The wavelengths of the mercury spectrum (in nm) are as follows; smallest value 387.9 nm, 427.3 nm, 580.0 nm, 681.8 nm largest value 681.8 nm.
The formula to find the wavelength of the mercury spectrum is given by;nλ = d sinθwhere;
n = 1
λ = wavelength
d = distance between the grating line
stheta (θ) = angle of diffraction from the central maximum
n = 1 (first-order maxima)
Given that;
Angle of diffraction from central maximum θ1 = 31.16°
Angle of diffraction from central maximum θ2 = 34.53°
Angle of diffraction from central maximum θ3 = 45.22°
Angle of diffraction from central maximum θ4 = 53.08°
Distance between grating lines, d = 1 / 13000 cm
= 7.692 × 10⁻⁵ cm
= 7.692 × 10⁻⁷ m
Now, let's find the wavelength for each angle of diffraction;
nλ₁ = d sinθ₁
λ₁ = d sinθ₁ / n
Substitute the given values
,λ₁ = (7.692 × 10⁻⁷) sin 31.16° / 1
= 3.879 × 10⁻⁷
m = 387.9 nm
Similarly,
λ₂ = d sinθ₂ / nλ₂
= (7.692 × 10⁻⁷) sin 34.53° / 1
= 4.273 × 10⁻⁷ m
= 427.3 nm
λ₃ = d sinθ₃ / n
λ₃ = (7.692 × 10⁻⁷) sin 45.22° / 1
= 5.800 × 10⁻⁷ m
= 580.0 nm
λ₄ = d sinθ₄ / n
λ₄ = (7.692 × 10⁻⁷) sin 53.08° / 1
= 6.818 × 10⁻⁷ m
= 681.8 nm
Therefore, the wavelengths of the mercury spectrum (in nm) are as follows; smallest value 387.9 nm, 427.3 nm, 580.0 nm, 681.8 nm largest value 681.8 nm.
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What is the frequency respsonse of this circuit? what is the expression for the magnitude of the frequency response. also sketch the magnitiude response. THANKS!
The frequency response of a circuit is the response of a system to an input signal of different frequencies. Frequency response is often used in signal processing, control systems, and other areas of electrical and electronic engineering.
In this circuit, the frequency response is
H(\omega) =
\frac{1}{(1 + j
\omega R_1 C_1)(1 + j
\omega R_2 C_2)}
The magnitude of the frequency response can be found as follows:
|H(\omega)| =
\left|
\frac{1}{(1 + j
\omega R_1 C_1)(1 + j
\omega R_2 C_2)}
\right|
Since the magnitude is the absolute value of a complex number, we can remove the absolute value signs and simplify the equation.
|H(\omega)| =
\frac{1}{
\sqrt{(1 + \omega^2 R_1^2 C_1^2)(1 + \omega^2 R_2^2 C_2^2)}
}
To sketch the magnitude response, we can use a logarithmic scale on the y-axis and plot the equation for different values of omega. The graph will show the gain of the circuit as a function of frequency, which will give us an idea of how the circuit responds to different frequencies of the input signal.
The plot shows that the circuit has a low-pass filter response, meaning it attenuates high frequencies and allows low frequencies to pass through.
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2) As measured in Earth's rest frame, a spaceship traveling at 0.980c takes 12.6 y to travel between planets. How long does the trip take as measured by someone on the spaceship? (Hint: The time interval taken by the trip as measured by someone on the spaceship is the proper time interval, ∆t_0. The time interval measured in Earth's rest frame is ∆t= 12.6 y. Apply Time Dilation equation to find ∆t_0.)
A) 2.98 y
B) 2.51 y
C) 3.75 y
D) 26.7 y
The time taken by the trip as measured by someone on the spaceship is the proper time interval, ∆t₀. The time interval measured in Earth's rest frame is ∆t = 12.6 y. Option C is the correct choice.
The Time Dilation equation is given as;
∆t₀ = ∆t / γ
where;∆t₀= proper time interval,
∆t = time interval measured in Earth's rest frame, and γ = Lorentz factor
The Lorentz factor, γ can be found as;
γ = 1 / √(1 - v²/c²)
where;
v = velocity of the spaceship,
c = speed of light.
The given velocity of the spaceship is 0.980c. Therefore;
v = 0.980c
Substituting the value of v in the equation of γ;
γ = 1 / √(1 - v²/c²)γ
= 1 / √[1 - (0.980c)²/c²]
γ = 1 / √[1 - 0.9604]
γ = 1 / 0.2917
γ = 3.4284
Now, substituting the values of γ and ∆t in the Time Dilation equation;
∆t₀ = ∆t / γ∆t₀ = 12.6 y / 3.4284
∆t₀ = 3.675 y
Therefore, the trip takes 3.675 years as measured by someone on the spaceship.
The time taken by the trip as measured by someone on the spaceship is 3.675 years, Option C.
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In relation to reverse-biased, explain the rate of change of voltage of a thyristor.
In relation to reverse-biased operation, the rate of change of voltage of a thyristor refers to the rate at which the voltage across the thyristor increases when it is subjected to a reverse bias.
When a thyristor is reverse-biased, the voltage applied to its cathode terminal becomes higher than that of the anode terminal. In this condition, the thyristor acts as an open circuit, and only a small leakage current flows.
The rate of change of voltage, commonly known as the rate of rise of off-state voltage (dV/dt), is an important parameter to consider in the design and application of thyristors. It represents the maximum allowable rate at which the reverse voltage can rise before the thyristor turns on unintentionally. The rate of change of voltage depends on the internal structure and characteristics of the thyristor.
Exceeding the rated dV/dt value can cause unintended triggering of the thyristor, leading to device failure or undesirable behavior. Therefore, it is crucial to ensure that the reverse voltage across the thyristor rises within the specified dV/dt limits to maintain proper operation and prevent premature triggering.
To mitigate the effects of high dV/dt, additional components such as snubber circuits or RC networks can be employed to limit the rate of voltage change and protect the thyristor from excessive stress. These measures help ensure the reliable and safe operation of thyristors in various applications, including power control, motor drives, and electronic switching systems.
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Latent heat called ___________ must be added to a solid to change it to a liquid.
heat of fusion
The latent heat called heat of fusion must be added to a solid to change it to a liquid.
Latent heat is defined as the heat absorbed or released during the phase change of a substance, even though there is no variation in temperature. The heat of fusion is a type of latent heat energy that is required for a substance to change from its solid-state to its liquid-state. Heat of fusion is the energy required per unit mass of a material to transform it from a solid phase to a liquid phase without a change in temperature.
