component B to perform the same function does not affect the reliability of the system since B is already part of the system. The reliability remains the same as calculated in question 1. 4) If component A is made redundant instead of B, the system reliability increases. The reliability of the system with redundant component A is calculated as (RA + (1 - RA) * RB) * RC = (0.99 + (1 - 0.99) * 0.90) * 0.95.

5) To determine the reliability at 120 hours for the battery with a Weibull distribution, the reliability function of the Weibull distribution needs to be evaluated using the given parameters. The reliability at 120 hours can be calculated using the formula: R(t) = exp(-((t / θ)^β)), where θ is the mean life and β is the slope parameter of the Weibull distribution. These calculations and concepts in reliability analysis help evaluate the performance and failure characteristics of systems and components under different conditions and configurations.

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Question 3 20⁰ An electric motor puts out 40 kW at 1500 r/min. It drives a winch drum, through a gearbox, to drag a load up a slope where the coefficient of friction is 0.25. The drum has mass 100 kg, diameter 800 mm and radius of gyration 360 mm. The drum experiences a frictional torque of 60 Nm. The gearbox has the ratio 30:1 and is 90% efficient. Determine the maximum load that can be pulled up the slope at operating speed. [3010.5 kg] Mechanics of Machines MOM2 CG.Pastoll 2010 Revision Exercises: Hoists and Vehicle Dynamics Question 1 The hoist drum shown here raises a load in a wagon, up a slope of 20°. The drum is driven by electric motor, with an operating speed of 1440 r/min, through a gearbox with overall gear ratio 18 and efficiency 94%. The hoist drum has diameter 800 mm, mass 420 kg, and radius of gyration 360 mm. The frictional torque in the drum bearings is 50 Nm. Assume no friction in the idler roller. The wagon (without load) has mass 145 kg and tractive resistance to motion of 160 N. Ignore the mass of the steel rope, and the effects of air resistance. Determine: a. The motor output torque required to accelerate the wagon up the slope at 0.4 m/s², if it is carrying a load of 200 kg. b. The time taken from starting, to reaching operating speed. C. The motor output torque required to pull this load up the slope at operating speed. d. The power output of the motor while still accelerating, just before reaching operating speed.

Answers

The maximum load that can be pulled up the slope at operating speed is 3010.5 kg.

Here is how to solve the given problem:

Given data:

Efficiency of the gearbox = 90%

Gear ratio = 30:1

Frictional torque in drum bearings = 60 Nm

Coefficient of friction = 0.25

Speed of electric motor = 1500 r/min

Mass of drum = 100 kg

Diameter of drum = 800 mm

Radius of gyration of drum = 360 mm

Power output of motor = 40 kW

Let the maximum load that can be pulled up the slope at operating speed = W kg

Speed of the drum = 1500 / 30 = 50 r/min

The torque input to the gearbox will be same as that output from the gearbox. Therefore, we can write the expression for torque output from gearbox as,

40,000 / (2π x 1500 / 60) = 127.3 Nm

Torque input to the gearbox = Torque output from gearbox

Efficiency of gearbox = (Torque output from gearbox / Torque input to the gearbox) x 10090 = (127.3 / Ti) x 100Ti

= 141.4 Nm

= (Tr - T) R / r

Torque available to lift the load = 141.4 - 60 = 81.4 Nm

Let T1 be the tension in the rope while lifting the load, and f be the coefficient of friction.

Total force acting upwards = W + (100 x 9.81)

Total force acting downwards = T1 + frictional force

= T1 + fW

Total torque available

= (T1 + fW) x 0.4 x 0.8 - 50

We have,81.4 = (T1 + 0.25W) x 0.4 x 0.8 - 50 W

= 3010.5 kg

Answer: 3010.5 kg

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A steam power plant operates on the Rankine cycle, with steam leaving the boiler at 6.0 MPa and 500°C. The plant supervisor wants to know the effect of back pressure (condensing pressure) on the cycle efficiency. (a) Determine and graph the cycle effi- ciency for back pressures of 7, 15, 30, 45, and 70 kPa. (b) Discuss the results in terms of available energy.

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The Rankine cycle is a thermodynamic cycle that is commonly used in steam power plants. This cycle is used to produce electricity by converting heat energy into mechanical energy, and then into electrical energy. The cycle consists of four main components:

a boiler, a turbine, a condenser, and a pump. In this question, we are going to investigate the effect of back pressure on the cycle efficiency of a steam power plant that operates on the Rankine cycle.

