Answer:
Following are the responses to the given question:
Explanation:
Effective red duration is applied each cycle r=30 second D/D/1 queuing
In total, its approach delay is 83.33 sec vehicle per cycle
Flow rate(s) of saturated = 1,000 vehicles each hour
Total vehicle delay per cycle[tex]= \frac{v \times 30^2}{2(1-\frac{v}{0.2778})}[/tex]
[tex]\to \frac{v\times 30^2}{2(1-\frac{v}{0.2778})}= 83.33\\\\\to 900v=166.66-599.928v\\\\\to v=0.111 \frac{veh}{sec}\\\\[/tex]
The flow rate for such total approach is 0.111 per second.
The overall flow velocity of the approach is 400 cars per hour
The approach capacity refers to the number of arrivals per cycle.
Environmentally friendly time ratio to cycle length:
[tex],\frac{g}{C} \ is = \frac{400}{1000}=0.4\\\\r= c-g\\\\30\ sec =C - 0.4 C\\\\C=50 \ sec[/tex]
7
Which wire can carry a higher current?
ered
tof
Select one:
A. AWG 6
B. AWG 18
C. AWG 12
D. AWG 24
Answer:
the wire that can carry much current is AWG 24
AWG 24 is the wire can carry a higher current. The diameter of the wire increases with decreasing gauge. The electrical resistance to the signals decreases with increasing wire diameter. Hence, option D is correct.
What is meant by high current?Any current above 10 mA has the potential to deliver an unpleasant to severe shock, while 200 mA and above is considered lethal. Despite the fact that currents above 200 mA might cause serious burns and unconsciousness, they usually do not cause death if the sufferer receives timely medical attention.
Higher voltage and lower current are frequently more effective combinations. The amount of current that a wire is rated to handle is frequently indicated by its capacity rating. People can use the same cable to drive a load twice as large by doubling the voltage and maintaining the same current.
Thus, option D is correct.
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True or false all workers who do class 1 asbestos work must be part of a medical surveillance program
Answer:
Yes
Explanation:
Answer:
true
Explanation:
hehehe
Provide two programming examples in which multithreading provides better performance than a single-threaded solution. Provide one example where singlethreaded solution performs better than multi-threaded solution
Answer:
I dont kno
Explanation:
Im so sorry
A main cable in a large bridge is designed for a tensile force of 2,600,000 lb. The cable consists of 1470 parallel wires, each 0.16 in. in diameter. The wires are cold-drawn steel with an average ultimate strength of 230,000 psi. What factor of safety was used in the design of the cable
Answer:
the factor of safety was used in the design of the cable is 2.6146
Explanation:
Given the data in the question;
Load on the main capable [tex]P_{initial[/tex] = 2600000 lb
number of parallel wires n = 1470
Diameter d = 0.16 in
average ultimate strength [tex]S_{ultimate[/tex] = 230000 psi
First we calculate the Load acting on each cable;
[tex]P_{initial[/tex] = P × n
P = [tex]P_{initial[/tex] / n
we substitute
P = 2600000 lb / 1470
P = 1768.70748 lb
Next we determine the working stress acting in a member;
[tex]S_{working[/tex] = P/A
{ Area A = [tex]\frac{\pi }{4}[/tex]d² }
[tex]S_{working[/tex] = P / [tex]\frac{\pi }{4}[/tex]d²
we substitute
[tex]S_{working[/tex] = 1768.70748 / [tex]\frac{\pi }{4}[/tex](0.16)²
[tex]S_{working[/tex] = 1768.70748 / 0.02010619298
[tex]S_{working[/tex] = 87968.29 psi
Now we calculate the factor of safety F.S
F.S = [tex]S_{ultimate[/tex] / [tex]S_{working[/tex]
we substitute
F.S = 230000 psi / 87968.29 psi
F.S = 2.6145785 ≈ 2.6146
Therefore, the factor of safety was used in the design of the cable is 2.6146
Consider the following example: The 28-day compressive strength should be 4,000 psi. The slump should be between 3 and 4 in. and the maximum aggregate size should not exceed 1 in. The coarse and fine aggregates in the storage bins are wet. The properties of the materials are as follows:________.
