a) The truck has traveled a distance of 47.5 m in five seconds ; b) The acceleration of the truck at t = 5 seconds is calculated as 3.4 m/s².
a) Given, The speed of the truck, y = (3p + 2) m/s Where, p is the elapsed time in seconds.(a) To find the distance traveled by the truck in five seconds We have, y = ds/dt Where, y = (3p + 2) m/s
Integrating both sides, we get, s = ∫y dt
Putting the limits of integration from 0 to 5 seconds, s = ∫3p+2 dp [∵ y = 3p + 2]s = 3/2 p² + 2p [integrating 3p and 2 with respect to p]
putting the limits of integration from 0 to 5 seconds, s = (3/2 × 5² + 2 × 5) − (3/2 × 0² + 2 × 0)s
= 47.5 m
Therefore, the truck has traveled a distance of 47.5 m in five seconds.
(b) To find the acceleration of the truck at t = 5 seconds
We have, y = ds/dt
Differentiating both sides with respect to time, we get, a = dy/dt
Where, a = acceleration of the truck in m/s²
Integrating both sides, we get, y = ∫a dt [∵ a = dy/dt]y = at + u Where, u is the initial velocity of the truck
Now, y = (3p + 2) m/s
So, y = (3 × 5 + 2) m/s = 17 m/s And, u = 0 [Given]
Putting the values of y and u, we get,17 = 5a + 0
Therefore, acceleration, a = 17/5 m/s²
Therefore, the acceleration of the truck at t = 5 seconds is 3.4 m/s².
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(a) During a thermodynamic cycle gas undergoes three different processes beginning at an initial state where pi=1.5 bar, V₁ -2.5 m³ and U₁ =61 kJ. The processes are as follows: (i) Process 1-2: Compression with pV= constant to p2 = 3 bar, U2 = 710 kJ 3 (ii) Process 2-3: W2-3 = 0, Q2-3= -200 kJ, and (iii) Process 3-1: W3-1 +100 kJ. Determine the heat interactions for processes 1-2 and 3-1 i.e. Q1-2 and Q3-1.
Heat interaction for process 1-2 (compression) is Q1-2 = -649 kJ and for process 3-1 (unknown process) is Q3-1 = 100 kJ.
To determine the heat interactions for processes 1-2 and 3-1, we can apply the First Law of Thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat added (Q) minus the work done (W) on the system.
For process 1-2, the compression process with pV = constant, the work done can be calculated as:
W1-2 = -ΔU1-2 = U2 - U1 = 710 kJ - 61 kJ = 649 kJ
Since the work done is negative, indicating work done on the system, the heat interaction Q1-2 for process 1-2 can be determined using the First Law of Thermodynamics:
Q1-2 = ΔU1-2 + W1-2
= 0 + (-649 kJ)
= -649 kJ
Therefore, the heat interaction for process 1-2 is Q1-2 = -649 kJ, indicating that 649 kJ of heat is removed from the system during the compression process.
For process 3-1, we have the work done given as W3-1 = +100 kJ. To determine the heat interaction Q3-1, we can again use the First Law of Thermodynamics:
Q3-1 = ΔU3-1 + W3-1
= 0 + 100 kJ
= 100 kJ
Therefore, the heat interaction for process 3-1 is Q3-1 = 100 kJ, indicating that 100 kJ of heat is added to the system during this process.
In summary, for the given thermodynamic cycle:
Heat interaction for process 1-2 (compression) is Q1-2 = -649 kJ (heat removed from the system).
Heat interaction for process 3-1 (unknown process) is Q3-1 = 100 kJ (heat added to the system).
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Because the current surge in starting multiple motors is too great for the system, there must be a delay between the starting of each motor.
Because the current surge in starting multiple motors is too great for the system, a delay between the starting of each motor is necessary.
When multiple motors start simultaneously, they draw a significant amount of current, resulting in a high inrush current that can overload the electrical system. To prevent this, a delay is introduced between the starting of each motor. This delay allows the system to stabilize and accommodate the initial surge in current before the next motor is started. By staggering the motor start times, the overall current demand is distributed more evenly, reducing the strain on the electrical system. This practice helps to prevent voltage drops, voltage fluctuations, and potential damage to electrical components. Therefore, introducing a delay between the starting of each motor is essential to ensure the proper functioning and longevity of the system.
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An induction motor that has the following characteristics, 220V,
50Hz, 2 poles. This motor is running at 5% slip. Find, 1) the rotor
speed in rpm, 2) the rotor slip speed, 3) the rotor frequency in
He
The rotor speed of the induction motor is 2850 RPM, the rotor slip speed is 150 RPM, and the rotor frequency is 47.5 Hz.
