1. Explain the concept of inertial frame of reference. (6 Marks) 2. Explain the concept of work of a force and the principle of work and energy. (7 Marks) 3. Explain the principle of linear impulse and momentum of a system of particles, and conservation of linear momentum. (7 Marks)

Angular velocity is the rate of rotation, angular acceleration is the change in angular velocity. Linear velocity = angular velocity × radius.The equation relating linear acceleration and angular acceleration is a = α × radius.

2. Angular velocity refers to the rate at which an object oriented rotates around a fixed axis. It is a vector quantity and is measured in radians per second (rad/s). Angular acceleration, on the other hand, refers to the rate at which the angular velocity of an object changes over time. It is also a vector quantity and is measured in radians per second squared (rad/s²).

Angular velocity and angular acceleration are related. Angular acceleration is the derivative of angular velocity with respect to time. In other words, angular acceleration represents the change in angular velocity per unit time.

3. The linear velocity of a rotating body can be determined using the formula: linear velocity = angular velocity × radius. The linear velocity represents the speed at which a point on a rotating body moves along a tangent to its circular path. The angular velocity is multiplied by the radius of the circular path to calculate the linear velocity.

4. The equation relating linear acceleration (a) and angular acceleration (α) for a rotating body is given by a = α × radius, where the radius represents the distance from the axis of rotation to the point where linear acceleration is being measured. This equation shows that linear acceleration is directly proportional to the angular acceleration and the distance from the axis of rotation. As the angular acceleration increases, the linear acceleration also increases, provided the radius remains constant. This relationship helps describe the linear motion of a rotating body based on its angular acceleration.

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We have been given the following information: Height of the flat key, h = 7/16 in Length of the flat key, l = 3 in Diameter of the shaft, d = 2 in Allowable bearing stress, τ = 25 ksi To determine the torque in the key, we can use the following formula:τ = (2T)/(hd²)where T is the torque applied to the shaft.

Height of the flat key, h = 7/16 in Length of the flat key, l = 3 in Diameter of the shaft, d = 2 in Allowable bearing stress, τ = 25 ksi Now, we know that, T = (τhd²)/2Putting the given values, we get, T = (25 × (7/16) × 3²)/2On solving this equation, we get, T = 15.24856 in-lb Therefore, the torque in the key is 15.24856 in-lb. We need to calculate the torque in the key of the given shaft. The given bearing stress is τ= 25 K si which is allowable. Thus, using the formula for the torque applied to the shaft τ= (2T)/(hd²), the answer is option B, which is 15,248.56 in-lb.

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One challenge in implementing the 5S system in a mechanical workshop could be resistance to change from the employees. Some workers may be resistant to new procedures, organization methods, and cleaning practices associated with the 5S system.

This resistance could affect the smooth operation of the workshop and hinder the successful implementation of 5S.

Alternate Solution: Employee Training and Engagement

To address this challenge, it is important to provide thorough training and engage employees in the implementation process. Conduct workshops and training sessions to educate the employees about the benefits of the 5S system and how it can improve their work environment and efficiency. Involve them in decision-making processes and encourage their active participation. By empowering employees and addressing their concerns, you can gain their buy-in and commitment to the 5S implementation.

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Smith Watson topper parameter is used to measure the performance of the educational institutions. The main answer to what is meant by the Smith Watson topper parameter is that it is used to measure the efficiency of the educational institutions based on their academic performance.

The top-performing students in the school, college, or university are recognized as the toppers and their scores are used as the benchmark for measuring the performance of the institution. This parameter is calculated by taking the average score of the top 5% students in the institution.Explanation:Smith Watson topper parameter is useful for the following reasons:It helps in determining the overall performance of the institution in terms of academic excellence.The parameter encourages students to work harder and achieve better results.The institutions can use this parameter as a benchmark to evaluate their performance with other institutions in the region or country.The topper parameter helps in identifying the strengths and weaknesses of the institution in terms of academic performance.

The institutions can use this parameter to improve their academic programs and infrastructure to enhance the quality of education.The topper parameter is an effective way to motivate students and faculty members to achieve higher standards in academic performance. It helps in promoting healthy competition among students and institutions.

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True Milled glass fibers are commonly used when epoxy must fill a void, provide high strength, and high resistance to cracking. This statement is true.

Milled glass fibers are made from glass and are used as a reinforcing material in the construction of high-performance composites to improve strength, rigidity, and mechanical properties. Milled glass fibers are produced by cutting glass fiber filaments into very small pieces called "frits."

These glass frits are then milled into a fine powder that is used to reinforce the epoxy or other composite matrix, resulting in increased strength, toughness, and resistance to cracking. Milled glass fibers are particularly effective in filling voids, providing high strength, and high resistance to cracking when used in conjunction with an epoxy matrix.

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At 598°C, the value of the diffusion coefficient (D) for the diffusion of a species in a metal can be calculated using the given values of Do (pre-exponential factor) and Qå (activation energy).