Cement : Type I, specific gravity = 3.15
Coarse Aggregate: Bulk specific gravity (SSD) = 2.70; absorption
capacity = 1.1%; dry-rodded unit weight = 105 lb./ft.3
surface moisture = 1%
Fine Aggregate: Bulk specific gravity (SSD) = 2.67; absorption
capacity = 1.3%; fineness modulus = 2.70;
surface moisture = 1.5%
Unit of rate of heat transfer
Answer:
The units on the rate of heat transfer are Joule/second, also known as a Watt.
Explanation:
Heat flow is calculated using the rock thermal conductivity multiplied by the temperature gradient. The standard units are mW/m2 = milli Watts per meter squared. Thus, think of a flat plane 1 meter by 1 meter and how much energy is transferred through that plane is the amount of heat flow.
hope it helps .
stay safe healthy and happy..The rate of heat transfer is measured in Joules per second, also known as Watts.
What is heat transfer?Heat transfer is a thermal engineering discipline that deals with the generation, use, conversion, and exchange of thermal energy between physical systems.
Heat transfer mechanisms include thermal conduction, thermal convection, thermal radiation, and energy transfer via phase changes.
The rate of heat transfer through a unit thickness of material per unit area per unit temperature difference is defined as thermal conductivity. Thermal conductivity varies with temperature and is measured experimentally.
Heat is typically transferred in a combination of these three types and occurs at random. Heat transfer rate is measured in Joules per second, also known as Watts.
Thus, Joules per second or watts is the unit of rate of heat transfer.
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1. (15) A truck scale is made of a platform and four compression force sensors, one at each corner of the platform. The sensor itself is a short steel cylinder, 22 mm in diameter. A single stain gauge is pre-stressed to 3% strain and bonded on the outer surface of the cylinder. The strain gauges have a nominal resistance (before pre-stressing) of 340 Ohms and a gauge factor of 6.9. The steel used for the cylinders has a modulus of elasticity of 30 GPa. Calculate: a. The maximum truck weight that the scale can measure. b. The change in resistance of the sensors for maximum weight. c. The sensitivity of the scale assuming the response of the strain gauges is linear.
Answer:
a). 139498.24 kg
b). 281.85 ohm
c). 10.2 ohm
Explanation:
Given :
Diameter, d = 22 m
Linear strain, [tex]$\epsilon$[/tex] = 3%
= 0.03
Young's modulus, E = 30 GPa
Gauge factor, k = 6.9
Gauge resistance, R = 340 Ω
a). Maximum truck weight
σ = Eε
σ = [tex]$0.03 \times 30 \times 10^9$[/tex]
[tex]$\frac{P}{A} =0.03 \times 30 \times 10^9$[/tex]
[tex]$P = 0.03 \times 30 \times 10^9\times \frac{\pi}{4}\times (0.022)^2$[/tex]
= 342119.44 N
For the four sensors,
Maximum weight = 4 x P
= 4 x 342119.44
= 1368477.76 N
Therefore, weight in kg is [tex]$m=\frac{W}{g}=\frac{1368477.76}{9.81}$[/tex]
m = 139498.24 kg
b). Change in resistance
[tex]k=\frac{\Delta R/R}{\Delta L/L}[/tex]
[tex]$\Delta R = k. \epsilon R$[/tex] , since [tex]$\epsilon= \Delta L/ L$[/tex]
[tex]$\Delta R = 6.9 \times 0.03 \times 340$[/tex]
[tex]$\Delta R = 70.38 $[/tex] Ω
For 4 resistance of the sensors,
[tex]$\Delta R = 70.38 \times 4 = 281.52$[/tex] Ω
c). [tex]$k=\frac{\Delta R/R}{\epsilon}$[/tex]
If linear strain,
[tex]$\frac{\Delta R}{R} \approx \frac{\Delta L}{L}$[/tex] , where k = 1
[tex]$\Delta R = \frac{\Delta L}{L} \times R$[/tex]
[tex]$\Delta R = 0.03 \times 340$[/tex]
[tex]$\Delta R = 10.2 $[/tex] Ω
Consider a single crystal of silver oriented such that tensile stress is applied along a (0 0 1) direction. If slip occurs on a (1 1 1) plane and in a (1 0 1) direction and is initiated at an applied tensile stress of 1.1 MPa (160 psi), compute the critical resolved shear stress.