Given, an induction motor has 220V, 50Hz, and 2 poles and runs at 5% slip. Synchronous speed of an induction motor can be calculated using the formula:
Synchronous speed = (120 x frequency) / number of poles. Therefore, synchronous speed = (120 x 50) / 2 = 3000 RPM.
Rotor speed of an induction motor can be calculated using the formula:
Rotor speed = synchronous speed x (1 - slip).
Therefore, rotor speed = 3000 x (1 - 0.05) = 2850 RPM. Rotor slip speed can be calculated using the formula:
Rotor slip speed = synchronous speed - rotor speed. Therefore, rotor slip speed = 3000 - 2850 = 150 RPM.
Rotor frequency can be calculated using the formula:
Rotor frequency = (rotor speed x number of poles) / 120. Therefore, rotor frequency = (2850 x 2) / 120 = 47.5 Hz.
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A 53 g ice cube can slide without friction up and down a 30∘ slope. The ice cube is prossed against a spring at the bottom of the slope, compressing the spring 10 cm. The spring constant is 25 N/m. When the ico cube is released, what total distance will it fravel up the slope before reversing direction? Express your answer with the appropriate units. Part B The ice cube is repleced by a 53 g. plastic cube whose coetlicient of kinotic friction is 0.20. How far wit the plastic cube travel up the slope? Express your answer with the appropriate units.
The total distance traveled by the ice cube before reversing direction is 0.2389 m.
The plastic cube with coefficient of kinetic friction of 0.20 will travel 0.1972 m up the slope before coming to a stop.
To find the total distance the ice cube will travel up the slope before reversing direction, we can use the concept of potential energy. When the ice cube compresses the spring, it gains potential energy. This potential energy will be converted to kinetic energy as the cube moves up the slope. At the highest point, all the potential energy will be converted back to kinetic energy, causing the cube to reverse direction.
The potential energy gained by compressing the spring is given by the formula
U = (1/2)kx^2,
where
U is the potential energy,
k is the spring constant,
x is the compression of the spring.
In this case, the spring constant is given as 25 N/m and the compression of the spring is 10 cm (which is equal to 0.1 m).
Substituting the given values into the formula, we have:
U = (1/2)(25 N/m)(0.1 m)^2
U = 0.125 J
This potential energy will be converted to kinetic energy as the ice cube moves up the slope. The kinetic energy is given by the formula
K = (1/2)mv^2,
where
K is the kinetic energy,
m is the mass of the ice cube,
v is its velocity
At the highest point, all the potential energy is converted to kinetic energy, so we can equate the two formulas:
0.125 J = (1/2)(0.053 kg)v^2
Solving for v, we have:
v^2 = (2 * 0.125 J) / (0.053 kg)
v^2 = 4.716 J/kg
Taking the square root of both sides, we find:
v = 2.17 m/s
Now, we can calculate the distance traveled by the ice cube before reversing direction. The total distance traveled is equal to twice the distance traveled while accelerating up the slope. This can be found using the equation of motion
s = ut + (1/2)at^2,
where
s is the distance traveled,
u is the initial velocity,
a is the acceleration,
t is the time
The initial velocity u is 0 m/s (since the ice cube starts from rest), the acceleration a is -9.8 m/s^2 (since it is moving against gravity), and the time t can be found using the formula v = u + at.
Substituting the given values, we have:
2s = 0 + (-9.8 m/s^2)t^2
2s = -4.9 m/s^2 * t^2
Solving for t, we have:
t^2 = (-2s) / (4.9 m/s^2)
Now, we can substitute the calculated velocity and solve for t:
2.17 m/s = 0 m/s + (-9.8 m/s^2)t
t = 0.22 s
Substituting the calculated time back into the equation for distance, we have:
2s = -4.9 m/s^2 * (0.22 s)^2
2s = -0.2389 m
Since distance cannot be negative, the total distance traveled by the ice cube before reversing direction is 0.2389 m.
Part B:
To find the distance the plastic cube will travel up the slope, we need to consider the additional force of friction acting against its motion. The force of friction can be calculated using the equation
f = μN,
where
f is the force of friction,
μ is the coefficient of kinetic friction,
N is the normal force
The normal force is equal to the weight of the cube, which is given by the formula
N = mg,
where
m is the mass of the cube
g is the acceleration due to gravity
In this case, the mass of the plastic cube is also 53 g (which is equal to 0.053 kg) and the coefficient of kinetic friction is 0.20.