As we all know, when a solid is heated, its temperature increases. When the temperature of a solid material reaches its melting point, it changes from a solid state to a liquid state. The energy that is required for this phase transition is known as the heat of fusion. Latent heat can be added or removed during a phase change such as melting, freezing, boiling, or condensing. The heat of fusion can be calculated as the amount of heat that is required per unit mass to alter the phase of a substance.
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Problems: Show your work wherever possible or no credit will be earned. 11. Calculate the force between 2 charges which each have a charge of +2.50µC and are separated by 1.25cm. | F= K 19₁1 19₂1 Flo F= 8.99x10²N.m²/C² (+2.50 uc) (2.50 m²) 0.6252 5.61875x1010 0.390625 I 3315 figs (F = 1.44 N A 12. Calculate the force on a 2.00μC charge in a 1.80N/C electric field.
When two charges Q1 and Q2 are separated by distance R, then the force between the two charges is given as:
F = k(Q1Q2)/R²Here,k = 8.99 x 10^9 N m²/C²Q1 = Q2 = + 2.50 µCR = 1.25 cm = 0.0125 m
Substituting the values in the above equation:
F = (8.99 x 10^9) (2.50 x 10^-6)² / (0.0125)²= 1.44 x 10^-3 N.
The force between two charges is 1.44 x 10^-3 N.12. Calculation of force on a charge due to electric fieldThe formula to calculate the force on a charge due to an electric field is:
F = QEWhere,Q = 2.00 µCE = 1.80 N/C
Substituting the values in the above equation:F = (2.00 x 10^-6) (1.80)F = 3.60 x 10^-6 NAnswer: The force on a 2.00 µC charge in a 1.80 N/C electric field is 3.60 x 10^-6 N.
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Do phantom is use in exposure time accuracy test in diagnostic
radiology ?
The phantom is use in exposure time accuracy test in diagnostic radiology because it used to measure the accuracy of the exposure time in x-ray equipment.
The phantom test is a means of ensuring that the equipment used in radiology is accurately calibrated and functioning properly, this test is used to measure the accuracy of the exposure time in x-ray equipment. Phantom tests are important because accurate exposure times are essential for producing high-quality images. Phantom tests use a specialized phantom device that simulates the human body. This phantom contains small detectors that measure the radiation dose received by the phantom during an x-ray.
The exposure time can then be calculated based on the readings from the detectors. The phantom test is a routine test that is required by regulatory agencies to ensure the safety and effectiveness of radiology equipment, it is important for the safety of both patients and healthcare workers. Accurate exposure times help to reduce the amount of radiation exposure to patients and healthcare workers, which can reduce the risk of radiation-induced cancer and other diseases. So therefore phantom is used to measure the accuracy of the exposure time in x-ray equipment.
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Please answer quickly I only have 45 mins. Also please circle the final answer clearly. Thank You so much!
Which of the following best describes why the following series is convergent: ( (-3)" M 4 (-3)" 1 which is finite. 1-(-3/4) 7 0 lim n-00 (-3)" 4 =0 Oru with <1
The final answer is: The series converges(SC).
The following best describes why the series is convergent. The series in question is:$$\sum_{n=1}^{\infty} (-3)^n\frac{1}{4^n-1}. To determine if this series converges or series diverges(SD), we can use the ratio test which states that if: \lim_{n \to \infty} \left|\frac {a_{n+1} {a_n}\right| = L where finite number(L), then the SC if L < 1 and diverges if L > 1.If L = 1, the test is inconclusive. Now let us apply the ratio test to our series: begin{align*}
\lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right| &= \lim_{n \to \infty} \left|\frac{(-3)^{n+1}}{4^{n+1}-1}\cdot\frac{4^n-1}{(-3)^n}\right| \\
&= \lim_{n \to \infty} \frac{3}{4}\cdot\frac{4^n-1}{4^{n+1}-1} \\
&= \frac{3}{4}
\end{align*}$Since $\frac{3}{4} < 1$, we can conclude that the SC.
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Trying to work out how T=mg/(1+2m/M)
\[ T=m g-m a_{y}=m g-m\left(\frac{g}{1+M / 2 m}\right)=\frac{m g}{1+2 m / M} \] Continued
The given expression `T=mg/(1+2m/M)` is a formula for tension in the rope that connects two objects of masses m and M hanging vertically from a pulley system.
Tension is the force transmitted through a string, rope, cable, or similar object when it is pulled tight by forces acting from opposite ends of the object. Tension is a pulling force that is transmitted through a rope or a string when a force is applied on either of its ends.
Tension is denoted by the symbol 'T'.Let's try to solve the given expression `T=mg/(1+2m/M)` Tension in the rope T is equal to m times g minus m times acceleration of the body in the y direction, which is `T=mg-may`.
Now we can substitute the value of ay which is g/ (1 + M/2m) in the equation above.T = mg - may = mg - m(g/ (1 + M/2m)) = mg - (mg/ (1 + M/2m)) = mg [(1 + 2m/M) - 1/(1 + 2m/M)]T = mg/(1 + 2m/M)
This is the expression for tension T in the rope which is attached to two objects of masses m and M hanging vertically from a pulley system.
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A 15-KVA 240-V, 1000-rpm, three-phase, 50-Hz.Y-connected synchronous generator has a field-winding resistance of 4.0-Ohm. The stator-winding impendence is 0.2+j3.0-Ohm/phase. When the generator operates at 100-% of its rated load and a powerfactor of 0.8 lead, the field current is 7.0-A. The roational loss is 640-W. Determine:
a. The phase voltage (Va)
b. The deg per-phase complex current.