Answer:
i don't know
Explanation:
sorry
Problem 1. Network-Flow Programming (25pt) A given merchandise must be transported at a minimum total cost between two origins (supply) and two destinations (demand). Destination 1 and 2 demand 500 and 700 units of merchandise, respectively. At the origins, the available amounts of merchandise are 600 and 800 units. USPS charges $5 per unit from origin 1 to demand 1, and $7 per unit from origin 1 to demand 2. From origin 2 to demand 1 and 2, USPS charges the same unit cost, $10 per unit, however, after 200 units, the unit cost of transportation increases by 50% (only from origin 2 to demand 1 and 2).
a) Formulate this as a network-flow problem in terms of objective function and constraint(s) and solve using Excel Solver.
b) How many units of merchandise should be shipped on each route and what is total cost?
Solution :
Cost
Destination Destination Destination Maximum supply
Origin 1 5 7 600
Origin 2 10 10 800
15, for > 200 15, for > 200
Demand 500 700
Variables
Destination 1 2
Origin 1 [tex]$X_1$[/tex] [tex]$$X_2[/tex]
Origin 2 [tex]$X_3$[/tex] [tex]$$X_4[/tex]
Constraints : [tex]$X_1$[/tex], [tex]$$X_2[/tex], [tex]$X_3$[/tex], [tex]$$X_4[/tex] ≥ 0
Supply : [tex]$X_1$[/tex] + [tex]$$X_2[/tex] ≤ 600
[tex]$X_3$[/tex] + [tex]$$X_4[/tex] ≤ 800
Demand : [tex]$X_1$[/tex] + [tex]$$X_3[/tex] ≥ 500
[tex]$X_2$[/tex] + [tex]$$X_4[/tex] ≥ 700
Objective function :
Min z = [tex]$5X_1+7X_2+10X_3+10X_4, \ (if \ X_3, X_4 \leq 200)$[/tex]
[tex]$=5X_1+7X_2+(10\times 200)+(X_3-200)15+(10 \times 200)+(X_4-200 )\times 15 , \ \ (\text{else})$[/tex]
Costs :
Destination 1 Destination 2
Origin 1 5 7
Origin 2 10 10
15 15
Variables :
[tex]$X_1$[/tex] [tex]$$X_2[/tex]
300 300
200 400
[tex]$X_3$[/tex] [tex]$$X_4[/tex]
Objective function : Min z = 10600
Constraints:
Supply 600 ≤ 600
600 ≤ 800
Demand 500 ≥ 500
700 ≥ 500
Therefore, the total cost is 10,600.
Identify the transformation. Note: you can only submit this question once for marking. translation rotation shear projection none of the above
Answer:
The answer is "shear".
Explanation:
Every transformation could be shown by some kind of conventional matrix.
Its standard matrices of shape k here could be any real value enabling shear transformation to parallel to the y axis.
[tex]\left[\begin{array}{cc}1&0\\k&1\\\end{array}\right][/tex]
This coefficient matrix A is the standard matrix during transformation. With the use of a the transformation could be entered into T(x)=Ax
And standard transfer function is standard.
[tex]\left[\begin{array}{cc}1&0\\6&1\\\end{array}\right][/tex]
The matrix in the form of the shear matrix.
Estimate the theoretical fracture strength of a brittle material if it is known that fracture occurs by the propagation of an elliptically shaped surface crack of length 0.25 mm (0.01 in) and tip radius of curvature of 1.2 x 10-3 mm (4.7 x 10-5 in.) when a stress of 1200 MPa (174,000 psi) is applied.
Answer:
the theoretical fracture strength of the brittle material is 5.02 × 10⁶ psi
Explanation:
Given the data in the question;
Length of surface crack α = 0.25 mm
tip radius ρ[tex]_t[/tex] = 1.2 × 10⁻³ mm
applied stress σ₀ = 1200 MPa
the theoretical fracture strength of a brittle material = ?