Substituting the given values into the equation, we have:
f = (0.20)(0.053 kg)(9.8 m/s^2)
f = 0.102 N
This force of friction acts in the opposite direction to the motion of the cube up the slope. The net force acting on the cube is the difference between the force of gravity and the force of friction. The force of gravity is given by the formula F = mg.
Substituting the given values, we have:
F = (0.053 kg)(9.8 m/s^2)
F = 0.5194 N
The net force is given by the formula Fnet = F - f.
Substituting the calculated values, we have:
Fnet = 0.5194 N - 0.102 N
Fnet = 0.4174 N
The acceleration of the plastic cube can be calculated using the formula Fnet = ma.
Substituting the calculated net force and the mass of the cube, we have:
0.4174 N = (0.053 kg)a
Solving for a, we find:
a = 7.88 m/s^2
Using the equation of motion s = ut + (1/2)at^2, we can find the distance traveled by the cube before it comes to a stop. The initial velocity u is 0 m/s (since the cube starts from rest), the acceleration a is -7.88 m/s^2 (since it is moving against gravity), and the time t can be found using the formula v = u + at.
Substituting the given values, we have:
s = 0 + (1/2)(-7.88 m/s^2)t^2
s = -3.94 m/s^2 * t^2
Solving for t, we have:
t^2 = (s) / (-3.94 m/s^2)
Now, we can substitute the calculated time and solve for s:
s = (-3.94 m/s^2)(0.22 s)^2
s = -0.1972 m
Since distance cannot be negative, the plastic cube will travel 0.1972 m up the slope before coming to a stop.
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air expands from 3.5MPa and 100°C to 500kPa in an adiabatic expansion valve. For environmental conditions of 101.3kPa and 25°C, calculate the temperature change across the valve, and specific irre- versibility of the process.
The given information is as follows: Initial pressure and temperature of air, P1 = 3.5 MPa and T1 = 100°C
Pressure after adiabatic expansion, P2 = 500 kPa
Environmental pressure and temperature, P3 = 101.3 kPa and T3 = 25°C
The adiabatic process is a process in which no heat transfer takes place, and no thermal energy enters or leaves the system. For an adiabatic process, PVγ = constant where P is the pressure, V is the volume, γ is the ratio of specific heats and is equal to CP/CV.CP and CV are the specific heats of the gas at constant pressure and constant volume respectively.
Since there is no heat transfer, PVγ = constant can be written as P1V1γ = P2V2γwhere V1 and V2 are the initial and final volumes of the gas respectively.
Now, from the ideal gas equation PV = nRT,
we have V1 = nRT1/P1 and V2 = nRT2/P2
where n is the number of moles of the gas and R is the universal gas constant.
Substituting the values, P1V1γ = P2V2γ gives T2 = T1(P2/P1)^(γ-1)
Using the values of T1, T3, P1, P3, and γ = 1.4, the temperature change across the valve can be calculated as follows:
T2 = T1(P2/P1)^(γ-1)
= 373.15 K (500/3500)^(1.4-1)
= 260.7 K
The specific irreversibility of the process can be calculated using the following formula:
σ = T0/SΔS
where T0 is the environmental temperature, ΔS is the change in entropy of the system, and S is the total entropy generated during the process.
Since the process is adiabatic, there is no heat transfer, and hence, ΔS = 0.So,
σ = T0/SΔS
= T0/S(0)
= undefined (since division by zero is not possible)Therefore, the specific irreversibility of the process is undefined.
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A flat glass slab of thickness 6 cm and refractive index 1.5 is placed in front of a plane mirror. An observer is standing behind the glass slab and looking at the mirror. The actual distance of the observer from the mirror is 50 cm. The observer sees the image at a distance of d1 cm from himself. Now the slab is removed and the observer sees his image in plane mirror at a distance of d2 cm from himself. What is the value of d2−d1 ?
The value of d2−d1 is 0 cm.
The value of d2−d1 can be calculated by considering the effects of the flat glass slab on the observer's perception of the image.
First, let's understand the role of the flat glass slab in this scenario. The slab has a thickness of 6 cm and a refractive index of 1.5. The refractive index indicates how much light is bent or refracted as it passes through a medium compared to its speed in a vacuum. In this case, the glass slab slows down the light passing through it.
When the observer is looking at the mirror through the glass slab, the light rays coming from the image behind the mirror undergo refraction as they pass through the slab. This refraction causes a shift in the apparent position of the image.
Now, let's analyze the situation step-by-step:
1. Observer's position with the glass slab:
- The observer is standing at a distance of 50 cm from the plane mirror.