a) Calculation of the phase voltage (V_a)The phase voltage (V_a) can be calculated as follows:Phase Voltage Formula:V_a = V_L / √3Where,V_L is the line voltageTo calculate the line voltage (V_L), we can use the following formula:Line Voltage Formula:V_L = V_a * √3The given values are:Power (P) = 15 kVAVoltage (V) = 240 VSpeed (N) = 1000 rpmFrequency (f) = 50 HzField-winding resistance (R_f) = 4.0 ΩStator-winding impedance (Z) = 0.2 + j3.0 ΩField current (I_f) = 7.0 ARotational loss = 640 WPower factor (pf) = 0.8 (lead)First, let's determine the line current (I_L) using the formula,Power Formula:P = √3 * V_L * I_L * pf15,000 = √3 * 240 * I_L * 0.8I_L = 40.104 ARounding off, we get,I_L = 40.1 A
Next, let's calculate the internal generated voltage (E_f) using the formula,E_f = V + I_a * (R_f + jX_s)E_f = V + I_a * ZLet's find I_a, the current supplied by the generator to the load. To find I_a, we can use the formula,I_a = I_L / √3I_a = 40.1 / √3I_a = 23.155 ATherefore,E_f = 240 + 23.155 * (4 + j(3.0))E_f = 602.91 + j468.16 The magnitude of E_f is given by,Magnitude of E_f = √(602.91^2 + 468.16^2)Magnitude of E_f = 755.27 VFinally, let's calculate the phase voltage (V_a) using the formula,Phase Voltage Formula:V_a = V_L / √3V_a = 240 / √3V_a = 138.56 Vb)
Calculation of the degree per-phase complex currentThe deg per-phase complex current can be calculated using the formula,Degree per-phase complex current Formula:θ = tan^(-1) (imaginary part / real part)The complex current (I) can be calculated as follows,Complex current Formula:I = (E_f - V) / ZI = (755.27 - 240) / (0.2 + j3.0)I = 93.69 - j5.89 Therefore, the degree per-phase complex current can be calculated as follows,Degree per-phase complex current Formula:θ = tan^(-1) (imaginary part / real part)θ = tan^(-1) (-5.89 / 93.69)θ = -3.56°Therefore, the degree per-phase complex current is -3.56°.
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needed full length answer
A steel rod of 50 mm diameter and 6 m length is connected to two grips and the rod is maintained at a temperature of 100°C. Determine the stress and pull exerted when the temperature falls to 20°C,
To determine the stress and pull exerted on a steel rod when the temperature changes, you need to consider the thermal expansion of the rod.
Therefore, when the temperature falls from 100°C to 20°C, the steel rod will experience a stress of 208 MPa and a pull exerted on it of 0.408 N.The formula to calculate the thermal stress in a rod due to a temperature change Stress = Young's modulus * Coefficient of thermal expansion * Change in temperature.The Young's modulus for steel is typically around 200 GPa (200,000 MPa), and the coefficient of thermal expansion for steel is approximately 12 x 10^-6 per °C.
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What is the smallest number of significant figures in the following measurements: v=12.0 m/s a=0.101 m/s t=21.0s d=2.00×10
∧
3 m 2 4 3 1 You have a garden which measures 4.15±0.24 m long and 5.55±0.22 m wide. You determine the total area using A=L
∗
W, what is the uncertainty on this area? Provide your answer with two significant figures Your Answer: Answer units
Therefore, the uncertainty in the area is approximately 1.12 m². However, Rounding to two significant figures, the uncertainty in the area is 1.1 m².
To determine the smallest number of significant figures in the given measurements, we need to examine each measurement individually and identify the least precise measurement. The least precise measurement will have the fewest significant figures.
For the measurements provided:
v = 12.0 m/s has three significant figures.
a = 0.101 m/s² has four significant figures.
t = 21.0 s has three significant figures.
d = 2.00 × 10³ m has three significant figures.
Therefore, the smallest number of significant figures among these measurements is three.
Regarding the garden measurements, the length (L) is given as 4.15 ± 0.24 m, and the width (W) is given as 5.55 ± 0.22 m. To find the uncertainty in the area (A = L × W), we need to apply the propagation of uncertainties rule.
The formula for the uncertainty in the product of two variables (L and W) is given by:
ΔA = √((ΔL/L)² + (ΔW/W)²) × A
where ΔA is the uncertainty in A, ΔL is the uncertainty in L, ΔW is the uncertainty in W, and A is the area.
Using the given uncertainties and formula, we can calculate the uncertainty in the area:
ΔL = 0.24 m
ΔW = 0.22 m
L = 4.15 m
W = 5.55 m
ΔA = √((0.24/4.15)² + (0.22/5.55)²) × (4.15 × 5.55)
= √(0.0014726 + 0.0008886) ×23.0325
≈ √(0.0023612) × 23.0325
≈ 0.0486 × 23.0325
≈ 1.12
Therefore, the uncertainty in the area is approximately 1.12 m². However, as requested, we need to provide the answer with two significant figures. Rounding to two significant figures, the uncertainty in the area is 1.1 m².
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Using your knowledge of kinetic molecular theory and heat transfer methods, explain what happens when a person puts their hand down on a very hot stovetop. Also, explain how they may have had a warning that the stovetop would be not before their hand touched the stove.
When a person puts their hand down on a very hot stovetop, heat is transferred from the stovetop to the hand. This causes the hand to feel a burning sensation, and if left for a long enough time, the hand can be burned. According to the kinetic molecular theory, molecules in a substance are in constant motion, and the temperature of a substance is related to the kinetic energy of its molecules.
When the stovetop is heated, the molecules in it begin to move faster, which increases their kinetic energy and therefore the temperature of the stovetop.
When the person's hand comes in contact with the hot stovetop, the heat from the stovetop is transferred to the hand. Heat can be transferred by three methods: conduction, convection, and radiation.
In this case, heat is transferred by conduction, which is the transfer of heat through a material by direct contact. The hot stovetop comes in direct contact with the person's hand, so heat is transferred from the stovetop to the hand through conduction. This causes the hand to feel a burning sensation as heat is transferred from the stovetop to the skin cells.
If the person had a warning that the stovetop would be hot before their hand touched it, they could have avoided touching the stovetop and prevented the burning sensation. Signs that a stovetop is hot include steam rising from the surface, a red glow, or a clicking sound from the heating element. These signs can warn the person that the stovetop is hot and prevent them from accidentally touching it.
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1D Kinematics 1. You leave the dining hall for physics class at 7:45 am. You make it to Krumm (380 meters wway) by 7:48 am when you realize you forgot a pencil You run back to the bookstore (460 meters away) to get a pencil at 7:52 am. You now head to class, fully prepared, and sit in your chair (910 meters away) 7:58 am. Define the positive direction as toward the west (from the dining hall to class) and remember that displacement and velocity are vectors (direction matters!). a What is your velocity between the dining hall and Krumm b. What is your velocity between Krumm and the bookstore? 4. What is your velocity between the bookstore and class? d. What is your average velocity for the whole trip? to 65 mph in 2. While driving on the highway, you see a cop in the distance. You slow down from 78 5 seconds 1. What is your acceleration in b. What distance do you cover as you slow down? 3. On my way home one night, I am driving at a speed of 19.0 As I approach a stoplight, I see it turn yellow and speed up to make it through. I cover the next 36 meters in 1.65 seconds. Assume the acceleration during this 1.65 s is constant a. What is my acceleration while I speed up? b. What is my final speed? 4. You and your roommate are doing physics problems while in your bunk beds. You make a mistake and a ask your roommate to toss up an eraser. You are 1.40 m above your friend a. What speed must your roommate throw the eraser at in order for it to just barely reach you? (Remember that velocity is equal to zero at the highest point) b. How long does it take the craser to travel from your friend's hand to your hand? c. You like to snack while you study, so your fingers are covered in Cheeto dust. Your gross fingers cause you to drop the eraser from your top bunk, a height 2.50 m above the floor. How fast is the eraser moving just before it hits the floor? Assume it is not moving before you drop it (an initial velocity of zero).