To determine the the theoretical fracture strength or maximum stress at crack tip, we use the following formula;
σ[tex]_m[/tex] = 2σ₀[tex]([/tex] α / ρ[tex]_t[/tex] [tex])^{\frac{1}{2}[/tex]
where α is the Length of surface crack,
ρ[tex]_t[/tex] is the tip radius,
and σ₀ is the applied stress.
so we substitute
σ[tex]_m[/tex] = (2 × 1200 MPa)[tex]([/tex] 0.25 mm / ( 1.2 × 10⁻³ mm ) [tex])^{\frac{1}{2}[/tex]
σ[tex]_m[/tex] = 2400 MPa × [tex]([/tex] 208.3333 [tex])^{\frac{1}{2}[/tex]
σ[tex]_m[/tex] = 2400 MPa × 14.43375
σ[tex]_m[/tex] = 34641 MPa
σ[tex]_m[/tex] = ( 34641 × 145 )psi
σ[tex]_m[/tex] = 5.02 × 10⁶ psi
Therefore, the theoretical fracture strength of the brittle material is 5.02 × 10⁶ psi
Example 12: Write an algorithm and draw a flowchart to calculate
the factorial of a number(N). Verify your result by a trace table by
assuming N = 5.
Hint: The factorial of N is the product of numbers from 1 to N)
Answer:
An algotherum is a finite set of sequential instructions to accomplish a task where instructions are written in a simple English language
whats is the purpose of the stator winding
Answer:
In an electric motor, the stator provides a magnetic field that drives the rotating armature; in a generator, the stator converts the rotating magnetic field to electric current. In fluid powered devices, the stator guides the flow of fluid to or from the rotating part of the system.
Analyze the rate of heat transfer through a wall of an industrial furnace which is constructed from 0.15-m-thick fireclay brick having a thermal conductivity of 1.7 W/m.K. Measurements made during steady state operation reveal temperatures of 1400 and 1150 K at the inner and outer surfaces, respectively. The wall dimension is 0.5 m by 1.2 m by side.
Answer:
1700 W
Explanation:
The heat transfer rate P = kA(T - T')/d where k = thermal conductivity of wall = 1.7 W/m-K, A = area of wall = 0.5 m × 1.2 m = 0.6 m², T = temperature of inner surface = 1400 K, T = temperature of outer surface = 1150 K and d = thickness of wall = 0.15 m
So, P = kA(T - T')/d
substituting the values of the variables into the equation, we have
P = 1.7 W/m-K × 0.6 m²(1400 K - 1150 K)/0.15 m
P = 1.7 W/m-K × 0.6 m² × 250 K/0.15 m
P = 255 Wm/0.15 m
P = 1700 W
So, the heat transfer rate through the wall is 1700 W
Find the velocity and rate of flow of water through a rectangular channel of 6m wide and 3m deep when it's running full. The channel is having a bed slope of 1 in 2000. Take Chezy's coefficient, C=55
Answer:
V = 1.5062 m/s
Explanation:
look to the photos
A steel bar with a diameter of .875 inches and a length of 15.0 ft is axially loaded with a force of 21.6 kip. The modulus of elasticity of the steel is 29 *106 psi. Determine
Answer:
35.92 kpsi
Explanation:
Given data:
diameter of the steel bar d = 0.875 in
Area A = πd^2/4 = π(0.875)^2/4
length L = 15.0 ft
Load P = 21.6 kip
Modulus of elesticity E = 29×10^6 Psi
Assume we are asked to determine axial stress in the bar which is given as
[tex]\sigma = Load, P/ Area, A[/tex]
[tex]\sigma = 4P/\pi d^2[/tex]
substitute the value
[tex]\sigma = \frac{4\times 21.6}{\pi \times (0.875)^2} \\=35.92\ kpsi[/tex]
Words and numbers can be
printed using many different
or type styles.
tech a says that a slightly lean mixture offers good fuel economy and low exhaust emissions. Tech b says that a mixture that is too rich fouls spark plugs and causes incomplete burning. Who is correct
Tech A says that some relays are equipped with a suppression diode in parallel with the winding. Tech B says that some relays are equipped with a resistor in parallel with the winding. Who is correct
Answer:
Both are correct.
Explanation:
Both the technician A and B are correct. Some relays are equipped with a suppression diode in parallel windings while some relays are equipped with resistors. This is due to different requirements of the electromagnetic objects. Some require resistors to stop the flow of current towards the magnet.
As an engineer which types of ethical issues or problem you can face in industrial environment.
Explanation:
Answer ⬇️
Social and ethical issues in engineering, ethical principles of engineering, professional code of ethics, some specific social problems in engineering practice: privacy and data protection, corruption, user orientation, digital divide, human rights, access to basic services.