- Due to the refraction caused by the glass slab, the observer sees the image at a distance of d1 cm from himself.
2. Observer's position without the glass slab:
- When the glass slab is removed, the observer looks directly at the plane mirror.
- The observer sees his image at a distance of d2 cm from himself.
We need to find the value of d2−d1.
To solve this, we need to understand that the refraction of light at the glass slab introduces an apparent shift in the image position. This shift can be calculated using the formula:
apparent shift = (refractive index - 1) x thickness of slab
Substituting the given values, we have:
apparent shift = (1.5 - 1) x 6 cm
= 0.5 x 6 cm
= 3 cm
Therefore, the image appears to shift by 3 cm when observed through the glass slab.
Now, let's find the value of d2−d1:
d2−d1 = d2 (without glass slab) - d1 (with glass slab)
= d2 (without glass slab) - (d1 (with glass slab) + 3 cm) (due to the apparent shift)
Since the observer sees his image at the same distance from himself with and without the glass slab, we can conclude that:
d2−d1 = 0 cm
In other words, there is no change in the apparent distance of the image from the observer when the glass slab is removed.
So, the value of d2−d1 is 0 cm.
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what happens when energy intake is high and energy demands are low?
When energy intake is high and energy demands are low, several things can occur in the body:
1. Energy storage: Excess energy from the high intake is typically stored in the form of fat. The body converts the excess energy into triglycerides and stores them in adipose tissue for later use.
2. Weight gain: The excess energy being stored as fat leads to weight gain. Over time, consistent high energy intake and low energy demands can contribute to obesity and associated health issues.
3. Metabolic slowdown: The body adjusts its metabolism based on energy intake and demands. In this scenario, where energy demands are low, the body may downregulate its metabolism to conserve energy. This can result in reduced energy expenditure and a decrease in overall metabolic rate.
4. Increased risk of chronic diseases: Consistently high energy intake coupled with low energy demands can increase the risk of developing chronic diseases such as type 2 diabetes, cardiovascular diseases, and metabolic syndrome.
It's important to maintain a balance between energy intake and energy demands to support overall health and well-being. Regular physical activity and a balanced diet that meets the body's energy requirements can help achieve this balance.
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An aircraft is flying at 90 kts with respect to the surrounding air. Its heading is 270∘. The wind speed is 20kts and its direction is from the west. What is the true airspeed and ground speed of that aircraft?
The aircraft's airspeed refers to its speed relative to the surrounding air. In this case, the aircraft is flying at 90 knots (kts) with respect to the surrounding air and the ground speed of the aircraft is 50 knots.
To determine the true airspeed, we need to take into account the effect of the wind. The wind is blowing from the west at a speed of 20 kts. Since the aircraft is heading west (270 degrees), it will experience a headwind.
To calculate the true airspeed, we can use the following formula:
True Airspeed = Indicated Airspeed + Headwind
Since the aircraft is flying at 90 kts with respect to the surrounding air, the indicated airspeed is 90 kts. The headwind is 20 kts (opposite direction of the aircraft's heading), so we can substitute these values into the formula:
True Airspeed = 90 kts + (-20 kts)
True Airspeed = 70 kts
Therefore, the true airspeed of the aircraft is 70 knots.
The ground speed of the aircraft refers to its speed relative to the ground.
To calculate the ground speed, we need to consider the effect of both the aircraft's airspeed and the wind.
Since the wind is blowing from the west at a speed of 20 kts, and the aircraft is heading west (270 degrees), it will experience a headwind. This means that the aircraft's ground speed will be lower than its true airspeed.
To calculate the ground speed, we can use the following formula:
Ground Speed = True Airspeed - Headwind
Using the true airspeed of 70 kts and the headwind of 20 kts, we can substitute these values into the formula:
Ground Speed = 70 kts - 20 kts
Ground Speed = 50 kts
Therefore, the ground speed of the aircraft is 50 knots.
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Section 22.7. The Electric Generator 9. A \( 120.0-\mathrm{V} \) motor draws a current of \( 7.00 \mathrm{~A} \) when running at normal speed. The resistance of the armature wire is \( 0.720 \Omega \)
(a) The back emf generated by the motor is approximately 114.96 V. (b) When the motor is just turned on and has not begun to rotate, the current is approximately 166.67 A.
(a) To determine the back electromotive force (emf) generated by the motor, we can use Ohm's Law and the relationship between voltage, current, and resistance.
The back emf (E) is given by:
E = V - I * R
where V is the applied voltage, I is the current, and R is the resistance.
