Given in the following v(t) signal.
a. Find the first 7 harmonics of the Fourier series function in cosine form.
b. Plot one side spectrum
c. Find the first 7 harmonics of the Fourier series function in exponential form.
d. Plot two side spectrum Given in the following v(t) signal.

Answer:

The answer is VN =37.416 m/s

Explanation:

Recall that:

Pressure (atmospheric) = 100 kPa

So. we solve for the maximum velocity (m/s) to which water can be accelerated by the nozzles

Now,

Pabs =Patm + Pgauge = 800 KN/m²

Thus

PT/9.81 + VT²/2g =PN/9.81  + VN²/2g

Here

Acceleration due to gravity = 9.81 m/s

800/9.81 + 0

= 100/9.81 + VN²/19.62

Here,

9.81 * 2= 19.62

Thus,

VN²/19.62 = 700/9.81

So,

VN² =1400

VN =37.416 m/s

Note: (800 - 100) = 700

Answer:

[tex]V2 = 37.417ms^{-1}[/tex]

Explanation:

Given the following data;

Water enters the turbine nozzles (inlet) = 800kPa = 800000pa.

Nozzle outlets = 100kPa = 100000pa.

Density of water = 1000kg/m³.

We would apply, the Bernoulli equation between the inlet and outlet;

[tex]\frac{P_{1} }{d}+\frac{V1^{2} }{2} +gz_{1} = \frac{P_{2} }{d}+\frac{V2^{2} }{2} +gz_{2}[/tex]

Where, V1 is approximately equal to zero(0).

Z[tex]z_{1} = z_{2}[/tex]

Therefore, to find the maximum velocity, V2;

[tex]V2 = \sqrt{2(\frac{P_{1} }{d}-\frac{P_{2} }{d}) }[/tex]

[tex]V2 = \sqrt{2(\frac{800000}{1000}-\frac{100000}{1000}) }[/tex]

[tex]V2 = \sqrt{2(800-100)}[/tex]

[tex]V2 = \sqrt{2(700)}[/tex]

[tex]V2 = \sqrt{1400}[/tex]

[tex]V2 = 37.417ms^{-1}[/tex]

Hence, the maximum velocity, V2 is 37.417m/s

Answer:

a) [tex]\ddot n = 50400\,\frac{rev}{min^{2}}[/tex], b) [tex]n = 2450\,rev[/tex]

Explanation:

a) The acceleration experimented by the grinding wheel is:

[tex]\ddot n = \frac{4200\,\frac{rev}{min} - 0 \,\frac{rev}{min} }{\frac{5}{60}\,min }[/tex]

[tex]\ddot n = 50400\,\frac{rev}{min^{2}}[/tex]

Now, the number of revolutions done by the grinding wheel in that period of time is:

[tex]n = \frac{(4200\,\frac{rev}{min} )^{2}-(0\,\frac{rev}{min} )^{2}}{2\cdot \left(50400\,\frac{rev}{min^{2}} \right)}[/tex]

[tex]n = 175\,rev[/tex]

b) The acceleration experimented by the grinding wheel is:

[tex]\ddot n = \frac{0 \,\frac{rev}{min} - 4200\,\frac{rev}{min} }{\frac{70}{60}\,min }[/tex]

[tex]\ddot n = -3600\,\frac{rev}{min^{2}}[/tex]

Now, the number of revolutions done by the grinding wheel in that period of time is:

[tex]n = \frac{(0\,\frac{rev}{min} )^{2} - (4200\,\frac{rev}{min} )^{2}}{2\cdot \left(-3600\,\frac{rev}{min^{2}} \right)}[/tex]

[tex]n = 2450\,rev[/tex]

Answer:

[tex]\mathbf{h_2 =1021.9 \ mm}[/tex]

Explanation:

Given that :

The initial volume of water [tex]V_1[/tex] = 1000.00 mL = 1000000 mm³

The initial temperature of the water  [tex]T_1[/tex] = 10° C

The height of the water column h = 1000.00 mm

The final temperature of the water [tex]T_2[/tex] = 70° C

The coefficient of thermal expansion for the glass is  ∝ = [tex]3.8*10^{-6 } mm/mm \ per ^oC[/tex]

The objective is to determine the the depth of the water column

In order to do that we will need to determine the volume of the water.