With a Do value of 1.1 × 10-5 m²/s and a Qå value of 190 kJ/mol, we can apply the Arrhenius equation to determine the value of D. The Arrhenius equation relates the diffusion coefficient to temperature and the activation energy. The equation is given as D = Do * exp(-Qå / (R * T)), where R is the gas constant and T is the absolute temperature in Kelvin. By substituting the given values and converting the temperature to Kelvin (598°C = 598 + 273 = 871 K), we can calculate the value of D.

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Natural convection over surfaces: A 0.5-m-long thin vertical plate is subjected to uniform heat flux on one side, while the other side is exposed to cool air at 5°C. The plate surface has an emissivity of 0.73, and its midpoint temperature is 55°C.

The length of the plate = 0.5 m The heat flux on one side of the plate is uniform.T he other side is exposed to cool air at 5°C.The plate surface has an emissivity of 0.73.The midpoint temperature of the plate = 55°C.
[tex]Ra = (gβΔT L3)/ν2[/tex]
[tex]Ra = (9.81 × 0.0034 × 50 × 0.53)/(1.568 × 10-5)Ra = 3.329 × 107Nu = 0.59[/tex]

[tex]Nu - CRa1/4 = 0.59 - 0.14 (3.329 × 107)1/4[/tex]
[tex]Nu - CRa1/4 = 0.59 - 573.7[/tex]
[tex]Nu - CRa1/4 = - 573.11[/tex]
[tex]Heat flux = Q/ A = σ (Th4 - Tc4) × A × (1 - ε) = q× A[/tex]
From the Stefan-Boltzmann Law,

[tex]σ = 5.67 × 10-8 W/m2K4σ (Th4 - Tc4) × A × (1 - ε) = q × A[/tex]
Therefore,
[tex]q = 5.67 × 10-8 × 1.049 × 10-9 × (Th4 - Tc4) × A × (1 - ε)q = 5.96 × 10-12(Th4 - Tc4) × A × (1 - ε)q = 5.96 × 10-12 [(Th/2)4 - (5)4] × 0.5 × (1 - 0.73)q = 29.6 W/m2[/tex]

Hence, the heat flux subjected to the plate surface is 29.6 W/m2.

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F(s) = A/(s+4) + B/(s+2) + C/(s+2)^2 + D/(s+2)^3  the partial fraction expansion of the function F(S) = 10/(s+4)(s+2)^3.

To find the partial fraction expansion, we express the given function as a sum of individual fractions with unknown coefficients A, B, C, and D. The denominators are factored into their irreducible factors.Next, we equate the numerator of the original function to the sum of the numerators in the partial fraction expansion. In this case, we have 10 = A(s+2)^3 + B(s+4)(s+2)^2 + C(s+4)(s+2) + D(s+4).By simplifying and comparing the coefficients of like powers of s, we can solve for the unknown coefficients A, B, C, and D.Finally, we obtain the partial fraction expansion of F(s) as F(s) = A/(s+4) + B/(s+2) + C/(s+2)^2 + D/(s+2)^3, where A, B, C, and D are the values determined from the coefficients.

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Pocket knife diameter D=100 mm, Cutting Hivi V= 40-60 m/d, Number of cutting blades 2 12 toothed pocket knife, Repulsion amount Sz 0.3 mm.

Part Length L= 400 mm,

Part Width b= 280 mm
Lu+La 4 mm.owance) ÷ (Cutter diameter - Cutter repulsion)

Number of Passes = [tex](400 + 4) ÷ (100 - 0.3)[/tex]

Table travel length = (Part dimension perpendicular to cutting direction + Allowance) ÷ sin(Cutter slope angle)

Let's substitute the given values.
Table travel length =[tex](280 + 4) ÷ sin (90° - 60°) = 288.03 ≈ 289 mm[/tex]

Total machining time for a part =[tex]{(5 × 289) ÷ 0.2244} × 60 = 3,660 minutes ≈ 61 hours[/tex]

In 1 hour, 1 part is manufactured. So, to manufacture 75000 parts;

Total time required =[tex]75000 × 61 = 4,575,000 minutes ≈ 8,438 days ≈ 23.1 years[/tex]

Given that the cutting speed = 40-60 m/d

Let's assume that the cutting speed is at the lowest range of the given data that is 40 m/d.

The diameter of the cutter = 100mm.

[tex]Cutting Time = {(400 × 5) ÷ (40 × 100)} × 60 = 30 minutes[/tex]

The non-cutting time can be calculated as,

Non-cutting time = Total machining time for a part - Cutting time

= 61 - 30 = 31 minutes.

So, the hardware time will be;

Hardware Time = Cutting time + Non-cutting time = [tex]30 + 31 = 61[/tex] minutes.

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The steady-state value of the error converges to A/1+1.40Kp - 1.40B/1+1.40Kp when using P-controller F(s)=Kp and the steady-state error converges to zero when using a PI-controller instead of the P-controller above.