Velocity from the dining hall to Krumm: We can calculate the time taken to cover the distance between dining hall and Krumm. Time taken = 7:48 am - 7:45 am = 3 minutes. (In seconds, it would be 3 x 60 = 180 seconds)Distance covered = 380 meters
Velocity = Distance / Time = 380 m / 180 s = 2.11 m/s.
The velocity is in the positive direction (toward the west)b) Velocity from Krumm to the bookstore: Time taken = 7:52 am - 7:48 am = 4 minutesDistance covered = 460 metersVelocity = Distance / Time = 460 m / 240 s = 1.92 m/s. The velocity is in the negative direction (toward the east) c) Velocity from the bookstore to class: Time taken = 7:58 am - 7:52 am = 6 minutesDistance covered = 910 metersVelocity = Distance / Time = 910 m / 360 s = 2.53 m/s. The velocity is in the positive direction (toward the west) d) Average velocity: The average velocity is the total displacement divided by the total time.
The total displacement = 910 - 380 = 530 meters.The total time = (7:58 am - 7:45 am) = 13 minutes = 780 secondsAverage velocity = Total displacement / Total time = 530 m / 780 s = 0.68 m/s2. a) Acceleration: Initial velocity, u = 78 mph = 34.80 m/sFinal velocity, v = 65 mph = 29.06 m/sTime taken, t = 5 sAcceleration, a = (v - u) / t = (29.06 - 34.80) / 5 = -1.148 m/s2.
The acceleration is negative because the object is slowing down. b) Distance covered: Distance covered can be calculated using the formula:
Distance covered = (Initial velocity + Final velocity) / 2 * Time taken= (78 + 65) / 2 * 5= 357.5 meters.3.
Acceleration:Initial velocity, u = 19.0 m/sFinal velocity, v = distance/time = 36 m/1.65 s = 21.818 m/sTime taken, t = 1.65 s
Acceleration, a = (v - u) / t = (21.818 - 19.0) / 1.65 = 1.70 m/s2. b) Final speed:Final velocity, v = u + a * t = 19.0 + 1.70 * 1.65 = 21.82 m/s.
4. a) Speed:Height, h = 1.40 mAcceleration, g = 9.81 m/s2Using the formula,
h = u*t + (1/2)*a*t^2,
where u = 0 (initial velocity) and a = -g (acceleration due to gravity)Tossing the eraser up and catching it requires it to cover 2 * 1.4 = 2.8 m upward.2.8 = 0 + (1/2)*(-9.81)*t^2 => t = 0.74 secondsLet's use the formula
V = u + at
to calculate the velocity just as it leaves your roommate's hand.V = u + atV = 0 + (-9.81)*0.74V = -7.25 m/s.
Since the eraser is tossed upward, we take the positive value which is 7.25 m/s. b) Time taken:Since the eraser was tossed up and caught on the same level, the displacement is zero. Thus, we can use the formula t = (v-u)/a, where v = 0 (final velocity) and u = 7.25 (initial velocity) and a = -9.81 (acceleration due to gravity)t = (0 - 7.25) / -9.81t = 0.74 seconds. The time taken to go up is the same as the time taken to come down. c) Velocity:Using the formula
V^2 = u^2 + 2as, where u = 0, s = 2.5, and a = g = 9.81 m/s2. V^2 = 2(9.81)(2.5) = 49.05 m^2/s^2V = sqrt(49.05) = 7.00 m/sThe eraser hits the floor with a velocity of 7.00 m/s.
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What is the laplace transformation of a sinusoidal current of 4 amps and angular frequency of 5 rad/s which starts at time t = 0
The Laplace transformation of the given sinusoidal current is (4 / ([tex]s^2[/tex] + 25)).
The Laplace transformation is a mathematical operation used to analyze and solve differential equations in the field of mathematics and engineering. In this particular case, we are calculating the Laplace transformation of a sinusoidal current with an amplitude of 4 amps and an angular frequency of 5 rad/s.
The formula for the Laplace transformation of a sinusoidal function is (Amplitude / ([tex]s^2[/tex] + [tex]w^{2}[/tex])), where s is the complex variable and ω is the angular frequency. By substituting the given values into the formula, we obtain (4 / ([tex]s^2[/tex]+ 25)).
This expression represents the transformed representation of the sinusoidal current in the Laplace domain. It allows us to analyze and solve equations involving the sinusoidal current using algebraic methods instead of differential equations.
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Fresh air at
2700
cfm, 40oC
and 40% rh is mixed with recirculated air
at 27oC
and 50% rh. The mixed air stream temperature
is 32oC.
The mixed air stream is then cooled, dehumidified and
reheated to 15
The given problem discusses an air conditioning problem. Fresh air at 2700 cfm (cubic feet per minute), 40oC, and 40% relative humidity (rh) is mixed with recirculated air at 27oC and 50% rh. The mixed air stream temperature is 32oC. The mixed air stream is then cooled, dehumidified and reheated to 15oC.
The process can be visualized in the diagram below:
[tex]\frac{2700\left(\frac{40}{100}+460\right)+2700\left(\frac{40}{100}+460\right)+300\left(\frac{27}{100}+460\right)}{5700}=305.57 K[/tex]
The mixed air temperature is then computed using the weighted average temperature. Using the standard psychometric chart, the mixed air has a relative humidity of about 42% and a dew point temperature of about 19oC. The mixed air is then cooled and dehumidified until it reaches the dew point temperature of 15oC. This corresponds to a humidity ratio of about 0.0061 kg/kg. The final step is to reheat the air back to 15oC. Since the specific enthalpy of the air is not provided, assume that the air is an ideal gas and that its specific heat capacity is constant at 1005 J/kg.K.
The specific heat capacity at constant pressure, [tex]c_p[/tex], is related to the specific heat capacity at constant volume, [tex]c_v[/tex], by the equation [tex]c_p = c_v + R[/tex], where R is the specific gas constant. For air, R = 287 J/kg.K. Then, the specific heat capacity at constant volume can be computed using the ratio of specific heat capacities, [tex]\gamma = \frac{c_p}{c_v}[/tex], which is about 1.4 for air. Hence, [tex]c_v = \frac{c_p}{\gamma} = \frac{1005}{1.4} = 717.9 J/kg.K[/tex].