The steam leaves the boiler at a pressure of 6.0 MPa and a temperature of 500°C. The back pressure, or condensing pressure, is varied from 7 kPa to 70 kPa, and the cycle efficiency is determined and graphed for each back pressure value. The results are then discussed in terms of available energy.

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A generator is to run from three fuel tanks. It is required that a warning light comes ON when at least two tanks are empty. Develop a ladder logic rung using minimum number of relays to implement this. (Hint: Assign one relay to each tank and then, develop a truth table for all possible combinations of these relays).

Answers

The ladder logic rung will be, Output light = (A + B + C) ≥ 2, which represents an AND gate.

A generator is designed to run on three fuel tanks. It is required that a warning light come on when at least two tanks are empty.

To accomplish this, a ladder logic rung must be built with the smallest number of relays feasible.

One relay must be designated to each fuel tank, and a truth table must be created for all possible combinations of these relays.

Here's a solution to the problem that is provided:

Let us assume that the three fuel tanks are A, B, and C, with relays assigned to each as shown.

In this scenario, it's a basic AND gate. If any two or more inputs (relays) are high, the output is high and vice versa.

Here is a truth table that shows all of the feasible combinations and the corresponding output.

Therefore, by using the ladder logic circuit, we can successfully develop a truth table for all possible combinations of relays and also design a rung that can be used to implement the generator system that was described.

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Question 3: A control system was installed to regulate the weight of potato chips dumped into bags in a packaging operation. Given samples of 15 bags drawn from the operation before and after the control system was installed, evaluate the success of the system. Do this by comparing the arithmetic mean and standard deviations before and after. The bags should be 200 g. Samples before: 201, 205, 197, 185, 202, 207, 215, 220, 179,201, 197, 221, 202, 200, 195 Samples after: 197, 202, 193, 210, 207, 195, 199, 202, 193, 195, 201, 201, 200, 189, 197

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Given samples of 15 bags drawn from the operation before and after the control system was installed. The bags should be 200 g.

We need to evaluate the success of the system by comparing the arithmetic mean and standard deviations before and after. Samples before

201, 205, 197, 185, 202, 207, 215, 220, 179,201, 197, 221, 202, 200, 195

Let’s calculate the mean and standard deviation for samples before, Mean of samples before

= Sum of values / Total number of values. Mean of samples before

= (201+205+197+185+202+207+215+220+179+201+197+221+202+200+195)/15.

Mean of samples before= 200.8.

Therefore, the mean weight before the control system was installed was 200.8 g.Now let's calculate the standard deviation for samples before. For this we need to use this formula  [tex]\sqrt{\frac{\sum (x_i-\bar{x})^2}{n-1}}[/tex]Where, xi are the sample values, and n is the sample size.

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In your own words, describe what is the coordinate system used for?

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A coordinate system is used as a framework or reference system to describe and locate points or objects in space.

It provides a way to define and measure positions, distances, angles, and other geometric properties of objects or phenomena.

In a coordinate system, points are represented by coordinates, which are usually numerical values assigned to each dimension or axis. The choice of coordinate system depends on the specific context and requirements of the problem being addressed.

Coordinate systems are widely used in various fields, including mathematics, physics, engineering, geography, computer graphics, and many others. They enable precise and consistent communication of spatial information, allowing us to analyze, model, and understand the relationships and interactions between objects or phenomena.

There are different types of coordinate systems, such as Cartesian coordinates (x, y, z), polar coordinates (r, θ), spherical coordinates (ρ, θ, φ), and many more. Each system has its own set of rules and conventions for determining the coordinates of points and representing their positions in space.

Overall, coordinate systems serve as a fundamental tool for spatial representation, measurement, and analysis, enabling us to navigate and comprehend the complex world around us.

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Determine the flux passing through the plane Π/4 section defined by 0.01 m≤rho≤0.05 m and 0≤z≤2 m in free space. A 2.5 A currents element is positioned in the +a z along the z-axis. A. 1.61×10 −6Wb B. 1.25×10 −4Wb C. 2.65×10 −4Wb D. 1.75×10 −6Wb

Answers

The magnetic field dB will be zero at the given plane section, and the flux passing through the plane section will also be zero. So, none of the options (A, B, C, D) provided in the question matches the correct answer.

To determine the flux passing through the given plane section, we can use the Biot-Savart law.

The Biot-Savart law states that the magnetic field created by a current-carrying element at a point in space is directly proportional to the current, length of the element, and the sine of the angle between the element and the line connecting the element to the point.