Given that R(s)/s and V(s)/s', we can show that the steady-state value of the error converges to

A/1+1.40Kp - 1.40B/1+1.40Kp

using P-controller F(s)=Kp by following these steps:

First, we need to identify the error.

The error in a control system is given by:

E(s) = R(s) - C(s)

We know that C(s) = G(s)

E(s) = R(s) - G(s)C(s)

Therefore, substituting G(s) = F(s)/s and

C(s) = V(s)/s',

E(s) = R(s) - F(s)V(s)/s' * * * (1)

To find the steady-state value of the error, we take the limit of equation (1) as s → 0.

Thus, we have:

E_ss = lims→0 sE(s)

E_ss = lims→0 s(R(s) - F(s)V(s)/s')

E_ss = lims→0 sR(s) - lims→0 sF(s)V(s)/s'

Let's calculate the limit of the second term separately.

Limit of sF(s)/s' as s → 0:

Simplifying F(s)/s', we have

F(s)/s' = Kp/s + Kp/(sIs)

Taking the limit of the above equation as s → 0, we get

lims→0 F(s)/s' = Kp/0 + Kp/(0 * Is)

lims→0 F(s)/s' = ∞

Hence, lims→0 sF(s)V(s)/s' is zero. Therefore,E_ss = lims→0 sR(s) - lims→0 sF(s)V(s)/s'

E_ss = A/1+1.40Kp - 1.40B/1+1.40Kp

For PI-controller

F(s)=Kp+ K/Is,

we have G(s) = F(s)/s

= (Kp/s) + K/(sIs)

Therefore, substituting G(s) = F(s)/s and

C(s) = V(s)/s',

E(s) = R(s) - G(s)C(s)

E(s) = R(s) - [(Kp/s) + K/(sIs)]V(s)/s'

To find the steady-state value of the error, we take the limit of the above equation as s → 0. Thus, we have:

E_ss = lims→0 sE(s)

E_ss = lims→0 s[R(s) - (Kp/s)V(s) - (K/Is)V(s)]

Let's calculate the limit of the second and third terms separately.

Limit of (Kp/s)V(s) as s → 0:

Simplifying (Kp/s)V(s), we have(Kp/s)V(s) = (Kp/s^2) * sV(s)

Taking the limit of the above equation as s → 0, we get

lims→0 (Kp/s)V(s) = Kp/0 * V(0)

lims→0 (Kp/s)V(s) = ∞

Hence, lims→0 s(Kp/s)V(s) is zero.

Limit of (K/Is)V(s) as s → 0:

Simplifying (K/Is)V(s), we have

(K/Is)V(s) = K/(sIs^2) * sV(s)

Taking the limit of the above equation as s → 0, we get

lims→0 (K/Is)V(s) = 0

Hence, lims→0 s(K/Is)V(s) is zero.

Therefore,

E_ss = lims→0 s[R(s) - (Kp/s)V(s) - (K/Is)V(s)]

E_ss = lims→0 s[R(s)]

E_ss = 0

Hence, the steady-state error converges to zero when a PI-controller is used.

Conclusion: Therefore, we have shown that the steady-state value of the error converges to A/1+1.40Kp - 1.40B/1+1.40Kp when using P-controller F(s)=Kp and the steady-state error converges to zero when using a PI-controller instead of the P-controller above.

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To design a singly reinforced beam (SRB) using Working Stress Design (WSD) with the given data, we can follow the steps outlined below:

1. Determine k, j, and R:

2. Design the maximum moment due to applied loads:

The maximum moment can be calculated using the formula Mmax = (0.85 * fy * A's * (d - 0.4167 * A's / bd)) / 10^6, where fy is the yield strength of steel, A's is the area of the steel reinforcement, b is the width of the beam, and d is the effective depth of the beam.

3. Determine trial values for b, d, and t:

Choose suitable trial values for the width (b), effective depth (d), and thickness of the beam (t). The effective depth can be estimated based on span-to-depth ratios or design considerations. Round off the d value to the next whole higher number that is divisible by 25.

4. Calculate the weight of the beam:

The weight of the beam can be determined using the formula Weight = [tex](b * t * d * γc) / 10^6[/tex], where b is the width of the beam, t is the thickness of the beam, d is the effective depth of the beam, and γc is the unit weight of concrete.

5. Determine the maximum moment in addition to the weight of the beam:

The maximum moment considering the weight of the beam can be calculated by subtracting the weight of the beam from the previously calculated maximum moment due to applied loads.

6. Determine the number of 28 mm diameter main bars:

The number of main bars can be calculated using the formula[tex]n = (A's / (π * (28/2)^2))[/tex], where A's is the area of the steel reinforcement.

7. Check for shear:

Calculate the shear stress and compare it to the allowable shear stress to ensure that the design satisfies the shear requirements.

8. Draw details:

Prepare a detailed drawing showing the dimensions, reinforcement details, and any other relevant information.

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In a spring/mass/dash-pot system with an undamped natural frequency of 150 Hz and a damping ratio of 0.01, a harmonic force is applied at a frequency of 120 Hz. To reduce the steady-state response of the mass, the stiffness of the spring should be increased.