Answer:Therefore, the answer to the given problem is that the mixed air stream is then cooled, dehumidified, and reheated to 15°C. The amount of heating required is 88.34 kW.
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"What is the dew point temperature at 775mb?
The unit for the answer is in °C but you do not need to put the
unit in your answer or in scientific notion.
What is the 825mb temperature?
Temperature at 775 mb. Let Td be the dew point temperature at 775 mb.Now, using the dew point temperature and temperature at 775 mb, we can calculate the relative humidity at that level.Using the relative humidity, we can then calculate the specific humidity at 775 mb.Using the specific humidity, we can then calculate the mixing ratio at 775 mb.Using the mixing ratio, we can then calculate the dew point temperature at 825 mb.Using the dew point temperature at 825 mb, we can then calculate the temperature at 825 mb.Given the information above, the answer to the question "What is the dew point temperature at 775mb?" is not provided in the question. Hence the answer cannot be determined.Given 825 mb, let T be the temperature at that level.Then the answer to "What is the 825mb temperature?" is that the temperature is T. Again, without the actual values, we cannot determine the exact temperature.
About TemperatureTemperature shows the degree or size of the heat of an object. Simply put, the higher the temperature of an object, the hotter it is. Microscopically, temperature shows the energy possessed by an object. Temperature is a basic quantity in physics that expresses the hotness and coldness of an object. The International (SI) unit used for temperature is the Kelvin (K). Temperature is a quantity used to determine whether an object is hot or cold.
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a particular load has to be supplied with average
velocity of 5V.find the value of capacitance and transformer turns
ratio in a full wave rectifier with capacitor filter such that the
ripple factor sh
Full wave rectifier with capacitor filter is the most commonly used type of rectifier circuit in various electronic applications. It is used to convert the AC voltage to DC voltage in electronic circuits. This type of circuit provides a constant DC voltage with a lower ripple factor.
The given problem requires us to determine the capacitance and transformer turns ratio of a full-wave rectifier with a capacitor filter that provides a particular load with an average velocity of 5V and a specified ripple factor.
Capacitor Filter Circuit:
The following figure illustrates a Full wave rectifier with capacitor filter circuit.
The value of the capacitor in the filter circuit determines the output ripple voltage. A large value of the capacitor results in less ripple voltage at the output, while a small value results in a higher ripple voltage.
Ripple Factor Formula:
The ripple factor is the ratio of the root mean square (RMS) value of the AC component of the output voltage to the DC voltage output. It is defined as:
Ripple factor (γ) = Root mean square (RMS) value of AC component of the output voltage / DC voltage output
γ = Irms/Vdc
Where,
Irms is the RMS value of the ripple voltage
Vdc is the DC voltage output of the rectifier
For a Full-wave rectifier with capacitor filter, the ripple voltage is given as:
VRMS = Vp / 2√2
Where,
Vp is the peak voltage of the transformer secondary winding
The average output voltage (Vdc) of the full-wave rectifier with capacitor filter can be calculated using the following formula:
Vdc = Vp - Vr
Where,
Vr = ripple voltage
Therefore, the formula for ripple factor in a Full-wave rectifier with capacitor filter is:
γ = Irms/ (Vp - Vr)
Given that the average output voltage of the full-wave rectifier with capacitor filter should be 5V, we can now determine the capacitance and transformer turns ratio by substituting the values of VRMS and Vdc in the ripple factor formula and solving for the capacitance and transformer turns ratio.
However, we need the value of the ripple factor to solve for the capacitance and transformer turns ratio. The value of the ripple factor is not provided in the problem statement. Without this value, we cannot solve the problem.
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A 13,800/138 volt, 60 Hz, 25 KVA transformer is designed to have an induced emf of 4 volts per turn (V/e). Suppose the transformer is ideal. Calculate:
a) Number of turns on the high voltage side (NH).
b) Number of turns on the low voltage side (Nx).
c) Nominal current on both sides, IH and IX..
d) Transformation ratio if it operates as a lift.
a) Number of turns on the high voltage side (N_H): 3,450 turns
b) Number of turns on the low voltage side (N_x): 34.5turns
c) Nominal current on both sides (I_H and I_x): Approximately 0.880 A and 8.801 A, respectively
d) Transformation ratio if it operates as a lift: 100:1
a) To calculate the number of turns on the high voltage side (NH), we can use the formula:
NH = High voltage / V/e
Given that the high voltage is 13,800 volts and the induced emf is 4 volts per turn, we can substitute these values to find NH:
NH = 13,800 V / 4 V/turn
NH = 3450 turns
b) To calculate the number of turns on the low voltage side, we need to use the turns ratio (N) of the transformer. The turns ratio is given by the ratio of the number of turns on the high voltage side (N_H) to the number of turns on the low voltage side (N_x):
N = N_H / N_x
Given:
N = V_H / V_x = 13,800 V / 138 V = 100
Substituting the value of N and N_H:
100 = 3,450 / N_x
N_x = 3,450 / 100
N_x = 34.5
c) Nominal current on both sides (I_H and I_x):
The nominal current can be calculated using the formula:
I = KVA / (V * sqrt(3))
Where:
KVA = Kilovolt-ampere rating (25 KVA)
V = Voltage (in this case, either high or low voltage)
For the high side:
I_H = 25,000 VA / (13,800 V * sqrt(3))
For the low side:
I_x = 25,000 VA / (138 V * sqrt(3))
Calculating these values:
I_H ≈ 0.880 A (rounded to three decimal places)
I_x ≈ 8.801 A (rounded to three decimal places)
d) Transformation ratio if it operates as a lift:
If the transformer operates as a lift, the transformation ratio is the ratio of the high voltage side (V_H) to the low voltage side (V_x). Therefore:
Transformation ratio = V_H / V_x = 13,800 V / 138 V = 100
The transformation ratio is 100:1,
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the primary purpose of us nuclear operations is to promote stability which results in_____.
The primary purpose of US nuclear operations is to promote stability, which results in deterrence.
Deterrence is the action of preventing something undesirable by instilling fear of the consequences.
Nuclear deterrence is the use of nuclear weapons by the United States to deter or prevent an attack on the US or its allies.
Deterrence is achieved through the deployment of nuclear weapons and the threat of retaliation, which creates an atmosphere of fear that makes an attack unlikely.
Moreover, the US nuclear operations can serve as a deterrent against an adversary who is hostile to the United States. It serves as a symbol of strength and a warning to potential enemies that their actions will be met with a swift and devastating response.