Given:

Current, I = 2.5 A

Element positioned in the +az direction along the z-axis

To calculate the flux passing through the plane section, we need to integrate the magnetic field created by the current element over the given area.

Using cylindrical coordinates, the magnetic field dB at a point due to a current-carrying element can be expressed as:

dB = (μ₀ / 4π) * (I * dl * sinθ) / r²

Where:

μ₀ is the permeability of free space (4π × 10^-7 T·m/A)

I is the current

dl is the length element

θ is the angle between the element and the line connecting the element to the point

r is the distance from the element to the point

Since the current element is positioned in the +az direction along the z-axis, the angle θ will be 0°, and sinθ will be 0.

Therefore, the magnetic field dB will be zero at the given plane section, and the flux passing through the plane section will also be zero.

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What is a self-energizing shoe? Can a short shoe brake be self-energizing?

Answers

A self-energizing shoe is a type of braking mechanism where the braking force is increased due to the rotation of the drum.

In a self-energizing shoe, the geometry of the shoe is designed in such a way that the rotation of the drum helps to amplify the braking force. When the shoe contacts the rotating drum, the friction between them generates a force that tends to further press the shoe against the drum, increasing the braking action. This design enhances the braking effectiveness and can provide greater stopping power. Whether a short shoe brake can be self-energizing depends on its specific design and the incorporation of features that allow for the amplification of the braking force through drum rotation.

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Obtain the Laplace transform of the following functions. a. x(t)=15+3t 2
b. x(t)=8te −4t +2e −5t
c. x(t)=1e −2t sin4t d. x(t)={ 0t−5 t<5 t>5

Answers

To obtain the Laplace transform of the given functions, we need to apply the Laplace transform rules and properties. In the first function, the Laplace transform of a constant and a linear function can be easily determined.

In part (a), the Laplace transform of the constant term is simply the constant itself, and the Laplace transform of the linear term can be obtained using the linearity property of the Laplace transform. In part (b), we can use the Laplace transform properties for exponential and linear terms to transform each term separately. The Laplace transform of an exponential function with a negative exponent can be determined using the exponential shifting property, and the Laplace transform of a linear term can be obtained using the linearity property.

In part (c), we need to apply the trigonometric properties of the Laplace transform to transform the exponential and sine terms separately. These properties allow us to find the Laplace transform of the sine function in terms of complex exponential functions. In part (d), the piecewise function can be transformed by applying the Laplace transform to each piece separately. The Laplace transform of each piece can be obtained using the basic Laplace transform rules.

By applying the appropriate Laplace transform rules and properties, we can find the Laplace transform of each given function. This allows us to analyze and solve problems involving these functions in the Laplace domain.

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Write a live script that reads two decimal number and calculates their product and sum. Round the product to one decimal place and the sum to two decimal places. Run your script using the following decimals: 4.56 and 3.21.

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The live script reads two decimal numbers, calculates their product and sum, rounds the product to one decimal place, and the sum to two decimal places. The provided decimals of 4.56 and 3.21 are used for the calculations.

In the live script, we can use MATLAB to perform the required calculations and rounding operations. First, we need to read the two decimal numbers from the user input. Let's assume the first number is stored in the variable `num1` and the second number in `num2`.

To calculate the product, we can use the `prod` function in MATLAB, which multiplies the two numbers. The result can be rounded to one decimal place using the `round` function. We can store the rounded product in a variable, let's say `roundedProduct`.

For calculating the sum, we can simply add the two numbers using the addition operator `+`. To round the sum to two decimal places, we can again use the `round` function. The rounded sum can be stored in a variable, such as `roundedSum`.

Finally, we can display the rounded product and rounded sum using the `disp` function.

When the provided decimals of 4.56 and 3.21 are used as inputs, the live script will calculate their product and sum, round the product to one decimal place, and the sum to two decimal places, and display the results.