Substituting the given values:
V = 120.0 V
I = 7.00 A
R = 0.720 Ω
E = 120.0 V - 7.00 A * 0.720 Ω
Calculating this, we find:
E = 114.96 V
Therefore, the back emf generated by the motor is approximately 114.96 V.
(b) When the motor is just turned on and has not begun to rotate, it is in a stall condition, meaning it is not moving and the back emf is negligible. In this case, the current is determined solely by the resistance of the armature wire.
Using Ohm's Law (V = I * R), we can calculate the current (I) at this instant:
V = I * R
Substituting the given values:
V = 120.0 V
R = 0.720 Ω
120.0 V = I * 0.720 Ω
Solving for I:
I = 166.67 A
Therefore, the current at the instant when the motor is just turned on and has not begun to rotate is approximately 166.67 A.
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Complete Question : The Electric Generator 9. A 120.0−V motor draws a current of 7.00 A when running at normal speed. The resistance of the armature wire is 0.720Ω. (a) Determine the back emf generated by the motor. (b) What is the current at the instant when the motor is just turned on and has not begun to rotate?
In certain fireworks, potassium nitrate breaks down into potassium oxide, nitrogen, and oxygen. This is an example of a decomposition reaction. The opposite process is a synthesis reaction.
The given statement is correct. The decomposition of potassium nitrate into potassium oxide, nitrogen, and oxygen is indeed an example of a decomposition reaction, and the opposite process is a synthesis reaction.
A decomposition reaction is a type of chemical reaction where a compound breaks down into simpler substances. In the case of potassium nitrate[tex](KNO_{3} )[/tex] in fireworks, it decomposes into potassium oxide ([tex]K_{2} O[/tex]), nitrogen gas ([tex]N_{2}[/tex]), and oxygen gas ([tex]O_{2}[/tex]). This reaction is typically initiated by heat or other sources of energy. The balanced chemical equation for this decomposition reaction is as follows:
2 KNO₃ → 2 K₂O + N₂ + 3 O₂
The decomposition of potassium nitrate releases energy and is an essential component of fireworks, contributing to their vibrant colors and explosive effects.
On the other hand, the opposite process of decomposition is a synthesis reaction, also known as a combination reaction. In a synthesis reaction, two or more simpler substances combine to form a more complex compound. In this case, the opposite of the decomposition of potassium nitrate would involve the synthesis of potassium nitrate from its constituent elements. The balanced chemical equation for this synthesis reaction is as follows:
2 K₂O + N₂ + 3 O₂ → 2 KNO₃
In this reaction, potassium oxide, nitrogen gas, and oxygen gas combine under suitable conditions to produce potassium nitrate.
Therefore, the given statement is correct. The decomposition of potassium nitrate into potassium oxide, nitrogen, and oxygen is an example of a decomposition reaction, and the opposite process is a synthesis reaction.
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3. A two loop AC circuit. We wish to analyze the circuit shown to the left. To this end analyze the complex DC circuit shown to the right. (a) [6 points] Impedances. What is (i) \( Z_{1} \) ? (ii) \(
A two-loop AC circuit is represented in the figure given below:Two loop AC circuitFigure 1: Two loop AC circuit(a) Impedances(i) Impedance, \(Z_{1}\)The impedance of the inductor is given as \(Z_{L} = j\omega L\)The impedance of the capacitor is given as \(Z_{C} = \frac{-j}{\omega C}\)
The impedance of the resistor is given as \(Z_{R} = R\)Since, the inductor and resistor are connected in series, their equivalent impedance will be:$$Z_{LR} = Z_{L}+Z_{R} = j\omega L + R$$Again, the capacitor is in parallel with the inductor-resistor combination. Therefore, the total circuit impedance will be:[tex]$$Z = Z_{LR} || Z_{C}$$$$[/tex]\Rightarrow Z = \frac{Z_{LR} \times Z_{C}}{Z_{LR}+Z_{C}} = \frac{R-j\omega L}{1-j\omega RC}$$Therefore, the impedance of the circuit will be $$\boxed{Z_1=\frac{R-j\omega L}{1-j\omega RC}}$$(ii) Impedance, \(Z_{2}\)The impedance of the capacitor is given as $$Z_{C} = \frac{-j}{\omega C}$$The impedance of the resistor is given as $$Z_{R} = R$$The capacitor and resistor are connected in series. Therefore, their equivalent impedance will be:[tex]$$Z_{RC} = Z_{R} + Z_{C} = R - j\frac{1}{\omega C}$$[/tex]Therefore, the impedance of the circuit will be:$$\boxed{Z_2 = R-j\frac{1}{\omega C}}$$
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Two coils,X and Y, having self inductances of 80mH and 60mH respectively, are magnetically coupled. Coil X has
200 turns and coil Y has 100 turns. When a current of 4A is reversed in coil X the change of flux in coil Y is
5mWb. Determine (a) the mutual inductance between the coils, and (b) the coefficient of coupling
The mutual inductance between the coils is 6.25μH. the coefficient of coupling between the coils is approximately 0.447.