➡️dhruv73143(⌐■-■)
An article gave a scatter plot along with the least squares line of x = rainfall volume (m3) and y = runoff volume (m3) for a particular location. The accompanying values were read from the plot.
c) Calculate a point estimate of the true average runoff volume when rainfall volume is 51. (Round your answer to four decimal places.)
(d) Calculate a point estimate of the standard deviation . (Round your answer to two decimal places.)
(e) What proportion of the observed variation in runoff volume can be attributed to the simple linear regression relationship between runoff and rainfall? (Round your answer to four decimal places.)
x 6 12 14 16 23 30 40 52 55 67 72 81 96 112 127
y 4 10 13 14 15 25 27 48 38 46 53 72 82 99 100
Answer:
y = 0.834X - 1.58015
Slope = 0.8340 ; Intercept = - 1.5802
y = 40.9539
19.93
0.9765
Explanation:
X: Rainfall volume
6
12
14
16
23
30
40
52
55
67
72
81
96
112
127
Y : Runoff
4
10
13
14
15
25
27
48
38
46
53
72
82
99
100
The scatterplot shows a reasonable linear trend between the Rainfall volume and run off.
The estimated regression equation obtained using a linear regression calculator is :
y = 0.834X - 1.58015
y = Runoff ; x = Rainfall volume
Slope = 0.8340 ; Intercept = - 1.5802
Point estimate for Runoff, when, x = 51
y = 0.834X - 1.58015
y = 0.834(51) - 1.58015
y = 40.95385
y = 40.9539
d.)
Point estimate for standard deviation :
s = 5.145
σ = s * √n
σ = √15 * 5.145
= 19.93
e.)
r² = Coefficient of determination gives the proportion of explained variance in Runoff due to the regression line. From the model output, the r² value = 0.9765. Which means That about 97.65% Runoff is due to Rainfall volume.
What would the Select lines need to be to send data for the fifth bit in an 8-bit system (S0 being the MSB and S2 being the LSB)?
A. S0 = 1, S1 = 0, S2 = 0
B. S0 = 0, S1 = 0, S2 = 0
C. S0 = 0, S1 = 1, S2 = 0
D. S0 = 0, S1 = 1, S2 = 1
Answer:
A. S0 = 1, S1 = 0, S2 = 0
lines need to send data for the fifth bit in an 8 bit system
A 2400-lb rear-wheel drive tractor carrying 900 lb of gravel starts from rest and accelerates forward at 3ft/s2. Determine the reaction at each of the two (a) rear wheels A, (b) front wheels B.
Answer:
Explanation:
The missing diagram attached to the question is shown in the attached file below:
The very first thing we need to do in other to solve this question is to determine the mass of both the tractor and the mass of the gravel
For tractor, the mass is:
[tex]m_1 = \dfrac{2400 \ lb }{32.2 \ ft/s^2}[/tex]
[tex]m_1 = 74.53 \ lb.s^2/ft[/tex]
For gravel, the mass is:
[tex]m_2 = \dfrac{900 \ lb}{32.2 \ft/s^2}[/tex]
[tex]m_2 = 27.95 \ lb.s^2/ft[/tex]
From the diagram, let's consider the force along the horizontal components and vertical components;
So,
[tex]\sum F_x = ma_x \\ \\ 2F = (m_1+m_2) a \\ \\ F = \dfrac{1}{2}(74.53 4 + 27.950)lb.s^2/ft(2 \ ft/s^2) \\ \\ F = 102.484 \ lb[/tex]
[tex]\sum F_y = 0 \\ \\ 2N_A+2N_B - 2400 -900 = 0 \\ \\ N_A +N_B = 1650 \ lb[/tex]
Consider the algebraic sum of moments in the plane of A, with counter-clockwise moments being positive.