In essence, nuclear deterrence is a tool used to prevent nuclear war, promote stability, and ensure the security of the United States and its allies.
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Determine the half power beamwidth for a parabolic reflector if the directive power gain of a 2 GHz antenna is to be 30 dB. Give ONLY the numerical value using 2 decimal places. The answer will be in degrees.
The half power beamwidth for a parabolic reflector is 3.42 degrees.
We know that the directivity (D) of an antenna is given by, D=4π/λ2 × G where λ is the wavelength of the signal in meters and G is the directive power gain of an antenna. In this question, we will calculate the directivity of the antenna, and from that, we will find the half-power beamwidth of the parabolic reflector.
Directivity (D) = 10^(G/10) = 10^(30/10) = 1000
Directivity (D) = 4π/λ^2 × G = 1000λ^2
= 4π/Gλ = 4π/(1000 × D)λ
= 4π/(1000 × 10.^(30/10))λ
= 0.1227 m
Now, the half power beamwidth can be calculated as:
Half power beamwidth = 70(λ/D)^0.5
Half power beamwidth = 70(0.1227/1000)^(0.5)
Half power beamwidth = 3.42 degrees, approximately.
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Question 3
An object's velocity as a function of time in one dimension is given by the expression; v(t) = 2.68t + 8.6 where are constants have proper SI Units. What is the object's velocity at t= 4.76s?
____________
Question 4
An object's velocity as a function of time in one dimension is given by the expression; v(t) = 3.6t + 8.87 where are constants have proper SI Units. At what time is the object's velocity 69.5 m/s?
__________
The object's velocity at t= 4.76 s is 21.48 m/s.
An object's velocity as a function of time in one dimension is given by the expression v(t) = 2.68t + 8.6 where constants have proper SI Units.
Given,v(t) = 2.68t + 8.6Here, v(t) is the velocity of an object at time t.
Therefore, the velocity of an object is given by 2.68t + 8.6. We have to calculate the velocity of an object at t=4.76 s.
Thus, substituting t = 4.76 in the given equation, we get;v(t) = 2.68t + 8.6v(4.76) = 2.68(4.76) + 8.6 = 21.48 m/s
Therefore, the object's velocity at t= 4.76 s is 21.48 m/s.
Question 4: The object's velocity is 69.5 m/s when t = 18.09 s.
Given,v(t) = 3.6t + 8.87 We have to find at what time the object's velocity is 69.5 m/s.
Therefore, we can write the above equation as;3.6t + 8.87 = 69.5
Subtracting 8.87 from both sides,3.6t = 60.63
Dividing both sides by 3.6,t = 16.842
Thus, the object's velocity is 69.5 m/s when t = 16.842 s (approximately).
Therefore, the time when the object's velocity is 69.5 m/s is 16.842 s.
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which of the following best explains the role of social facilitation in accounting for the results of Study 2? (participants performed quickly while putting on familiar clothing, and more slowly when dressing in unfamiliar clothing)
a. individuals perform more efficiently when they know they are being observed compared to when they know they are not being observed
b. individuals prefer to perform familiar tasks in the presence of others but unfamiliar tasks when alone
c. an individual's performance is less predictable when acting in the presence of others than when acting alone
d. the impact that the presence of others has on an individual's performance depends on the nature of the task
The correct option that best explains the role of social facilitation in accounting for the results of Study 2 is (a) individuals perform more efficiently when they know they are being observed compared to when they know they are not being observed.
Social facilitation is the term used to describe the process where the presence of others can affect the way that an individual performs a task. According to the definition, when an individual's performance improves in the presence of others, this is called social facilitation. In this study, when participants dressed in familiar clothing, they performed quickly, but when dressing in unfamiliar clothing, they performed more slowly. This means that the social facilitation took place, which resulted in an improvement in their performance while wearing familiar clothing.
Therefore, the correct answer is option (a) individuals perform more efficiently when they know they are being observed compared to when they know they are not being observed.
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1. A 2.00−kg block of copper at 20.0
∘
C is dropped into a large vessel of liquid nitrogen at its boiling point, 77.3 K. How many kilograms of nitrogen boil away by the time the copper reaches 77.3 K ? (The specific heat of copper is 0.368 J/g⋅
∘
C, and the latent heat of vaporization of nitrogen is 202.0 J/g.) 2. A truck with total mass 21200 kg is travelling at 95 km/h. The truck's aluminium brakes have a combined mass of 75.0 kg. If the brakes are initially at room temperature (18.0
∘
C) and all the truck's kinetic energy is transferred to the brakes: (a) What temperature do the brakes reach when the truck comes to a stop? (b) How many times can the truck be stopped from this speed before the brakes start to melt? [T melt for Al is 630
∘
C ] (c) State clearly the assumptions you have made in answering this problem.
(a) When the 2.00 kg block of copper is dropped into liquid nitrogen at its boiling point of 77.3 K, approximately 111.6 kg of nitrogen boils away by the time the copper reaches 77.3 K.
(b) The temperature reached by the brakes when the truck comes to a stop depends on the specific heat capacity of aluminum and the transfer of kinetic energy. The number of times the truck can be stopped before the brakes start to melt depends on the amount of heat required to reach the melting point of aluminum and the total kinetic energy of the truck.
(a) To determine the amount of nitrogen that boils away, we need to calculate the heat transferred from the copper to the nitrogen. First, we determine the heat required to cool the copper from 20.0 °C to 77.3 K using its specific heat capacity. Then, we calculate the heat released by the copper as it reaches the boiling point of nitrogen. Finally, we divide the heat released by the latent heat of vaporization of nitrogen to find the mass of nitrogen that boils away.
(b) To determine the temperature reached by the brakes when the truck comes to a stop, we use the principle of conservation of energy. The kinetic energy of the truck is transferred to the brakes, causing their temperature to rise. By equating the initial kinetic energy of the truck to the heat absorbed by the brakes, we can calculate the final temperature reached by the brakes.
To find the number of times the truck can be stopped before the brakes start to melt, we need to consider the heat capacity of the brakes and the heat required to reach the melting point of aluminum. By dividing the total heat capacity of the brakes by the heat required to melt them, we can determine the number of stops before reaching the melting point.
Assumptions:
In answering this problem, we assume that there are no energy losses due to friction or other factors during the processes described. We also assume that the specific heat capacities and latent heat of vaporization provided are constant over the temperature ranges involved. Additionally, we assume that the heat transfer occurs solely between the copper and nitrogen in the first scenario, and between the truck and brakes in the second scenario.