The mutual inductance between the coils can be determined using the formula:M = (Δφ_Y) / (N_X * ΔI_X)
Where M represents the mutual inductance, Δφ_Y is the change in flux in coil Y, N_X is the number of turns in coil X, and ΔI_X is the change in current in coil X.
Plugging in the values given, we have: M = (5mWb) / (200 * 4A)
M = 5mWb / 800A
M = 6.25μH. Therefore, the mutual inductance between the coils is 6.25μH.
(b) The coefficient of coupling (k) can be calculated using the formula:
k = M / √(L_X * L_Y)
Where k represents the coefficient of coupling, M is the mutual inductance, L_X is the self-inductance of coil X, and L_Y is the self-inductance of coil Y.
Substituting the given values: k = (6.25μH) / √((80mH) * (60mH))
k = 6.25μH / √(4.8mH^2)
k ≈ 0.447. Therefore, the coefficient of coupling between the coils is approximately 0.447.
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Because of their current amplification, phototransistors have much less sensitivity than photodiodes. Select one: O True O False
False Phototransistors have much higher sensitivity than photodiodes since they have the added advantage of current amplification. They have a much higher gain than photodiodes and can detect very low-level light, and they also require less external circuitry to amplify the current, making them ideal for a variety of applications
Phototransistors are similar to photodiodes in that they are both types of light detectors that convert light into a current. The difference between them is that phototransistors have an additional layer of a semiconductor that amplifies the current. As a result, phototransistors can detect even lower levels of light than photodiodes, and they are also less susceptible to external noise. They are frequently used in low-light applications where a high degree of sensitivity is needed.
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from a practical standpoint, the chief function of lighting is
The chief function of lighting is to provide illumination, making objects visible to the human eye. It also enhances the aesthetics of a space and serves various practical applications such as reading, studying, and working.
From a practical standpoint, the chief function of lighting is to provide illumination. Illumination refers to the process of lighting up a space or object, making it visible to the human eye. Lighting allows us to see and navigate our surroundings, ensuring safety and comfort.
Lighting serves several practical functions in our daily lives. It plays a crucial role in enhancing the aesthetics of a space, creating ambiance, highlighting architectural features, or setting the mood for different activities. Moreover, lighting is essential for various practical applications such as reading, studying, working, cooking, and performing tasks that require visual precision.
Different types of lighting fixtures, such as incandescent bulbs, fluorescent lights, and LED lights, are used to fulfill these functions. Incandescent bulbs produce light by heating a filament, while fluorescent lights use gas discharge to produce light. LED lights, on the other hand, use semiconductors to emit light efficiently.
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The chief function of lighting from a practical standpoint is to provide illumination to an environment. It helps in visibility in various activities, in addition to enhancing the beauty of a room. Light is necessary for human activities, especially when it comes to night time.
The light will make it possible for people to carry out their activities without any difficulties and also make the environment look beautiful. In general, the function of lighting is to provide illumination, which is significant in different situations and environments. For instance, street lighting is essential because it enhances visibility at night, making it safe for pedestrians and motorists to move around. It also acts as a deterrent to crime, such as robberies, muggings, and other forms of criminal activities that may occur at night. Similarly, home lighting is necessary because it enhances the beauty of the home and provides visibility to the occupants.
It allows people to carry out their activities effectively, read, study, and do other things without straining their eyes. In offices, lighting is necessary because it improves the working environment and reduces accidents that may occur due to poor visibility. Furthermore, it is essential in factories, production lines, and other industrial settings where workers need adequate lighting to carry out their tasks effectively. Finally, lighting is significant in public places like parks, museums, and stadiums, where it enhances the beauty of the surroundings and makes it possible for people to enjoy themselves during the day and night.
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Problem 2. 20 points For the following circuit solve for the steady-state value if \( i_{1}, i_{2} \), \( i_{3} \), is and \( v_{e} \). Assume that the switch has been closed for long time.