[tex]\sum M_A = I_o \alpha + \sum ma (d) \\ \\ = -2400 (20) + 2N_B (60) -900(110) = 0 - (74.534)(2)(20) - (27.950)(2)(40)[/tex]
[tex]=-48000 + 2N_B (60) -99000 = -2981.36-2236 \\ \\ = + 2N_B (60) = -2981.36-2236+48000+99000 \\ \\ = + 2N_B (60) = 141782.64 \\ \\ N_B = \dfrac{141782.64}{120} \\ \\ N_B = 1181.522 \ lb[/tex]
Replacing the value of 1181.522 lb for [tex]N_B[/tex] in equation (1)
[tex]N_A[/tex] + 1181.522 lb = 1650 lb
[tex]N_A[/tex] = (1650 - 1181.522)lb
[tex]N_A[/tex] = 468.478 lb
The net reaction on each of the rear wheels now is:)
[tex]F_R = \sqrt{N_A^2 +F^2}[/tex]
[tex]F_R = \sqrt{(468.478)^2 + (102.484)^2}[/tex]
[tex]\mathbf{F_R =479.6 \ lb}[/tex]
Now, we can determine the angle at the end of the rear wheels at which the resultant reaction force is being made in line with the horizontal
[tex]\theta = tan ^{-1}( \dfrac{468.478 }{102.484})[/tex]
[tex]\theta = 77.7^0[/tex]
Finally, the net reaction on each of the front wheels is:
[tex]F_B = N_B[/tex]
[tex]F_B =[/tex] 1182 lb
What is code in Arduino to turn led on and off
here's your answer..
A cylinder is internally pressurized to a pressure of 100 MPa. This causes tangential and axial stresses in the outer surface of 400 and 200 MPa, respectively. Make a Mohr circle representation of the stresses in the outer surface. What maximum normal and shear stresses are experienced by the outer surface?
Answer:
[tex]\mu_{max}=200Mpa[/tex]
Explanation:
From the question we are told that:
Internally pressurized [tex]P_i=100MPa[/tex]
Tangential Stress [tex]P_t=400mpa[/tex]
Axial stress [tex]P_a=200mpa[/tex]
Generally the equation for maximum normal and shear stresses are experienced by the outer surface is mathematically given by
[tex]\mu_{max}=|\frac{P_t-P_a}{2}|,|\frac{P_t}{2}|,|\frac{P_t}{2}|[/tex]
Therefore
[tex]\mu_{max}=|\frac{400-200}{2}|,|\frac{400}{2}|,|\frac{200}{2}|[/tex]
[tex]\mu_{max}=200Mpa[/tex]
A Si pin photodiode has an active light-receiving area of diameter 0.4 mm. When radiation of wavelength 700 nm (red light and intensity 0.1 mW cm^-2 is incident it generates a photocurrent of 56.6 nA. What is the responsivity (A W^-1) and quantum efficiency (QE) of the photodiode at 700 nm?
Answer:
Explanation:
here is your answer:
The responsivity will be 0.45 A / W. Then the quantum efficiency will be 80%.
How to calculate responsivity and quantum efficiency?A Si pin photodiode has an active light-receiving area of a diameter of 0.4 mm.
When radiation of wavelength 700 nm (red light and intensity 0.1 mW cm^-2 is incident it generates a photocurrent of 56.6 nA.
Diameter (d) = 0.4 mm = 0.04 cm
Then the area will be
Area (A) = π / 4 x d²
Area (A) = π / 4 x 0.04²
Area (A) = 1.26 x 10⁻³ square cm
Then the incident power will be
P₀ = intensity of light x area
P₀ = 1.26 x 10⁻³ x 0.1 x 10⁻³
P₀ = 0.126 x 10⁻⁶ μW
Then the responsivity will be
R = photocurrent / power
R = 56.6 x 10⁻⁹ / 0.126 x 10⁻⁶
R = 0.4492
R ≅ 0.45 A / W
Then the quantum efficiency will be
η = Rhc / qλ
h = plank constant
c = speed of light
q = charge of an electron
Then we have
η = 0.45 x 6.62 x 10⁻³⁴ x 3 x 10⁸ / 1.6 x 10⁻¹⁹ x 700 x 10⁻⁹
η = 0.7979
η = 0.8
η = 80%
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Fill in the truth table for output A.
A = (x+y)(x'+z')(x'+z')
Answer:
1+1×1 multiplay then you get the answer
A small ship capable of making a speed of 6 knots through still water maintains a heading due east while being set to the south by an ocean current. The actual course of the boat is from A to B, a dis- tance of 10 nautical miles that requires exactly 2 hours. Determine the speed vC of the current and its direction measured clockwise from the north.