We obtain the data for physical properties of water at standard sea level atmospheric from pressure tables; So:

At temperature [tex]T_1 = 10 ^ 0C[/tex]  the density of the water is [tex]\rho = 999.7 \ kg/m^3[/tex]

At temperature [tex]T_2 = 70^0 C[/tex]  the density of the water is [tex]\rho = 977.8 \ kg/m^3[/tex]

The mass of the water is  [tex]\rho V = \rho _1 V_1 = \rho _2 V_2[/tex]

Thus; we can say [tex]\rho _1 V_1 = \rho _2 V_2[/tex];

⇒ [tex]999.7 \ kg/m^3*1000 \ mL = 977.8 \ kg/m^3 *V_2[/tex]

[tex]V_2 = \dfrac{999.7 \ kg/m^3*1000 \ mL}{977.8 \ kg/m^3 }[/tex]

[tex]V_2 = 1022.40 \ mL[/tex]

[tex]v_2 = 1022400 \ mm^3[/tex]

Thus, the volume of the water after heating to a required temperature of  [tex]70^0C[/tex] is 1022400 mm³

However; taking an integral look at this process; the volume of the water before heating can be deduced by the relation:

[tex]V_1 = A_1 *h_1[/tex]

The area of the water before heating is:

[tex]A_1 = \dfrac{V_1}{h_1}[/tex]

[tex]A_1 = \dfrac{1000000}{1000}[/tex]

[tex]A_1 = 1000 \ mm^2[/tex]

The area of the heated water is :

[tex]A_2 = A_1 (1 + \Delta t \alpha )^2[/tex]

[tex]A_2 = A_1 (1 + (T_2-T_1) \alpha )^2[/tex]

[tex]A_2 = 1000 (1 + (70-10) 3.8*10^{-6} )^2[/tex]

[tex]A_2 = 1000.5 \ mm^2[/tex]

Finally, the depth of the heated hot water is:

[tex]h_2 = \dfrac{V_2}{A_2}[/tex]

[tex]h_2 = \dfrac{1022400}{1000.5}[/tex]

[tex]\mathbf{h_2 =1021.9 \ mm}[/tex]

Hence the depth of the heated hot  water is [tex]\mathbf{h_2 =1021.9 \ mm}[/tex]

Answer:

The minimum allowable bolt diameter required to support an applied load of P = 450 kN is 45.7 milimeters.

Explanation:

The complete statement of this question is "Five bolts are used in the connection between the axial member and the support. The ultimate shear strength of the bolts is 320 MPa, and a factor of safety of 4.2 is required with respect to fracture. Determine the minimum allowable bolt diameter required to support an applied load of P = 450 kN"

Each bolt is subjected to shear forces. In this case, safety factor is the ratio of the ultimate shear strength to maximum allowable shear stress. That is to say:

[tex]n = \frac{S_{uts}}{\tau_{max}}[/tex]

Where:

[tex]n[/tex] - Safety factor, dimensionless.

[tex]S_{uts}[/tex] - Ultimate shear strength, measured in pascals.

[tex]\tau_{max}[/tex] - Maximum allowable shear stress, measured in pascals.

The maximum allowable shear stress is consequently cleared and computed: ([tex]n = 4.2[/tex], [tex]S_{uts} = 320\times 10^{6}\,Pa[/tex])

[tex]\tau_{max} = \frac{S_{uts}}{n}[/tex]

[tex]\tau_{max} = \frac{320\times 10^{6}\,Pa}{4.2}[/tex]

[tex]\tau_{max} = 76.190\times 10^{6}\,Pa[/tex]

Since each bolt has a circular cross section area and assuming the shear stress is not distributed uniformly, shear stress is calculated by:

[tex]\tau_{max} = \frac{4}{3} \cdot \frac{V}{A}[/tex]

Where:

[tex]\tau_{max}[/tex] - Maximum allowable shear stress, measured in pascals.

[tex]V[/tex] - Shear force, measured in kilonewtons.

[tex]A[/tex] - Cross section area, measured in square meters.

As connection consist on five bolts, shear force is equal to a fifth of the applied load. That is:

[tex]V = \frac{P}{5}[/tex]

[tex]V = \frac{450\,kN}{5}[/tex]

[tex]V = 90\,kN[/tex]

The minimum allowable cross section area is cleared in the shearing stress equation:

[tex]A = \frac{4}{3}\cdot \frac{V}{\tau_{max}}[/tex]

If [tex]V = 90\,kN[/tex] and [tex]\tau_{max} = 76.190\times 10^{3}\,kPa[/tex], the minimum allowable cross section area is:

[tex]A = \frac{4}{3} \cdot \frac{90\,kN}{76.190\times 10^{3}\,kPa}[/tex]

[tex]A = 1.640\times 10^{-3}\,m^{2}[/tex]

The minimum allowable cross section area can be determined in terms of minimum allowable bolt diameter by means of this expression:

[tex]A = \frac{\pi}{4}\cdot D^{2}[/tex]

The diameter is now cleared and computed:

[tex]D = \sqrt{\frac{4}{\pi}\cdot A}[/tex]

[tex]D =\sqrt{\frac{4}{\pi}\cdot (1.640\times 10^{-3}\,m^{2})[/tex]

[tex]D = 0.0457\,m[/tex]

[tex]D = 45.7\,mm[/tex]

The minimum allowable bolt diameter required to support an applied load of P = 450 kN is 45.7 milimeters.