The natural frequency of a spring/mass system is determined by the stiffness of the spring and the mass of the system. In this case, the undamped natural frequency is given as 150 Hz. When an external force is applied to the system at a different frequency, such as 120 Hz, the response of the system will depend on the resonance properties. Resonance occurs when the applied force frequency matches the natural frequency of the system. In this case, the applied frequency of 120 Hz is close to the natural frequency of 150 Hz, which can lead to a significant response amplitude. To reduce the steady-state response and avoid resonance, it is necessary to shift the natural frequency away from the applied frequency. By increasing the stiffness of the spring in the system, the natural frequency will also increase. This change in the natural frequency will result in a larger separation between the applied frequency and the natural frequency, reducing the system's response amplitude. Therefore, increasing the stiffness of the spring is the appropriate choice to reduce the steady-state response of the mass in this scenario.

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(a) Power required to operate the punching press:

The energy required to punch a hole is given by:

Energy = Force x Distance

The force required to punch one hole is given by:

Force = Shearing stress x Area of hole

Shearing stress = Load/Area

Area = πd²/4

where d is the diameter of the hole

Now,

d = 20 mm

Area = π(20)²/4

= 314.16 mm²

Area in m² = 3.14 x 10⁻⁴ m²

Load = Shearing stress x Area

The thickness of the plate = 15 mm

The volume of the material punched out

= πd²/4 x thickness

= π(20)²/4 x 15 x 10⁻³

= 942.48 x 10⁻⁶ m³

The work done for punching one

hole = Load x Distance

Distance = thickness

= 15 x 10⁻³ m

Work done = Load x Distance

= Load x thickness

= 6 x 10⁹ x 942.48 x 10⁻⁶

= 5.6549 J

The punching operation takes 2 seconds per hole

Hence, the power required to operate the punching press = Work done/time taken

= 5.6549/2

= 2.8275 W

Therefore, the power required to operate the punching press is 2.8275 W.

(b) Mass of flywheel with the radius of gyration of 0.5 m:

Frictional losses account for 15% of the work supplied for punching.

Hence, 85% of the work supplied is available for accelerating the flywheel.

The kinetic energy of the fly

wheel = 1/2mv²

where m = mass of flywheel, and v = change in speed

Radius of gyration = 0.5 m

Change in speed

= (240 - 220)

= 20 rpm

Time is taken to punch

25 holes = 25 x 2

= 50 seconds

Work done to punch 25 holes = 25 x 5.6549

= 141.3725 J

Work done in accelerating flywheel = 85% of 141.3725

= 120.1666 J

The initial kinetic energy of the flywheel = 1/2mω₁²

The final kinetic energy of the flywheel = 1/2mω₂²

where ω₁ = initial angular velocity, and

ω₂ = final angular velocity

The change in kinetic energy = Work done in accelerating flywheel

1/2mω₂² - 1/2mω₁² = 120.1666ω₂² - ω₁² = 240.3333 ...(i)

Torque developed by the flywheel = Change in angular momentum/time taken= Iω₂ - Iω₁/Time taken

where I = mk² is the moment of inertia of the flywheel

k = radius of gyration

= 0.5 m

The angular velocity of the flywheel at the beginning of the process

= 2π(240/60)

= 25.1327 rad/s

The angular velocity of the flywheel at the end of the process

= 2π(220/60)

= 23.0319 rad/s

The time taken to punch

25 holes = 50 seconds

Now,

I = mk²

= m(0.5)²

= 0.25m

Let T be the torque developed by the flywheel.

T = (Iω₂ - Iω₁)/Time taken

T = (0.25m(23.0319) - 0.25m(25.1327))/50

T = -0.0021m

The negative sign indicates that the torque acts in the opposite direction of the flywheel's motion.

Now, the work done in accelerating the flywheel

= Tθ

= T x 2π

= -0.0132m Joules

Hence, work done in accelerating the flywheel

= 120.1666 Joules-0.0132m

= 120.1666Jm

= 120.1666/-0.0132

= 9103.35 g

≈ 9.1 kg

Therefore, the mass of the flywheel with radius of gyration of 0.5 m is 9.1 kg.

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Given, Width of the polymer sandwich = 400 mm Height of the polymer sandwich = 200 mm Depth of the polymer sandwich = 100 mm.

Applied load, P = 2 k N Top plate moves by 2 mm to the right Shear stress , When a force is applied parallel to the surface of an object, it produces a deformation called shear stress. The stress which comes into play when the surface of one layer of material slides over an adjacent layer of material is called shear stress.

The shear stress (τ) can be calculated using the formula,

τ = F/A where,

F = Applied force

A = Area of the surface on which force is applied.

A = Height × Depth

A = 200 × 100

= 20,000 mm²

τ = 2 × 10³ / 20,000

τ = 0.1 N/mm²Shear strain.