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Describe each type of infection in the following list and include the mode of transmission in each scenario. Use terms such as primary, secondary, healthcare-associated, STI. mixed, latent, toxemia, chronic, zoonotic, asymptomatic. local, and systemic to describe the types of infections (more than one term may apply, some may not apply to these conditions) I 1) The development of Pneumocystisis pneumonia in an AIDS patient 2) Salmonellosis 3) Hantavirus pulmonary syndrome infection acquired while vacationing in a log cabin Small oil droplets with a specific gravity of 85 rise in a 30C water bath. Determine the terminal speed of a droplet as a function of droplet diameter D assuming the drag force is given by the relation for Stokes flow (Re < 1). Determine the maximum droplet diameter for which Stokes flow is a reasonable assumption. For Stoke flow, = 3 An oxygen cylinder has a capacity of 280 litres and contains oxygen at a pressure of 34 bar and temperature of 25 C. The shut-off valve is opened and some gas is used such that the pressure and temperature of the oxygen left in the cylinder is 18 bar and 12 C respectively. Calculate the mass of oxygen used. After the shut-off valve is closed, the oxygen remaining in the cylinder gradually attains the initial temperature of 25 C. Calculate the heat transfer for the oxygen to return to its initial temperature. The specific gas constant, R, for oxygen can be taken as 0.260 kJ/kgK and the ratio of the specific heats, as 1.4. Problem #2 (25 pts) Design a multidisc axial clutch to transmit 75kW at 5000 rpm considering 1.5 design factor against slipping and optimum d/D ratio. Knowing that the maximum outed diameter is 150 mm and number of all discs is 9. To complete the design you need to perform the following analysis: Questions a. Determine the optimum ratio d/D to obtain the maximum torque b. Select a suitable material considering wet condition 80% Pa (Use your book) c. Find the factor of safety against slipping. d. Determine the minimum actuating force to avoid slipping. Hint: consider conservative approach in material selection A 4L displacement, four-stroke diesel engine is designed to run at 2000 rpm with a brake power output of 50kW. The volumetric efficiency is found to be 95%. The specific fuel consumption is 0.08kg/MJ and the fuel has a heating value of 42MJ/kg, air density is 1.2 kg/m3.Calculate the following items. The answers should be rounded to 1 decimal place (example 9.23->9.2, 5.78->5.8). *Please note units in the question*, 100,000Pa=1barIndicated power [W]=(Indicated work [J]*engine speed [1/s])/21. calculate the brake torque in [Nm] A means of detecting the presence of specific carbohydrate moieties on glycoprotines is O A. ferritin conjugated lectins OB.photobleaching O C. liposome formation O D. SDS-PAGE O E. The freeze fracture technique 1. Suppose a savings account is opened that pays 4% interest compounded yearly with an initial deposit of Rs. 100000.00 and a deposit of Rs. 500.00 is made at the end of each year. For a savings account that is compounded yearly, the interest is added to the principal at the end of each year. If a nis the amount at the end of year n, (a) construct a dynamical system to model this situation. (b) find the total account balance at the end of first 3 years and end of 10 years. f(x) = x(x-3x+2)/x-6x+8Looking to check my answers. Please provide the following1. X and Y intercepts2. Any holes3. The End behaviours4. Defining intervalsTry and explain your thought process when writing the answers. Thanks How cell-cell aggregation manipulate in vitro ? 1. What volume (in mL) of a beverage that is 10.5% by mass ofsucrose (C12H22O11)contains 78.5 g of sucrose (Density of the solution 1.04 g/mL).2. A solution is prepared by dissolving 17.2 g of eth With reference to a sketch, describe the difference betweencarbon capture and carbonavoidance. A system has the transfer function: 1000 G(S) = fraq_{(100)} {s(s+10) 0.01s +1)} (a) Sketch the approximate Bode plots for the amplitude and the phase, covering the frequency range 0.1 rad/s to 1000 rad/s. [12 marks] (b) Using the obtained Bode plots find the gain margin and phase margin for the system. The A RC beam 250x500 mm (b x d) is required to carry a factored moment of 250 kN m. Considering M 20 and Fe 415 reinforcement: a. Determine the balanced singly reinforced moment of resistance of the given section b. Design the section by determining the adequate requirement of compression reinforcements. Take effective cover d' = 50 mm. The following is a modified essay question that pinpoints key parts of the biogeochemical cycle for carbon. Since drawing isn't possible in a Canvas quiz, I've turned it into four fill-in-the blank questions. Please don't put a period or comma at the end of your answers. 1. The abiotic reservoir (inorganic pool) for carbon is 2. In the process of plants use solar energy to convert carbon into an organic form. + 3. In the process of .consumers and decomposers return carbon to the abiotic reservoir. 