Given the circuit diagram below:The given circuit diagram comprises an operational amplifier, 2 input resistors R1 and R2, a feedback resistor Rf, and a switch. To find the steady-state value, first, the transfer function is to be calculated. It is observed that the non-inverting terminal of the operational amplifier is grounded.
Now, using the voltage divider rule, the output voltage of the voltage divider network at the inverting terminal of the operational amplifier is given by:[tex]$$v_i=\frac{R_1}{R_1+R_2}v_{e}$$[/tex]Since, the operational amplifier is assumed to be in the ideal condition, the current entering the inverting terminal is negligible.
Therefore, the current flowing through the feedback resistor Rf is the sum of the currents flowing through R1 and R2. Hence, the expression for output voltage Vout is given by:[tex]$$V_{out}=-\frac{R_f}{R_1+R_2}v_{e}$$[/tex]To determine the steady-state value, we assume that the switch has been closed for a long time, and as a result, the capacitor is fully charged. Therefore, the capacitor acts as an open circuit and can be removed from the circuit diagram.
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True or False
Electron microscopes and e-beam writers cost about the same.
EUV is a very recent innovation.
EUV light is generated by a mercury arc.
The given statements are False. Let's take each statement and discuss them one by one. Electron microscopes and e-beam writers cost about the same - False
Electron microscopes and e-beam writers do not cost about the same. Electron microscope cost ranges between $50,000 to $500,000 and e-beam writer cost ranges between $250,000 to $10,00,000. So, this statement is false. EUV is a very recent innovation - False
Extreme ultraviolet lithography (EUV) is not a very recent innovation. It has been in use for around two decades and has been used to print circuitry for DRAM memory chips and some other electronics. So, this statement is false. EUV light is generated by a mercury arc - False
EUV light is not generated by a mercury arc. It is generated by a laser beam that is focused on a droplet of liquid tin to produce plasma that emits light with a wavelength of 13.5 nm. So, this statement is also false. Hence, the main answer to the question is: The given statements are False.
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4.4A flywheel has a mass of 60 kg and a radius of gyration kg = 150 mm about an axis of rotation passing through its mass center. If a motor supplies a clockwise torque having a magnitude of M= 5t Nm, where t is in seconds, determine the flywheel's angular impulse at t=3s. Initially the flywheel is rotating clockwise at oo1 = 3 rad/s. a) 18.5 b) 22.5 c) 45
Mass of flywheel, m = 60 kg Radius of gyration,
k = 150 mm
= 0.15 m Clockwise torque supplied,
M = 5t Nm Time,
t = 3 s Angular velocity,
[tex]ω₀ = 3 rad/s[/tex] Let's first calculate the moment of inertia of the fly wheel.
[tex]I = mk²[/tex]
[tex]I = 60 × (0.15)²[/tex]
[tex]I = 1.35 kg m²[/tex]Now, the formula for the angular impulse is given as
J = ΔL Where,
L = Iω Therefore,
[tex]J = Iω - Iω₀.[/tex]
Therefore, the angular impulse of the flywheel is 11 Nms. Hence the correct option is option B, 22.5.
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A tourist looks up at a tall obelisk and desires to determine the height of this object. He estimates that he is 257 meters from the base of the obelisk and the angle from the horizontal is 56.7 degrees. At that moment, a bird drops a twig from the top of the obelisk. How long, in seconds, does it take for the twig to fall to the ground?
Assume no initial downward velocity and no drag.
The time taken by the twig to fall to the ground is 27.8 seconds (approx).
Given that a tourist looks up at a tall obelisk and desires to determine the height of this object.
He estimates that he is 257 meters from the base of the obelisk and the angle from the horizontal is 56.7 degrees.
At that moment, a bird drops a twig from the top of the obelisk. We need to find how long, in seconds, it takes for the twig to fall to the ground when there is no initial downward velocity and no drag. Let's begin our solution by drawing a diagram for the given situation. We are given that the tourist estimates that he is 257 meters from the base of the obelisk and the angle from the horizontal is 56.7 degrees.
tan 56.7° = height of obelisk/distance from the base of the obelisk to the tourist
Therefore, the height of the obelisk = distance from the base of the obelisk to the tourist × tan 56.7°= 257 × tan 56.7°Now, we can find the time taken by the twig to reach the ground using the formula:t = sqrt(2h/g)
Where h is the height of the obelisk and g is the acceleration due to gravity.