We have that the minimum allowable bolt diameter is mathematically given as

From the question we are told

Generally the equation for the stress   is mathematically given as

[tex]\mu= 320/4.2 \\\\\mu= 76.190 N/mm^2[/tex]

Therefore

Force = Stress * area

Force = P/2

F= 425,000 N / 2 = 212,500 N

Hence area of each bolt is given as

212,500 = 76.190*( 5* area of each bolt)

area of each bolt = 557.815

Since

area of each bolt=\pi*d^2/4

\pi*d^2/4 = 557.815

For more information on diameter visit

https://brainly.com/question/8552546

Answer:

South Pole and South Pole or North Pole and North Pole.

Answer:

a. [tex]\dfrac{D_{1}}{ D_{2}} = \left (\dfrac{ \left{D_1} }{ {D_2}} \right )^{-3\times n}[/tex] which is constant therefore, n = constant

b. The temperature at the end of the process is 109.6°C

c. The work done by the balloon boundaries = 10.81 MJ

The work done on the surrounding atmospheric air = 10.6 MJ

Explanation:

p₁ = 100 kPa

T₁ = 27°C

D₁ = 10 m

v₂ = 1.2 × v₁

p ∝ α·D

α = Constant

[tex]v_1 = \dfrac{4}{3} \times \pi \times r^3[/tex]

[tex]\therefore v_1 = \dfrac{4}{3} \times \pi \times \left (\dfrac{10}{2} \right )^3 = 523.6 \ m^3[/tex]

v₂ = 1.2 × v₁ = 1.2 × 523.6 = 628.32 m³

Therefore, D₂ = 10.63 m

We check the following relation for a polytropic process;

[tex]\dfrac{p_{1}}{p_{2}} = \left (\dfrac{V_{2}}{V_{1}} \right )^{n} = \left (\dfrac{T_{1}}{T_{2}} \right )^{\dfrac{n}{n-1}}[/tex]

We have;

[tex]\dfrac{\alpha \times D_{1}}{\alpha \times D_{2}} = \left (\dfrac{ \dfrac{4}{3} \times \pi \times \left (\dfrac{D_2}{2} \right )^3}{\dfrac{4}{3} \times \pi \times \left (\dfrac{D_1}{2} \right )^3} \right )^{n} = \left (\dfrac{ \left{D_2} ^3}{ {D_1}^3} \right )^{n}[/tex]

[tex]\dfrac{D_{1}}{ D_{2}} = \left (\dfrac{ \left{D_2} }{ {D_1}} \right )^{3\times n} = \left (\dfrac{ \left{D_1} }{ {D_2}} \right )^{-3\times n}[/tex]

[tex]\dfrac{ D_{1}}{ D_{2}} = \left ( 1.2 \right )^{n} = \left (\dfrac{ \left{D_2} ^3}{ {D_1}^3} \right )^{n}[/tex]

[tex]log \left (\dfrac{D_{1}}{ D_{2}}\right ) = -3\times n \times log\left (\dfrac{ \left{D_1} }{ {D_2}} \right )[/tex]

n = -1/3

Therefore, the relation, pVⁿ = Constant

b. The temperature T₂ is found as follows;

[tex]\left (\dfrac{628.32 }{523.6} \right )^{-\dfrac{1}{3} } = \left (\dfrac{300.15}{T_{2}} \right )^{\dfrac{-\dfrac{1}{3}}{-\dfrac{1}{3}-1}} = \left (\dfrac{300.15}{T_{2}} \right )^{\dfrac{1}{4}}[/tex]

T₂ = 300.15/0.784 = 382.75 K = 109.6°C

c. [tex]W_{pdv} = \dfrac{p_1 \times v_1 -p_2 \times v_2 }{n-1}[/tex]

[tex]p_2 = \dfrac{p_{1}}{ \left (\dfrac{V_{2}}{V_{1}} \right )^{n} } = \dfrac{100\times 10^3}{ \left (1.2) \right ^{-\dfrac{1}{3} } }[/tex]

p₂ =  100000/0.941 = 106.265 kPa

[tex]W_{pdv} = \dfrac{100 \times 10^3 \times 523.6 -106.265 \times 10^3 \times 628.32 }{-\dfrac{1}{3} -1} = 10806697.1433 \ J[/tex]

The work done by the balloon boundaries = 10.81 MJ

Work done against atmospheric pressure, Pₐ, is given by the relation;

Pₐ × (V₂ - V₁) = 1.01×10⁵×(628.32 - 523.6) = 10576695.3 J

The work done on the surrounding atmospheric air = 10.6 MJ

Answer:

The reason for their unusual properties of the greasy feel and low hardness is that the chemical bonds between the sheets is so weak that very low stresses can allow slip between the sheets.

Explanation:

Talc is a monoclinic mineral with a sheet structure similar to the micas and also has perfect cleavage that follows planes between the weakly bonded sheets.