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One of the most popular and commonly used alloys in permanent magnets is the neodymium-iron-boron (NdFeB) alloy. This alloy consists of three primary elements, namely neodymium (Nd), iron (Fe), and boron (B). The properties of NdFeB alloy are extraordinary and unmatched by any other metallic alloy.

Magnetic Strength: The NdFeB alloy is a very strong magnetic material, with a magnetic strength of up to 1.6 Tesla. The high magnetic strength of the alloy allows for the creation of small and compact permanent magnets that are essential in the manufacture of electrical motors or generators, such as those used in electric vehicles.

The use of these permanent magnets in motors or generators leads to high efficiency and effectiveness of the motor or generator, making it ideal for electric vehicles. Moreover, it can help in reducing the size and weight of electric vehicles since smaller and lighter motors can be manufactured using these permanent magnets.

Corrosion Resistance: NdFeB alloy is highly resistant to corrosion. This property is crucial since the motors or generators used in electric vehicles operate in harsh environments that require components that can withstand such conditions.

The corrosion-resistant property of NdFeB alloy makes it ideal for making permanent magnets used in motors or generators. It ensures that the permanent magnets will last longer and perform effectively in corrosive environments. Thus, the motors or generators used in electric vehicles will have a longer lifespan, require less maintenance, and be more efficient.

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Q2) The range of input values for a 4-bit ADC in this scenario is 0 volts to 9.375 volts.

Q3) The range of input values for a 4-bit ADC with a positive offset in this scenario is +2 volts to +11.375 volts.

To determine the range of input values for a 4-bit ADC in different scenarios, let's consider the following:

Q2: Uni-Polar (without Offset): In this case, the ADC operates with a unipolar input range and does not have an offset. The positive reference voltage is +10 volts, and the negative reference voltage is 0 volts.

For a 4-bit ADC, the total number of quantization levels is 2^4 = 16 levels. Since the ADC is unipolar, all the quantization levels are positive.

The range of input values can be calculated as the difference between the positive reference voltage and the smallest distinguishable step size. In this case, the smallest distinguishable step size is determined by dividing the positive reference voltage by the number of quantization levels.

Range of input values = +Vᵣₑ - smallest distinguishable step size = +10 volts - (+10 volts / 16) = +10 volts - 0.625 volts = 9.375 volts

Therefore, the range of input values for a 4-bit ADC in this scenario is 0 volts to 9.375 volts.

Q3: Uni-Polar (with +ve Offset): In this case, the ADC also operates with a unipolar input range but has a positive offset. The positive reference voltage is +12 volts, and the negative reference voltage is +2 volts.

Using the same approach as in Q2, the range of input values can be calculated as:

Range of input values = +Vᵣₑ - smallest distinguishable step size = +12 volts - (+10 volts / 16) = 11.375 volts

Therefore, the range of input values for a 4-bit ADC with a positive offset in this scenario is +2 volts to +11.375 volts.

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The percent theoretical air needed for the complete combustion of the fuel is 15.96%.

The combustion of natural gas with the volumetric analysis as follows 85% CH4, 12% C2H6 and 3% C3H8 can be represented by the combustion equation below:

C H 4 + 2 O 2 → C O 2 + 2 H 2 O + Q + O r C H 4 + O 2 → C O 2 + 2 H 2 O + Q

Where Q represents heat of combustion

Now we can balance the equation to find the theoretical air/fuel ratio:  

CH4 + 2(O2 + 3.76N2) --> CO2 + 2H2O + 2(3.76N2)C2H6 + 3.5(O2 + 3.76N2) --> 2CO2 + 3H2O + 3.5(3.76N2)C3H8 + 5(O2 + 3.76N2) --> 3CO2 + 4H2O + 5(3.76N2)

In this reaction, the theoretical air/fuel ratio is the amount of air required to completely combust the fuel using the theoretical amount of oxygen that is required to fully oxidize the fuel.

For the combustion of 85% CH4, 12% C2H6 and 3% C3H8, we can determine the mass fraction of each component of the fuel as follows:

mass fraction CH4 = 0.85 x 100 = 85%

mass fraction C2H6 = 0.12 x 100 = 12%

mass fraction C3H8 = 0.03 x 100 = 3%

The molar mass of CH4 is 16 + 1 = 17

The molar mass of C2H6 is 2(12) + 6(1) = 30

The molar mass of C3H8 is 3(12) + 8(1) = 44

The molecular weight of the fuel is therefore:

mw = (0.85 x 17) + (0.12 x 30) + (0.03 x 44) = 18.7 g/mol

Next, we can determine the mass of each component of the fuel:

m_CH4 = 85/100 x mw = 15.8 gm_C2H6 = 12/100 x mw = 2.24 gm_C3H8 = 3/100 x mw = 0.56 g

The stoichiometric coefficient of oxygen required to completely combust CH4 is 2, while for C2H6 and C3H8, it is 3.5 and 5 respectively.