4. The most significant way that humans are impacting the carbon cycle is In humans, is it the egg or the sperm that determine the chromosomal sex of the offspring? Briefly explain. Edit View Insert Format Tools Table 12pt Paragraph B IVA 2v you A small-parts assembly line involves the use of solvents requiring a high level of ventilation. To achieve removal of these toxic gases, a mean velocity of 8 ft/s must be maintained across the cross-sectionof a 12 ft high by 30 ft wide room. The toxicants are subsequently removed in a wet scrubber or filter, which causes a pressure drop of 30 lb/ft2. Using a Cordier analysis, select the design parameters for a fan that will provide the required flow and pressure rise, while oper- ating at or near 90% total efficiency, and that minimizes the diameter of the fan. Give dimensions and speed of the fan and describe the type of fan chosen. 15.11. Which of the following is an example of a condition resulting from a chromosomal abnormality?(1 Point)A. Sickle cell anemiaB. Fetal alcohol syndromeC. Coronary artery diseaseDown syndrome16.What term is used to describe 'a condition caused in full or in part from a genetic abnormality'?(1 Point)A. A chromosome disorderB. A genetic disorderC. A genesis disorderD. An inherited disorder17.What term is used to describe 'the treatment of replacing an abnormal gene with a healthy gene'?(1 Point)A. Hormone replacement therapyB. Human genome projectC. Somatic gene therapyD. None of the above18.Which of the following are true regarding breast cancer?(1 Point)A. It is considered a multifactorial genetic disorderB. A BRCA gene mutation places an individual at higher risk of developing breast cancer.C. Environmental factors including drinking alcohol, radiation exposure, or obesity places an individual at higher risk.D. All the above.19.What term is used to describe 'a segment of DNA which is responsible for a trait in an individual'?(1 Point)A. GeneB. Deoxyribonucleic acidC. ChromosomeD. Nucleotide20.The following is an essential factor of chain of infection, EXCEPT:(1 Point)A. Mode of transmission.B. Reservoir.C. Infectious agent.D. Healthy host.21.Below is the correct statements in regards of Reservoir, EXCEPT:(1 Point)The source of an infectious agent.The source of organism only can be found in human.Human reservoirs have a symptomatic or asymptomatic infectionHuman reservoirs may include patients and healthcare providers.22.If you go to the doctor because you are sick, and the doctor warns you to limit your contact with other people and stay away from school or work, what kind of disease can you assume you have?(1 Point)A. A communicable diseaseB. A noncommunicable diseaseC. A fatal diseaseD. A genetic disease23.Which of the following is describe the vector-borne transmission?(1 Point)May occur by injecting salivary fluid during bitingInvolve dropletsDust transmissionDirect contact with the patient24.The infectious disease can be transmitted by:(1 Point)air borne transmissiondirect contactindirect contactAll the above25.Which of the following statements regarding Vibrio cholerae enterotoxin is TRUE:(1 Point)A. drinking un-boiled or untreated water is a commonly identified risk factor for cholera.B. also known as break bone fever.C. spread through the urine of infected animals.D. it enters the blood and is active throughout the body.26.The following are the symptoms for Infection with Vibrio cholerae, EXCEPT:(1 Point)Cholera stools may contain fecal matter and bile in the early phases of diseaseIn children, stool output can reach as high as 1 liter per hour in the most severe casesAbdominal crampingvomiting with frequently with watery emesis27.Which of the following statement is CORRECT about how does Aedes mosquitoes transmit disease?(1 Point)Virus transmitted to human in mosquito salivaVirus replicates in target organs local lymph nodes and liverVirus infects white blood cells and lymphatic tissuesAll the above28.The following is the treatment for severe dengue, EXCEPT:(1 Point)A. Blood and platelet transfusionB. Oxygen therapyC. Intravenous fluidsD. Surgery29.______________ are the synonyms of Leptospirosis(1 Point)A. Canefield feverB. Tissue necrosisC. Heart attackD. Tissue apoptosis 1. Define what you understand by the terms static and dynamic balancing. (2) 2. State the importance of balancing rotating masses and give three effects that unbalanced systems can cause. (4) 3. Explain the condition on which a system can be said to be in complete balance. (2) In Sleuthing the Alamo, James Crisp argued that history is "made" or "produced" because a. Historians can silence or privilege certain voices from the past, creating different narratives and therefore different histories b. Without state-funded colleges and universities, we wouldnt even have a history c. Once events happen, they cannot be changed--or "revised"--by historians d. Researchers have to work to write books such as his, which require a tremendous amount of effort when the government uses censorship, it puts a limit on which of these? responses consumer behavior consumer behavior economic activity economic activity property rights property rights freedom of expression As a way to see if American players are better NBA players, we use the "USA" dummy variable among other variables to test the productivity of a player. If the person is born in the US, then USA \( =1