Now, these sheets are held together only by van der Waals bonds and this allows them to slip past each other easily. Thus, this unique characteristic is responsible for talc's extreme softness, its greasy, soapy feel, and its value as a high-temperature lubricant.

While for graphite, it's carbon atoms are linked in a hexagonal network which forms sheets that are one atom thick. It's sheets are poorly connected and easily cleave or slide over one another when subjected to a small amount of force. Thus, gives graphite its very low hardness, its perfect cleavage, and its slippery feel.

So, we can conclude that the reason for their unusual properties is that the chemical bonds between the sheets is so weak that very low stresses can allow slip between the sheets; hence, the greasy feel and low hardness.

Answer:

Answer:

• it charges banks more interest

• it sells more securities

• it decreases the money supply

Explanation:

hope this help edge 21

Answer:

We can describe 15×-10 as an expression. we would describe 6×-2< 35 as an...

Explanation:

We can describe 15×-10 as an expression. we would describe 6×-2< 35 as an...

Answer:

s = v√[2(H - h)/g]

This formula describes the distance from the building that Prof Murthy must be when you release the egg

Explanation:

First, we need to find the time required by the egg to reach the head of Professor. For that purpose, we use 1st equation of motion in vertical form:

Vf = Vi + gt

where,

Vf = Velocity of egg at the time of hitting head of the Professor

Vi = initial velocity of egg = 0 m/s  (Since, egg is initially at rest)

g = acceleration due to gravity

t = time taken by egg to come down

Therefore,

Vf = 0 + gt

t = Vf/g   ----- equation (1)

Now, we use 3rd euation of motion for Vf:

2gs = Vf² - Vi²

where,

s = height dropped = H - h

Therefore,

2g(H - h) = Vf²

Vf = √[2g(H - h)]

Therefore, equation (1) becomes:

t = √[2g(H - h)]/g

t = √[2(H - h)/g]

Now, consider the horizontal motion of professor. So, the minimum distance of professor from building can be found out by finding the distance covered by the professor in time t. Since, the professor is running at constant speed of v m/s. Therefore:

s = vt

s = v√[2(H - h)/g]

This formula describes the distance from the building that Prof Murthy must be when you release the egg

Answer:

Total contraction on the bar = 1.238 mm

Explanation:

Modulus of Elasticity, E = 85 GN/m²

Diameter of the aluminium bar, [tex]d_{Al} = 40 mm = 0.04 m[/tex]

Load, P = 160 kN

Cross sectional area of the aluminium bar without hole:

[tex]A_1 = \frac{\pi d_{Al}^2 }{4} \\A_1 = \frac{\pi 0.04^2 }{4}\\A_1 = 0.00126 m^2[/tex]

Diameter of hole, [tex]d_h = 30 mm = 0.03 m[/tex]

Cross sectional area of the aluminium bar with hole:

[tex]A_2 = \frac{\pi( d_{Al}^2 - d_{h}^2)}{4} \\A_2 = \frac{\pi (0.04^2 - 0.03^2) }{4}\\A_2 = 0.00055 m^2[/tex]

Length of the aluminium bar, [tex]L_{Al} = 600 mm = 0.6 m[/tex]

Length of the hole, [tex]L_h = 100mm = 0.1 m[/tex]

Contraction in aluminium bar without hole  [tex]= \frac{P * L_{Al}}{A_1 E}[/tex]

Contraction in aluminium bar without hole  [tex]= \frac{160*10^3 * 0.6}{0.00126 * 85 * 10^9 }[/tex]

Contraction in aluminium bar without hole = 96000/107100000

Contraction in aluminium bar without hole = 0.000896

Contraction in aluminium bar with hole  [tex]= \frac{P * L_{h}}{A_2 E}[/tex]

Contraction in aluminium bar without hole  [tex]= \frac{160*10^3 * 0.1}{0.00055 * 85 * 10^9 }[/tex]

Contraction in aluminium bar without hole = 16000/46750000

Contraction in aluminium bar without hole = 0.000342

Total contraction = 0.000896 + 0.000342

Total contraction = 0.001238 m = 1.238 mm

Answer:

Time delay increases

Explanation:

Time delay is the delay between occurance of signal. If sampling time that is time between two samples is increased, the delay in the occurance of regenerated samples is also increased.

Answer:

The final temperature and pressure in the insulated rigid tank are [tex]48\,^{\circ}C[/tex] and [tex]375\,kPa[/tex].

Explanation:

An ideal gas is represented by the following model:

[tex]P\cdot V = \frac{m}{M}\cdot R_{u} \cdot T[/tex]

Where:

[tex]P[/tex] - Pressure, measured in kilopascals.

[tex]V[/tex] - Volume, measured in cubic meters.

[tex]m[/tex] - Mass of the ideal gas, measured in kilograms.

[tex]M[/tex] - Molar mass, measured in kilograms per kilomole.