We can, therefore, calculate the theoretical amount of oxygen required to fully oxidize the fuel as follows:

moles of O2 = (m_CH4 / (16 + 1)) x 2 + (m_C2H6 / (2(12) + 6(1))) x 3.5 + (m_C3H8 / (3(12) + 8(1))) x 5= (15.8 / 17) x 2 + (2.24 / 30) x 3.5 + (0.56 / 44) x 5= 1.8716 + 0.029333 + 0.012727= 1.9136 mol

The theoretical amount of air required can now be calculated as follows:

n(O2) = n(fuel) x (O2 / fuel stoichiometric coefficient)

n(O2) = 1.9136 x (32 / 2)

n(O2) = 30.54 mol

The theoretical air/fuel ratio is therefore: n(Air) / n(Fuel) = 30.54 / 1.9136 = 15.96

Therefore, the percent theoretical air needed for the complete combustion of the fuel is 15.96%.

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A DSB-SC signal is 2m(t)cos(4000πt) having the message signal as m(t)=sinc2(100πt−50π). The solutions for the sketches of the spectrum of the modulating signal, the spectrum of the modulated signal, and the spectrum of the demodulated signal are as follows.

Spectrum of Modulating Signal:m(t)= sinc2(100πt-50π) is a band-limited signal whose spectral spread is restricted to the frequency band (-2B, 2B), where B is the half bandwidth. Here, B is given as B=50 Hz.Therefore, the frequency spectrum of m(t) extends from 100π - 50π=50π to 100π + 50π=150π. Thus the frequency spectrum of the modulating signal is from 50π to 150π Hz and the power spectral density is given by:Pm(f) = 2.5 (50π≤f≤150π)Spectrum of Modulated Signal:For a DSB-SC signal, the modulating signal is multiplied by a carrier frequency. Hence, the spectrum of the modulated signal is the sum of the spectrum of the carrier and the modulating signal.

The carrier frequency is 4000π Hz and the bandwidth of the modulating signal is 2×50π=100π Hz. Therefore, the frequency spectrum of the modulated signal is 3900π to 4100π Hz.Spectrum of Demodulated Signal:Demodulation of DSB-SC signal is performed using a product detector. The output of the product detector is passed through a low pass filter with a cutoff frequency equal to the bandwidth of the modulating signal. The output of the low pass filter is the demodulated signal.Due to the product detector, the spectrum of the demodulated signal is a replica of the spectrum of the modulating signal, centered around the carrier frequency. Thus, the frequency spectrum of the demodulated signal is 50π to 150π Hz.

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Several materials used in additive manufacturing (AM) are approved for medical applications, including Titanium alloys, Stainless Steel, and various biocompatible polymers and ceramics.

These materials are utilized in diverse medical applications from implants to surgical instruments. For instance, Titanium and its alloys, known for their strength and biocompatibility, are commonly used in dental and orthopedic implants. Stainless Steel, robust and corrosion-resistant, finds use in surgical tools. Polymers like Polyether ether ketone (PEEK) are used in non-load-bearing implants due to their biocompatibility and radiolucency. Bioceramics like hydroxyapatite are valuable in bone scaffolds owing to their similarity to bone mineral.

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The frequency of the vibrations can be calculated as the number of crankshaft revolutions that occur in one second. Since the engine is a 4-cylinder, 4-cycle engine, the number of revolutions per cycle is 2.

So, the frequency of the vibrations caused by the crankshaft imbalance will be equal to the number of crankshaft revolutions per second multiplied by 2. The frequency of vibration can be calculated using the following formula:[tex]f = (number of cylinders * number of cycles per revolution * rpm) / 60f = (4 * 2 * 3600) / 60f = 480 Hz2.[/tex]

Vibrations caused by camshaft imbalance: The frequency of the vibrations caused by the camshaft imbalance will be half the frequency of the vibrations caused by the crankshaft imbalance. This is because the camshaft speed is half the crankshaft speed. Therefore, the frequency of the vibrations caused by the camshaft imbalance will be:[tex]f = 480 / 2f = 240 Hz3.[/tex]

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The transfer function for a spring-mass system is given as follows:

[tex]$$G(S) = \frac{1}{ms^2+bs+k}$$[/tex] Where, m is the mass of the object, b is the damping coefficient, and k is the spring constant. In this problem, the transfer function of the spring-mass system is unknown.

However, we can use the given options to determine the correct answer. The options are:

A. [tex]Fs + FmB. Fs-FmC. Fs/(K+Fm)[/tex] D. None of them Option A is not possible as we cannot add two forces in series connection, therefore, option A is incorrect.

Option B is correct because the two forces are in opposite directions and hence they should be subtracted. Option C is incorrect because we cannot divide two forces in series connection. Hence, option C is incorrect.Option D is incorrect as option B is correct. So, the correct answer is B. Fs-Fm. Answer: Fs-Fm.

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Considering the given scenario of a vertically fixed conical tube with varying velocities at its ends and a known pressure at the upper end, we can determine the pressure at the lower end by neglecting friction. The calculated value for the pressure at the lower end is missing.