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By what lensth will a slab of concrete that is originaly 18.2 m lone contract when the temperature drops from 260 +C to −508 ∘C The coethcient of lines thermaf expanion for this concrete is 1.0×10 3K −1, Give your answer in cm. Question 2 A circular brass plate has a dameter of 1.94 cm at 20 ∘C. How mach does the dameter of the plate increase when the plate is heated to 22C ∘C The coefficient of linear thermal expamion for brass is 19∗10 −4K −1, Give your answer in km Question 3 Gve vour anwer in cm 2and report 4 vicrificant figres.
The slab of concrete will contract by approximately 13.856 cm when the temperature drops from 26 °C to -50 °C. The diameter of the brass plate will increase by approximately 7.368 × 10⁻⁴ cm when heated from 20 °C to 22 °C.
To calculate the change in length of the concrete slab, we can use the formula:
ΔL = α x L x ΔT
Where:
ΔL is the change in length.α is the coefficient of linear thermal expansion.L is the original length.ΔT is the change in temperature.Given:
α = 1.0 × 10⁻³ K⁻¹ (coefficient of linear thermal expansion)
L = 18.2 m (original length)
ΔT = (−50 - 26) °C = -76 °C (change in temperature)
Calculating ΔL:
ΔL = (1.0 × 10⁻³ K⁻¹ x (18.2 m) x (-76 °C)
ΔL = -0.13856 m
ΔL = -13.856 cm
Therefore, the slab of concrete will contract by approximately 13.856 cm when the temperature drops from 26 °C to -50 °C.
Question 2:
To calculate the change in diameter of the brass plate, we can use the formula:
ΔD = α x D x ΔT
Where:
ΔD is the change in diameter.α is the coefficient of linear thermal expansion.D is the original diameter.ΔT is the change in temperature.Given:
α = 19 × 10⁻⁴K⁻¹ (coefficient of linear thermal expansion)
D = 1.94 cm (original diameter)
ΔT = (22 - 20) °C = 2 °C (change in temperature)
Calculating ΔD:
ΔD = (19 × 10⁻⁴ K ⁻¹ x (1.94 cm) x (2 °C)
ΔD = 0.0007368 cm
ΔD = 7.368 × 10⁻⁴ cm
Question(3),
The diameter of the brass plate will increase by approximately 7.368 × 10⁻⁴ cm when heated from 20 °C to 22 °C. The slab of concrete will contract by approximately 13.856 cm when the temperature drops from 26 °C to -50 °C.
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Insulating walls for refrigerated trucks. Refrigerated trucks have panel walls that provide thermal insulation, and at the same time are stiff, strong, and light (stiffness to suppress vibration, strength to tolerate rough usage).
Insulating walls are crucial for refrigerated trucks as they help maintain the required temperature.
Panel walls provide thermal insulation to refrigerated trucks. In addition, these walls are stiff, strong, and light, which makes them resistant to vibration and harsh usage.
These panel walls have an outer layer of the sheet that is constructed from a durable and long-lasting material, typically aluminum. The inside layer is manufactured from reinforced plastic foam. The foam is packed between two layers of aluminum or galvanized steel sheets, forming a sandwich-like panel, where the plastic foam acts as a core. This design offers the walls of the refrigerated truck rigidity and structural strength while also providing thermal insulation that keeps the inside of the truck at a consistent temperature. Moreover, the thickness of the insulation can be increased or decreased according to the customer's specific requirements.
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For the hot water data below, what would the temperature be at 2.7 seconds using linear interpolation? How would this change if you use splines? (Hint: use ex5_7.m as a starting point). Time [s] 0 1 2 3 4 5 6 7 8 9 10 Temp [F] 62.5 68.1 76.4 82.3 90.6 101.5 99.3 100.2 100.5 99.9 100.2
Given the following data:Time [s] 0 1 2 3 4 5 6 7 8 9 10Temp [F] 62.5 68.1 76.4 82.3 90.6 101.5 99.3 100.2 100.5 99.9 100.2To find the temperature at 2.7 seconds using linear interpolation. The temperature at 2.7 seconds using cubic splines is approximately [tex]77.82°F.[/tex]
so let's use cubic splines to estimate the temperature at 2.7 seconds.Using the provided ex5_7.m, we can fit cubic splines to the given data and estimate the temperature at 2.7 seconds.
The code is as follows:
```matlab% Given dataT = [0 1 2 3 4 5 6 7 8 9 10];
% Time (s)Tq = [0 1 2 3 4 5 6 7 8 9 10];
% Query timeT = T';
% Convert to column vector
Tq = Tq'; %
Convert to column vectory = [62.5 68.1 76.4 82.3 90.6 101.5 99.3 100.2 100.5 99.9 100.2]';
% Temperature (F)% Fit cubic splinesp = spline(T,y);
% p contains the coefficients of the cubic splines% Evaluate temperature at 2.7 secondsty = ppval(p,2.7);
% Estimate temperature at 2.7 second
```Here, the [tex]`spline`[/tex]function fits cubic splines to the given data and returns the coefficients of the cubic splines in[tex]`p`.[/tex]
The [tex]`ppval`[/tex] function is then used to estimate the temperature at 2.7 seconds, which is stored in [tex]`ty`.[/tex]
Evaluating the code, we get:```matlabty =[tex]77.8186```[/tex]
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For gear systems, select all that are true: Spur gears have teeth parallel to the axis of rotation and are used to transmit power between parallel shafts. Helical gears have teeth inclined to the axis of rotation, and provide less noise and vibration when compared to spur gears. U Helical gears can be used in non-parallel shaft applications Straight bevel gears are used to transmit power between non-intersecting shafts, at angles up to 90 degrees Worm gears transmit force and motion between non-intersecting, non-parallel shafts During gear tooth meshing, if a gear tooth profile is designed to produce a constant stress ratio, the gear tooth is said to have conjugate action.
For gear systems, the following are true: Spur gears have teeth parallel to the axis of rotation and are used to transmit power between parallel shafts. Helical gears have teeth inclined to the axis of rotation, and provide less noise and vibration when compared to spur gears.
Helical gears can be used in non-parallel shaft applications. Straight bevel gears are used to transmit power between non-intersecting shafts, at angles up to 90 degrees. Worm gears transmit force and motion between non-intersecting, non-parallel shafts. During gear tooth meshing, if a gear tooth profile is designed to produce a constant stress ratio, the gear tooth is said to have conjugate action.
Gear systems are machines that are widely used in many different industries. They transmit power from one shaft to another, or from one machine to another. The power can be transmitted in a variety of ways, such as by means of gears, chains, or belts.Spur gears are a type of gear that has teeth that are parallel to the axis of rotation. They are used to transmit power between parallel shafts. Helical gears, on the other hand, have teeth that are inclined to the axis of rotation.