[tex]T[/tex] - Temperature, measured in Kelvin.

[tex]R_{u}[/tex] - Universal constant of ideal gases, equal to [tex]8.314\,\frac{kPa\cdot m^{3}}{kmol\cdot K}[/tex]

As tank is rigid and insulated, it means that no volume deformations in tank, heat and mass interactions with surroundings occur during expansion process. Hence, final pressure is less that initial one, volume is doubled (due to equal partitioning) and temperature remains constant. Hence, the following relationship can be derived from model for ideal gases:

[tex]\frac{P_{1}\cdot V_{1}}{T_{1}} = \frac{P_{2}\cdot V_{2}}{T_{2}}[/tex]

Now, final pressure is cleared:

[tex]P_{2} = P_{1}\cdot \frac{T_{2}}{T_{1}}\cdot \frac{V_{1}}{V_{2}}[/tex]

[tex]P_{2} = (750\,kPa)\cdot 1 \cdot \frac{1}{2}[/tex]

[tex]P_{2} = 375\,kPa[/tex]

The final temperature and pressure in the insulated rigid tank are [tex]48\,^{\circ}C[/tex] and [tex]375\,kPa[/tex].

Answer:

(i) IR = 100.167 A Iy = 75.125∠-120 IB = 50.083 ∠+120 (ii) IN =43.374∠ -30°

Explanation:

Solution

Given that:

Three loads  24 kW, 18 kW, and 12 kW are connected between the neutral.

Voltage = 415V

Now,

(1)The current in each line conductor

Thus,

The Voltage Vpn = vL√3

Gives us, 415/√3 = 239.6 V

Then,

IR = 24 K/ Vpn ∠0°

24K/239.6 ∠0°= 100.167 A

For Iy

Iy = 18k/239. 6

= 75.125A

Thus,

Iy = 75.125∠-120 this is as a result of the 3- 0 system

Now,

IB = 12K /239.6

= 50.083 A

Thus,

IB is =50.083 ∠+120

(ii) We find the current in the neutral conductor

which is,

IN =Iy +IB +IR

= 75.125∠-120 + 50.083∠+120 +100.167

This will give us the following summation below:

-37.563 - j65.06 - 25.0415 +j 43.373 + 100.167

Thus,

IN = 37.563- j 21.687

Therefore,

IN =43.374∠ -30°

Answer:

George  Floyd (BLACK  LIFES  MATTER)

C O V I D - 19

Quarantine  

no sports

wearing a mask

and a whole lot of other stuff

Explanation:

Answer:

(a) 2.39 MPa (b) 3.03 kJ (c) 3.035 kJ

Explanation:

Solution

Recall that:

A 10 gr of air is compressed isentropically

The initial air is at = 27 °C, 110 kPa

After compression air is at = a450 °C

For air,  R=287 J/kg.K

cv = 716.5 J/kg.K

y = 1.4

Now,

(a) W efind the pressure on [MPa]

Thus,

T₂/T₁ = (p₂/p₁)^r-1/r

=(450 + 273)/27 + 273) =

=(p₂/110) ^0.4/1.4

p₂ becomes  2390.3 kPa

So, p₂ = 2.39 MPa

(b) For the increase in total internal energy, is given below:

ΔU = mCv (T₂ - T₁)

=(10/100) (716.5) (450 -27)

ΔU =3030 J

ΔU =3.03 kJ

(c) The next step is to find the total work needed in kJ

ΔW = mR ( (T₂ - T₁) / k- 1

(10/100) (287) (450 -27)/1.4 -1

ΔW = 3035 J

Hence, the total work required is = 3.035 kJ

Answer:

The correct answer to the following question will be "1.23 mm".

Explanation:

The given values are:

Average normal stress,

[tex]\sigma=200 \ MPa[/tex]

Elastic module,

[tex]E = 77 \ GPa[/tex]

Length,

[tex]L = 570 \ mm[/tex]

To find the deformation, firstly we have to find the equation:

⇒  [tex]\delta=\Sigma\frac{N_{i}L_{i}}{E \ A_{i}}[/tex]

⇒     [tex]=\frac{P(\frac{L}{H})}{E(bt)} +\frac{P(\frac{L}{2})}{E (bt)(\frac{2}{3})}+\frac{P(\frac{L}{H})}{Ebt}[/tex]

On taking "[tex]\frac{PL}{Ebt}[/tex]" as common, we get

⇒     [tex]=\frac{\frac{PL}{Ebt}}{[\frac{1}{4}+\frac{3}{4}+\frac{1}{4}]}[/tex]

⇒     [tex]=\frac{5PL}{HEbt}[/tex]

Now,

The stress at the middle will be:

⇒  [tex]\sigma=\frac{P}{A}[/tex]

⇒     [tex]=\frac{P}{(\frac{2}{3})bt}[/tex]