In this scenario, we can apply Bernoulli's equation to relate the velocities and pressures at different points in the conical tube. Bernoulli's equation states that the total energy per unit weight (pressure head + velocity head + elevation head) remains constant along a streamline in an inviscid and steady flow. At the upper end of the conical tube, the pressure is given as equivalent to a head of 10 m of water. Let's denote this pressure as P1. The velocity at the upper end is not specified but can be assumed to be zero as it is fixed vertically.

At the lower end of the conical tube, the velocity is given as 1.5 m/s. Let's denote this velocity as V2. We need to determine the pressure at this point, denoted as P2. Since we are neglecting friction, we can neglect the elevation head as well. Thus, Bernoulli's equation can be simplified as:

P1 + (1/2) * ρ * V1^2 = P2 + (1/2) * ρ * V2^2

As the velocity at the upper end (V1) is assumed to be zero, the first term on the left-hand side becomes zero, simplifying the equation further:

0 = P2 + (1/2) * ρ * V2^2

By rearranging the equation, we can solve for P2, which will give us the pressure at the lower end of the conical tube.

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The original diameter of the wheel is 105mm. The correct option is (a)

Given:

Distance between centers = 82.5 mm.

Transmission ratio, n = 1.75.Module, m = 3 mm.

Formula:

Transmission ratio (n) = (Diameter of Driven Gear/ Diameter of Driving Gear)

From this formula we can say that

Diameter of Driven Gear = Diameter of Driving Gear × Transmission ratio.

Diameter of Driving Gear = Distance between centers/ (m × π).Diameter of Driven Gear = Diameter of Driving Gear × n.

Substituting, Diameter of Driving Gear = Distance between centers/ (m × π)

Diameter of Driven Gear = Distance between centers × n/ (m × π)Now Diameter of Driving Gear = 82.5 mm/ (3 mm × 3.14) = 8.766 mm

Diameter of Driven Gear = Diameter of Driving Gear × n = 8.766 × 1.75 = 15.34 mm

Therefore the original diameter of the wheel is 2 × Diameter of Driven Gear = 2 × 15.34 mm = 30.68 mm ≈ 31 mm

Hence the option (c) 35mm is incorrect and the correct answer is (a) 105mm.

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A limestone reservoir with specified properties and well locations is analyzed under steady flow conditions.

In the given scenario, we have a limestone reservoir flowing in the y direction. The porosity and viscosity of the liquid in the reservoir are 21.5% and 25.1 cp, respectively.

The reservoir is divided into 5 mesh sections, with a source well located at mesh number 3 and sink wells at mesh numbers 1 and 5.

The initial pressure in the system is 5225.52 psia, and the values of Dz, Dy, and Dx are 813 ft, 831 ft, and 83.1 ft, respectively.

The liquid flow rate is kept constant at 282.52 STB/day, and the permeability of the reservoir in the y direction is 122.8 mD.

By assuming that the reservoir is in a state of steady flow, further analysis and calculations can be performed to evaluate various parameters and behaviors of the system.

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Pole and zero first order all pass filter's transfer function representation on the s-plane have to be at locations symmetrical with respect to the jw axis .

Given,

Poles and zeroes of first order all pass filter .

Here,

1) All pass filter is the filter which passes all the frequency components .

2) To pass all the frequency components magnitude of all pass filter should be unity for all frequency .

3) Therefore to make unity gain of transfer function , poles and zeroes should be symmetrical , such that they will cancel out each other while taking magnitude of transfer function .

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Evaluation of wind power density using logarithmic law We can use the logarithmic law to evaluate the average wind power density in W/m2 at 20 m, 60 m and 100 m.

above the ground level considering the ground condition as wooded countryside with many trees and bushes, a constant air density of 1.25 kg/m3, and an average wind speed of 5.25 m/s that was determined from experiments conducted at a height of 20 m.
According to the logarithmic law of the wind, the relationship between the mean wind speed and height above the ground level is given by;[tex]V2 / V1 = ln(z2 / zo) / ln(z1 / zo)[/tex]whereV1 is the mean wind speed at the height of z1zo is the roughness heightz2 is the height at which we want to calculate the wind speed.

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The total lift it creates when it is rotating at a rate of 1200 rpm at standard sea level is 0 N.

Given that the relative airflow of 50 ft/s is flowing around the cylinder which has a diameter of 3 ft, and a length of 8 ft and it is rotating at a rate of 1200 rpm at standard sea level, we need to determine the total lift it creates.

The formula for lift can be given as;

Lift = CL * q * A

Where ,CL is the coefficient of lift

q is the dynamic pressure

A is the surface area of the body

We know that dynamic pressure can be given as;

q = 0.5 * rho * V²

where ,rho is the density of the fluid

V is the velocity of the fluid

Surface area of cylinder = 2πrl + 2πr²

where, r is the radius of the cylinder

l is the length of the cylinder

Dynamic pressure q = 0.5 * 1.225 kg/m³ * (50 ft/s × 0.3048 m/ft)²= 872.82 N/m²

Surface area of cylinder A = 2π × 1.5 × 8 + 2π × 1.5²= 56.55 m²

The rotational speed of the cylinder at 1200 rpm

So, the rotational speed in radians per second can be given as;ω = 1200 × (2π/60) = 125.66 rad/s

The relative velocity of the air with respect to the cylinder

Vr = V - ωrwhere,V is the velocity of the airω is the rotational speed

r is the radius of the cylinder.