This question is incomplete, the missing diagram is uploaded along this answer below;
Answer:
the speed Vc of the current and its direction measured clockwise from the north is 0.71 m/s and 231.02° respectively
Explanation:
Given the data in the question and as illustrated in the diagram below;
The absolute velocity of the ship Vs is 6 Knots due east
so we convert to meter per seconds
Vs = 6 Knots × [tex]\frac{0.51444 m/s}{1 Knots}[/tex] = 3.0866 m/s
Next we determine the relative velocity of the ship Vs/c
Vs/c = AB / t
given that distance between A to B = 10 nautical miles which requires 2 hours
so we substitute
Vs/c = 10 nautical miles / 2 hrs
Vs/c = [10 nautical miles × [tex]\frac{1852 m}{1 nautical-miles}[/tex] ] / [ 2 hrs × [tex]\frac{3600s}{1hr}[/tex] ]
Vs/c = 18520 / 7200
Vs/c = 2.572 m/s
Now, from the second diagram below, { showing the relative velocity polygon }
Now, using COSINE RULE, we calculate the velocity current.
Vc = √( V²s + V²s/c - 2VsSs/ccos10 )
we substitute
Vc = √( (3.0866)² + (2.572)² - (2 × 3.0866 × 2.572 × cos10 ) )
Vc = √( (3.0866)² + (2.572)² - (2 × 3.0866 × 2.572 × 0.9848 ) )
Vc = √( 9.527099 + 6.615184 - 15.6361 )
Vc = √0.506183
Vc = 0.71 m/s
Next, we use the SINE RULE to calculate the direction;
Vc/sin10 = Vs/c / sinθ
we substitute
0.71 / sin10 = 2.572 / sinθ
0.71 / 0.173648 = 2.572 / sinθ
4.0887 = 2.572 / sinθ
sinθ = 2.572 / 4.0887
sinθ = 0.62905
θ = sin⁻¹( 0.62905 )
θ = 38.98°
So, angle measured clock-wise will be;
θ = 270° - 38.98°
θ = 231.02°
Therefore, the speed Vc of the current and its direction measured clockwise from the north is 0.71 m/s and 231.02° respectively
A lamp and a coffee maker are connected in parallel to the same 120-V source. Together, they use a total of 140 W of power. The resistance of the coffee maker is 300 Ohm. Find the resistance of the lamp.
Answer:
Resistance of the lamp (r) = 156.52 ohm (Approx.)
Explanation:
Given:
Total power p = 140 W
Resistance of the coffee maker = 300 Ohm
Voltage v = 120 V
Find:
Resistance of the lamp (r)
Computation:
We know that
p = v² / R
SO,
Total power p = [Voltage²/Resistance of the lamp (r)] + [Voltage²/Resistance of the coffee maker]
140 = [120² / r] + [120²/300]
140 = 120²[1/r + 1/300]
140 = 14,400 [1/r + 1/300]
Resistance of the lamp (r) = 156.52 ohm (Approx.)
Air is compressed by a 40-kW compressor from P1 to P2. The air temperature is maintained constant at 25°C during this process as a result of heat transfer to the surrounding medium at 20°C. Determine the rate of entropy change of the air. State the assumptions made in solving this problem
Answer:
the rate of entropy change of the air is -0.1342 kW/K
the assumptions made in solving this problem
- Air is an ideal gas.
- the process is isothermal ( internally reversible process ). the change in internal energy is 0.
- It is a steady flow process
- Potential and Kinetic energy changes are negligible.
Explanation:
Given the data in the question;
From the first law of thermodynamics;
dQ = dU + dW ------ let this be equation 1
where dQ is the heat transfer, dU is internal energy and dW is the work done.
from the question, the process is isothermal ( internally reversible process )
Thus, the change in internal energy is 0
dU = 0
given that; Air is compressed by a 40-kW compressor from P1 to P2
since it is compressed, dW = -40 kW
we substitute into equation 1
dQ = 0 + ( -40 kW )
dQ = -40 kW
Now, change in entropy of air is;
ΔS[tex]_{air[/tex] = dQ / T
given that T = 25 °C = ( 25 + 273.15 ) K = 298.15 K
so we substitute
ΔS[tex]_{air[/tex] = -40 kW / 298.15 K
ΔS[tex]_{air[/tex] = -0.13416 ≈ -0.1342 kW/K
Therefore, the rate of entropy change of the air is -0.1342 kW/K
the assumptions made in solving this problem
- Air is an ideal gas.
- the process is isothermal ( internally reversible process ). the change in internal energy is 0.
- It is a steady flow process
- Potential and Kinetic energy changes are negligible.