⇒     [tex]=\frac{3P}{2bt}[/tex]

⇒  [tex]\frac{P}{bt} =\frac{2 \sigma}{3}[/tex]

Hence,

⇒  [tex]\delta=\frac{5 \sigma \ L}{6E}[/tex]

On putting the estimated values, we get

⇒     [tex]=\frac{5\times 200\times 570}{6\times 77\times 10^3}[/tex]

⇒     [tex]=\frac{570000}{462000}[/tex]

⇒     [tex]=1.23 \ mm[/tex]  

Answer:

Heat rejected to cold body = 3.81 kJ

Explanation:

Temperature of hot thermal reservoir Th = 1600 K

Temperature of cold thermal reservoir Tc = 400 K

efficiency of the Carnot's engine = 1 - [tex]\frac{Tc}{Th}[/tex]

eff. of the Carnot's engine = 1 - [tex]\frac{400}{600}[/tex]

eff = 1 - 0.25 = 0.75

efficiency of the heat engine = 70% of 0.75 = 0.525

work done by heat engine = 2 kJ

eff. of heat engine is gotten as = W/Q

where W = work done by heat engine

Q = heat rejected by heat engine to lower temperature reservoir

from the equation, we can derive that

heat rejected Q = W/eff = 2/0.525 = 3.81 kJ

Answer:

Explanation:

Given that,

The area of glass [tex]A_g[/tex] = [tex]0.11m^2[/tex]

The thickness of the glass [tex]t_g=4mm=4\times10^-^3m[/tex]

The area of the styrofoam [tex]A_s=11m^2[/tex]

The thickness of the styrofoam [tex]t_s=0.20m[/tex]

The thermal conductivity of the glass [tex]k_g=0.80J(s.m.C^o)[/tex]

The thermal conductivity of the styrofoam  [tex]k_s=0.010J(s.m.C^o)[/tex]

Inside and outside temperature difference is ΔT

The heat loss due to conduction in the window is

[tex]Q_g=\frac{k_gA_g\Delta T t}{t_g} \\\\=\frac{(0.8)(0.11)(\Delta T)t}{4.0\times 10^-^3}\\\\=(22\Delta Tt)j[/tex]

The heat loss due to conduction in the wall is

[tex]Q_s=\frac{k_sA_s\Delta T t}{t_g} \\\\=\frac{(0.010)(11)(\Delta T)t}{0.20}\\\\=(0.55\Delta Tt)j[/tex]

The net heat loss of the wall and the window is

[tex]Q=Q_g+Q_s\\\\=\frac{k_gA_g\Delta T t}{t_g}+\frac{k_sA_s\Delta T t}{t_g}\\\\=(22\Delta Tt)j +(0.55\Delta Tt)j \\\\=(22.55\Delta Tt)j[/tex]

The percentage of heat lost by the window is

[tex]=\frac{Q_g}{Q}\times 100\\\\=\frac{22\Delta T t}{22.55\Delta T t}\times 100\\\\=97.6 \%[/tex]

Answer:

Explanation:

a ) for transformer which steps down voltage , if V₁ and V₂ be voltage of primary and secondary coil and n₁ and n₂ be the no of turns of wire in them

V₁ /V₂ = n₁ / n₂

Here V₁ = 220 V , V₂ = 5V , n₁ = 2200 n₂ = ?

220 /5 = 2200 / n₂

n₂ = 2200 x 5 / 220

= 50

b )

for 100 % efficiency

input power = output power

V₁ I₁ = V₂I₂

I₁ and I₂ are current in primary and secondary coil

220 x I₁ = 5 x .5

I₁ = .01136 A .

c )

If n₂ = 100

V₁ /V₂ = n₁ / n₂

220 / V₂ = 2200 / 100

V₂ = 10 V

V₁ I₁ = V₂I₂

220 x .01136 = 10 I₂

I₂ = .25 A.

Answer:

Explanation:

A negative binary number is represeneted by its 2's complement value. To get 2's complement, you just need to invert the bits and add 1 to it. So the formula is:

  twos_complement = ~val + 1

So you start out with 22 and you want to make it negative.

22₁₀ = ‭0001 0110‬₂    

~22₁₀ = ‭1110 1001‬₂   inverting the bits

~22₁₀ + 1 = ‭1110 1010‬₂   adding 1 to it.

so -22₁₀ == ~22₁₀ + 1 == ‭1110 1010‬₂

Do the same process for 16-bits and 32-bits and you'll find that the most significant bits will be padded with 1's.