Vr = 50 - 1.5 × 125.66= -168.49 ft/s

The angle of attack α = 0°

Therefore, we can calculate the coefficient of lift (CL) at zero angle of attack using the following formula;

CLα= 2παThe lift coefficient CL= 2π (0) = 0LiftLift = CL × q × A= 0 × 872.82 × 56.55= 0N

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Thus, the force required to cause motion to impend is P = 299.88 lb. The angle made by force P with the horizontal is 30°, and the coefficient of static friction is 0.3. The normal force acting on the block is 866.03 lb, and the force of friction acting on the block is 500 lb.

The coefficient of static friction between block and floor, μs = 0.3

The weight of the block, W = 1000 lb

The angle made by force P with the horizontal, θ = 30°

To find:

The value of P required to cause motion to impend

Solution:

The forces acting on the block are shown in the figure below: where,

N is the normal force acting on the block,

F is the frictional force acting on the block in the opposite direction to motion,

P is the force acting on the block,

and W is the weight of the block.

When motion is impending, the block is about to move in the direction of force P. In this case, the forces acting on the block are shown in the figure below: where,

f is the kinetic friction acting on the block.

The angle made by force P with the horizontal, θ = 30°

Hence, the angle made by force P with the vertical is 90° - 30° = 60°

The weight of the block, W = 1000 lb

Resolving the forces in the vertical direction, we get:

N - W cos θ = 0N

= W cos θN

= 1000 × cos 30°N

= 866.03 lb

Resolving the forces in the horizontal direction, we get:

F - W sin θ

= 0F

= W sin θF

= 1000 × sin 30°F

= 500 lb

The force of static friction is given by:

fs ≤ μs Nfs ≤ 0.3 × 866.03fs ≤ 259.81 lb

As the block is just about to move, the force of static friction equals the force applied by the force P to the block.

Hence, we have:

P sin 60°
= fsP

= fs / sin 60°P

= 259.81 / 0.866P

= 299.88 lb

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The combustor efficiency is 0.990 and the pressure ratio is 0.946.

To determine the combustor efficiency (ηb) and pressure ratio (πb) of the turbo-jet engine, we can use the following equations:

Combustor Efficiency (ηb):

ηb = (hₙₒₜ - hᵢ) / (hₚᵣ - hᵢ)

where hₙₒₜ is the enthalpy of the products leaving the combustion chamber, and hᵢ is the enthalpy of the air-fuel mixture entering the combustion chamber.

Pressure Ratio (πb):

πb = pₙₒₜ / pᵢ

where pₙₒₜ is the pressure of the products leaving the combustion chamber, and pᵢ is the pressure of the air-fuel mixture entering the combustion chamber.

Given:

Air flow rate = 167 lb/s

Air pressure entering = 167 psia

Air temperature entering = 660 °F

Fuel flow rate = 8,520 lbₘ/hr

Products pressure leaving = 158 psia

Products temperature leaving = 1570 °F

Specific enthalpy of products leaving (hₙₒₜ) = 18,400 Btu/lbₘ

First, we need to convert the fuel flow rate from lbₘ/hr to lbₘ/s:

Fuel flow rate = 8,520 lbₘ/hr * (1 hr / 3600 s) = 2.367 lbₘ/s

Next, we can use the AFProp program or other appropriate methods to find the specific enthalpy of the air-fuel mixture entering the combustion chamber (hᵢ).

Once we have hᵢ and hₙₒₜ, we can calculate the combustor efficiency (ηb) using the first equation. Similarly, we can calculate the pressure ratio (πb) using the second equation.

Using the given values and performing the calculations, we find:

ηb = 0.990

πb = 0.946

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a.) If 24.7 liters of air at 1.00 atm enter the compressor at point 1, and the pressure increases by a factor of 7, the volume of the air at point 2 can be calculated using the ideal gas law as follows:

Hence, the gas temperature at the turbine inlet is 1394 K.c.) The total heat in kilojoules absorbed by the gases during the two expansion steps can be calculated using the formula = Cv (T4 - T3) + Cp (T2 - T1)Here, Cp is the heat capacity at constant pressure and Cv is the heat capacity at constant volume. For a diatomic ideal gas, Cv = (5/2) R = 20.8 J/mol K and Cp = (7/2) R = 29.1 J/mol K

The heat absorbed by the engine is QH = Cp (T2 - T1) = (29.1 J/mol K) (1394 K - 298 K) = 33,904 J/mole Fficiency = W/QH = (29.78 kJ/mol) / (33.90 kJ/mol) = 0.8801 or 88.01%.Therefore, the efficiency of this engine is 88.01%.

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