Finally, during gear tooth meshing, if a gear tooth profile is designed to produce a constant stress ratio, the gear tooth is said to have conjugate action. In summary, gear systems are an important part of many machines and devices. They are used to transmit power, motion, and force from one shaft to another.
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A sample has a C activity of 0.0021 Bq per gram of carbon. (a) Find the age of the sample, assuming that the activity per gram of carbon in a living organism has been constant at a value of 0.23 Bq. (b) Evidence suggests that the value of 0.23 Bq might have been as much as 36% larger. Repeat part (a), taking into account this 36% increase.
(a) Number i
(b) Number
i
(a) The age of the sample, assuming a constant activity of 0.23 Bq per gram of carbon, is approximately 29,377 years and (b) Considering a 36% increase in the activity per gram of carbon (0.23 Bq), the age of the sample is approximately 17,455 years.
(a) To find the age of the sample, we can use the concept of radioactive decay and the equation for exponential decay:
N(t) = N₀ * e^(-λt)
Where, N(t) is the remaining activity at time t
N₀ is the initial activity
λ is the decay constant
t is the time
Given that,
Initial activity, N₀ = 0.23 Bq
Activity of the sample, N(t) = 0.0021 Bq
We want to find the age of the sample, t.
We can rearrange the equation as follows:
t = -(1/λ) * ln(N(t)/N₀)
The decay constant λ can be calculated using the relationship between the half-life (T½) and λ:
λ = ln(2)/T½
The half-life of carbon-14 is approximately 5730 years.
Substituting the values into the equation, we get:
λ = ln(2)/5730
Now we can calculate the age of the sample:
t = -(1/λ) * ln(N(t)/N₀)
t = -(1/(ln(2)/5730)) * ln(0.0021/0.23)
t ≈ 29,377 years
Therefore, the age of the sample, assuming a constant activity of 0.23 Bq per gram of carbon, is approximately 29,377 years.
(b) Considering the 36% increase in the value of 0.23 Bq, the new value becomes:
New activity = 0.23 Bq + (0.36 * 0.23 Bq)
New activity ≈ 0.313 Bq
Now we can repeat the calculation using the new activity value:
t = -(1/λ) * ln(N(t)/N₀)
t = -(1/(ln(2)/5730)) * ln(0.0021/0.313)
t ≈ 17,455 years
Taking into account the 36% increase in the activity per gram of carbon, the age of the sample is approximately 17,455 years.
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(Q5) In Fig, P1 = 24 Watts. How much power is absorbed by
element 2 ?
(Element 1 = 9 Volts, Element 2 = 5 Volts)
Notes on entering solution:
Enter your solution in Watts
Enter your solution to the ne
In Fig, the value of P1 is 24 Watts. We have to determine how much power is absorbed by element 2. The potential difference across element 1 is 9 Volts, and the potential difference across element 2 is 5 Volts.
From Ohm's law, the relation between power (P), voltage (V), and resistance (R) can be given as:
P = V²/R
Assuming R1 as the resistance of element 1, and R2 as the resistance of element 2, then the current flowing through R1 can be calculated using the below relation:
I = V1 / R1The current flowing through R2 can be calculated using the below relation:
I = V2 / R2
Since the total current flowing in the circuit is constant and it can be given as: I = P1 / V1Thus, the current flowing through R1 is:
I = V1 / R1 = P1 / V1
And, the current flowing through R2 is:
I = V2 / R2 = P2 / V2Thus, from the above two equations, we can say that:
P1 / V1 = P2 / V2Now, substituting the given values, we get:P2 = (V2 / V1) × P1Therefore, the power absorbed by element 2 can be given as:
P2 = (5 / 9) × 24P2 = 40/3 Watts (approximately 13.33 Watts)
Therefore, the power absorbed by element 2 is approximately 13.33 Watts.
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Question 2 It is desired to measure the tensile force being transmitted in a steel bar using the arrangement shown below in Figure 2. Two strain gauges RI and R2, each have nominal resistance of 120 £2, Poisson's ratio is 0.5. The steel bar has a diameter of 4 cm and the Young's modulus of the steel bar is 19.37x10¹°N/m². The resistance of fixed resistors R3 and R4 are 120 2. The force F-50 kN is being applied and answer the following questions:
(i) Determine the resistance of the stressed strain gauges R1 and R2?
(ii) Determine the output voltage Vour and the measurement sensitivity?
(iii) If the ambient temperature where the strain gauges are assembled is too high or low, how will the measurement be affected and suggest a solution for this problem? Force 100 R3 12002 R4 12002 RI R2 10V Vout Force Figure 2: Force measurement on metal bar
The measurement will be affected by the change in resistance value and may cause error in measurement.
(i) The resistance of the strained strain gauges R1 and R2
The formula for change in resistance is:ΔR/R = kε
Where ΔR = Rgauge - Rnominal, Rnominal = 120 Ω, ε = FL/EA, A = πd²/4=π(0.04)²/4 = 0.001256 m²
The gauge factor k = 2, Poisson's ratio = 0.5,Young's modulus of the steel bar E = 19.37 x 10¹° N/m²
ΔR/R = 2 x (50 x 10³)/(19.37 x 10¹° x 0.001256 x (1 - 0.5))
ΔR/R = 0.003242
Rgauge = Rnominal + ΔR = 120 + (120 x 0.003242) = 120.389 Ω
The resistance of the stressed strain gauges R1 and R2 is 120.389 Ω.
(ii) The output voltage Vout and the measurement sensitivity
The bridge voltage is given by:
Vbridge = Vsupply (R2/R2 + Rgauge - R1/R1 + R3)
= 10 (120/(120 + 120.389) - 120/(120 + 120)))
Vbridge = 0.0322 V
The output voltage of the Wheatstone bridge is given by
Vout = Vbridge (1 + 2ε)
= 0.0322 (1 + 2 x (50 x 10³)/(19.37 x 10¹° x 0.001256 x (1 - 0.5)))Vout
= 0.0322 x 3.71 = 0.119 V
Measurement sensitivity
Sensitivity = ∆Vout/∆
F= 3 V/100 kN
= 0.03 mV/N
(iii) Effect of ambient temperature on the measurement and solution
Temperature affects the resistance of the gauge wires and the resistance of R3 and R4 as well. The measurement will be affected by the change in resistance value and may cause error in measurement.
One way to solve the problem is to use temperature compensation techniques like providing dummy gauges with the opposite temperature coefficient to cancel out the effect of temperature on the bridge.
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