-22₁₀ = ‭1110 1010‬₂     8-bits

-22₁₀ = ‭1111 1111 1110 1010‬‬₂     16-bits

-22₁₀ = ‭‭1111 1111 1111 1111 1111 1111 1110 1010‬‬‬₂  32-bits

Answer:

The dimension of the  square cross section is = 30mm * 30mm

Explanation:

Before proceeding with the calculations convert MPa to Kpsi

Sut ( ultimate strength ) = 770 MPa * 0.145 Kpsi/MPa = 111.65 Kpsi

the fatigue strength factor of Sut at 10^3 cycles for Se = Se' = 0.5 Sut

at 10^6 cycles" for 111.65 Kpsi  = f ( fatigue strength factor) = 0.83

To calculate the endurance limit  use  Se' = 0.5 Sut      since Sut < 1400 MPa

Se'( endurance limit ) = 0.5 * 770 = 385 Mpa

The surface condition modification factor

Ka = 57.7 ( Sut )^-0.718

Ka = 57.7 ( 770 ) ^-0.718

Ka = 0.488

Assuming the size modification factor (Kb) = 0.85 and also assuming all modifiers are equal to one

The endurance limit at the critical location of a machine part can be expressed as :

Se = Ka*Kb*Se'

Se = 0.488 * 0.85 * 385 = 160 MPa

Next:

Calculating the constants to find the number of cycles

α = [tex]\frac{(fSut)^2}{Se}[/tex]

α =[tex]\frac{(0.83*770)^2}{160}[/tex]  =  2553 MPa

b = [tex]-\frac{1}{3} log(\frac{fSut}{Se} )[/tex]

b = [tex]-\frac{1}{3} log (\frac{0.83*770}{160} )[/tex]  = -0.2005

Next :

calculating the fatigue strength using the relation

Sf = αN^b

N = number of cycles

Sf = 2553 ( 10^4) ^ -0.2005

Sf = 403 MPa

Calculate the maximum moment of the beam

M = 2000 * 0.6 = 1200 N-m

calculating the maximum stress in the beam

∝ = ∝max = [tex]\frac{Mc}{I}[/tex]

Where c = b/2 and   I = b(b^3) / 12

hence ∝max = [tex]\frac{6M}{b^3}[/tex]  =  6(1200) / b^3   =  7200/ b^3   Pa

note: b is in (meters)

The expression for the factor of safety is written as

n = [tex]\frac{Sf}{\alpha max }[/tex]

Sf = 403, n = 1.5 and ∝max = 7200 / b^3

= 1.5 = [tex]\frac{403(10^6 Pa/Mpa)}{7200 / B^3}[/tex]   making b subject of the formula in other to get the value of b

b = 0.0299 m * 10^3 mm/m

b = 29.9 mm therefore b ≈ 30 mm

since  the size factor  assumed is near the calculated size factor using this relation : de = 0.808 ( hb)^1/2

the dimension = 30 mm by 30 mm

Image of wheel is missing, so i attached it.

Answer:

ω = 14.95 rad/s

Explanation:

We are given;

Mass of wheel; m = 20kg

T = 20 N

k_o = 0.3 m

Since the wheel starts from rest, T1 = 0.

The mass moment of inertia of the wheel about point O is;

I_o = m(k_o)²

I_o = 20 * (0.3)²

I_o = 1.8 kg.m²

So, T2 = ½•I_o•ω²

T2 = ½ × 1.8 × ω²

T2 = 0.9ω²

Looking at the image of the wheel, it's clear that only T does the work.

Thus, distance is;

s_t = θr

Since 4 revolutions,

s_t = 4(2π) × 0.4

s_t = 3.2π

So, Energy expended = Force x Distance

Wt = T x s_t = 20 × 3.2π = 64π J

Using principle of work-energy, we have;

T1 + W = T2

Plugging in the relevant values, we have;

0 + 64π = 0.9ω²

0.9ω² = 64π

ω² = 64π/0.9

ω = √64π/0.9

ω = 14.95 rad/s

Answer:

4.75m^2

Explanation:

Given:-

- Temperature of hot fluid at inlet:  [tex]T_h_i = 300[/tex] °C

- Temperature of cold fluid at outlet: [tex]T_c_o = 120[/tex] °C

- Temperature of cold fluid at inlet: [tex]T_c_i = 35[/tex] °C

- The overall heat transfer coefficient: U = 1500 W / m^2 K

- The flow rate of cold fluid: m_c = 10,00 kg/ h

- The flow rate of hot fluid: m_h = 5,000 kg/h

Solution:-

- We will evaluate water properties at median temperatures of each fluid using table A-4.

Cold fluid:   Tci = 35°C , Tco = 35°C

                            Tcm = 77.5 °C ≈ 350 K  --- > [tex]C_p_c = 4195 \frac{J}{kg.K}[/tex]

 Hot fluid:     Thi = 300°C , Tho = 150°C ( assumed )

                             Thm = 225 °C ≈ 500 K --- > [tex]C_p_h = 4660 \frac{J}{kg.K}[/tex]

- We will use logarithmic - mean temperature rate equation as follows:

                             [tex]A_s = \frac{q}{U*dT_l_m}[/tex]

Where,

                 A_s : The surface area of heat exchange

                 ΔT_lm: the logarithmic differential mean temperature

                 q: The rate of heat transfer

- Apply the energy balance on cold fluid as follows:

                   [tex]q = m_c * C_p_c * ( T_c_o - T_c_i )\\\\q = \frac{10,000}{3600} * 4195 * ( 120 - 35 )\\\\q = 9.905*10^5 W[/tex]

- Similarly, apply the heat balance on hot fluid and evaluate the outlet temperature ( Tho ) :

                   [tex]T_h_o = T_h_i - \frac{q}{m_h * C_p_h} \\\\T_h_o = 300 - \frac{9.905*10^5}{\frac{5000}{3600} * 4660} \\\\T_h_o = 147 C[/tex]

- We will use the experimental results of counter flow ( unmixed - unmixed ) plotted as figure ( Fig . 11.11 ) of the " The fundamentals to heat transfer" and determine the value of ( P , R , F ).

- So the relations from the figure 11.11 are:

                  [tex]P = \frac{T_c_o - T_c_i}{T_h_i - T_c_i} \\\\P = \frac{120 - 35}{300 - 35} \\\\P = 0.32[/tex]    

                 [tex]R = \frac{T_h_i - T_h_o}{T_c_o - T_c_i} \\\\R = \frac{300 - 147}{120 - 35} \\\\R = 1.8[/tex]

Therefore,         P = 0.32 , R = 1.8 ---- > F ≈ 0.97

- The log-mean temperature ( ΔT_lm - cf ) for counter-flow heat exchange can be determined from the relation:

                        [tex]dT_l_m = \frac{( T_h_i - T_c_o ) - ( T_h_o - T_c_i ) }{Ln ( \frac{( T_h_i - T_c_o )}{( T_h_o - T_c_i )} ) } \\\\dT_l_m = \frac{( 300 - 120 ) - ( 147 - 35 ) }{Ln ( \frac{( 300-120 )}{( 147-35)} ) } \\\\dT_l_m = 143.3 K[/tex]

- The log - mean differential temperature for counter flow is multiplied by the factor of ( F ) to get the standardized value of log - mean differential temperature:

                       [tex]dT_l = F*dT_l_m = 0.97*143.3 = 139 K[/tex]

- The required heat exchange area ( A_s ) can now be calculated:

                     [tex]A_s = \frac{9.905*10^5 }{1500*139} \\\\A_s = 4.75 m^2[/tex]

Answer:

Pressure difference (ΔP) = 63,519.75 kpa

Explanation:

Given:

ρ = 1,000 kg/m³

Height of cylindrical container used (h) = 7m / 2 = 3.5m

Specific gravity (sg) = 0.85

Find:

Pressure difference (ΔP).

Computation:

⇒ Pressure difference (ΔP) = h g [ ρ(sg) + ρ]                ∵ [ g = 9.81]

⇒ Pressure difference (ΔP) = (3.5)(9.81) [ 1,000(0.85) + 1,000]

⇒ Pressure difference (ΔP) = 34.335 [8,50 + 1,000]

⇒ Pressure difference (ΔP) = 34.335 [1,850]

⇒ Pressure difference (ΔP) = 63,519.75 kpa

Answer:

Explanation:

The solution of all the four parts is provided in the attached figures

Answer:

The goal of the software is to observe the software behavior to meet its requirement expectation. In software engineering, validating software might be harder since client's expectation may be vague or unclear.

Explanation:

Answer:

Develop social skills

Explanation:

Answer:

strengthen your college applications

Explanation:

Answer:

(1). False, (2). True, (3). False, (4). False, (5). True.

Explanation:

The term ''contouring'' in this question does not have to do with makeup but it has to deal with the measurement of all surfaces in planes. It is a measurement in which the rough and the contours are being measured. So, let us check each questions again.

(1). In contouring, it is necessary to measure position and not velocity for feedback.

ANSWER : b =>False. IT IS NECESSARY TO MEASURE BOTH FOR FEEDBACK.

(2). In contouring during 2-axis NC machining, the two axes are moved at the same speed to achieve the desired contour.

ANSWER: a=> True.

(3). Job shop is another term for process layout.

ANSWER: b => False

JOB SHOP IS A FLEXIBLE PROCESS THAT IS BEING USED during manufacturing process and are meant for job Production. PROCESS LAYOUT is used in increasing Efficiency.

(4). Airplanes are normally produced using group technology or cellular layout.

ANSWER: b => False.

(5). In manufacturing, value-creating time is greater than takt time.

ANSWER: a => True.

Answer:

A. True

Explanation:

When an electromagnetic field wave strikes a conductor, say a wire, it induces an alternating current that is proportional to the wave in the conductor. This is a reversal of generating electromagnetic wave from accelerating a charged particle. This phenomenon is used in radio antena for receiving radio wave signals and also use in medicine for body scanning.