Substituting the given values, we have:t = sqrt(2 × 257 × tan 56.7° / 9.81)= sqrt(515 × tan 56.7° / 9.81)= sqrt(515 × 1.5)= sqrt(772.5)= 27.8
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1. Figure 1 shows a particle with energy E moving in the positive x direction towards a step potential Vo. Given E< Vo. Particle Region I V(x) Vo E 0 Region II Figure 1 X (a) Solve the Schrödinger equation in order to obtain the solutions for the region I and II. (b) Solve the coefficient of the wave numbers for the regions above. (c) Find the reflection coefficient R (d) Find the transmission coefficient T. (e) Discuss the result obtained with those expected from the classical physics. (50 marks)
The solution of the Schrödinger equation is obtained by solving it in two parts for the regions I and II. The Schrödinger equation for both the regions is given by:Region I: [tex]-h^2/2m (d^2ψ/dx^2) = EψRegion II: -h^2/2m (d^2ψ/dx^2) + V_0ψ = Eψ[/tex]
For the Region I, the solution of the Schrödinger equation is given by:
[tex]ψ(x) = Ae^(ikx) + Be^(-ikx)Where k = √(2mE/h^2)[/tex]
For the Region II, the solution of the Schrödinger equation is given by:
[tex]ψ(x) = Ce^(k_1x) + De^(-k_1x)Where k_1 = √(2m(V_0 - E)/h^2)b)[/tex]
The coefficients of the wave numbers for the regions above are given as:In Region I: A = 1 and B = RIn Region II: C = T and D = R^*Where R* is the complex conjugate of R.c)
The reflection coefficient and transmission coefficient are related by the equation:R + T = 1e) The classical physics suggests that if a particle does not have enough energy to overcome the potential barrier, it will be reflected back with R = 1. However, the Schrödinger equation predicts that there is always a finite probability of the particle tunneling through the barrier with T > 0. This phenomenon is known as quantum tunneling and is a purely quantum mechanical effect.
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A monochromatic wave with frequency f = 12 [MHz] propagates in a lossy medium with relative constitutive parameters , = 4. &, = 4.5. The frequency and the phase constant of the wave are given as and = 10 [rad/m], respectively. Calculate the conductivity of the medium.
The conductivity of a medium can be calculated using the following equation:σ = ωε tan δwhere,σ: conductivityω: angular frequency of the waveε: permittivity of the medium tan δ: loss tangent Given that a monochromatic wave with frequency f = 12 [MHz] propagates in a lossy medium with relative constitutive parameters
εr = 4 and
μr = 4.5.
The frequency and the phase constant of the wave are given as ω and β = 10 [rad/m], respectively.The angular frequency can be calculated asω = 2πfω = 2π × 12 × 10^6ω
= 75.4 × 10^6 rad/sNow, we need to calculate the permittivity of the medium using the relative permittivity.
εr = 4ε0 => ε = εr × ε0ε
= 4 × 8.85 × 10^(-12)ε
= 35.4 × 10^(-12) F/mGiven that the lossy medium is characterized by relative constitutive parameters
εr = 4 and
μr = 4.5, we can assume it to be a dielectric medium.
Hence, μr = 1 and
hence μ = μ0. Here, μ0 is the permeability of free space.
The conductivity can now be calculated using the formula:σ = ωε tan δWe have ω = 75.4 × 10^6 rad/s and
ε = 35.4 × 10^(-12) F/m. Now, we need to find the value of the loss tangent, tan δ.The phase constant is given as
β = 10 [rad/m]. It is related to the loss tangent as
β = ω√(με) √(1 + jtanδ)
β = 2πf√(με) √(1 + jtanδ)
β = ω √(εμ) √(1 + jtanδ)Comparing the real and imaginary parts of the above equation, we can get expressions for the loss tangent and the relative permittivity.
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A 3-phase, 4500 kVA, 13 kV, 50 Hz, 4-pole, star-connected synchronous generator has synchronous reactance of 8 ohm/phase and an armature resistance of 0.5 ohm/phase. With an assumption that the mechanical stray loss is 30 kW and power factor of 0.8 lagging, determine the followings: i) Stator current il) Excitation voltage iii) Voltage regulation iv) Efficiency of the generator
The values are,
i) Stator current is 254.12 Amps
ii) Excitation voltage is 757.1 Volts
iii) Voltage regulation is 5.60%
iv) Efficiency of the generator is 94.4%.
A 3-phase, 4500 kVA, 13 kV, 50 Hz, 4-pole, star-connected synchronous generator has synchronous reactance of 8 ohm/phase and an armature resistance of 0.5 ohm/phase.
With an assumption that the mechanical stray loss is 30 kW and power factor of 0.8 lagging, determine the following:
i) Stator current
ii) Excitation voltage
iii) Voltage regulation
iv) Efficiency of the generator
Stator current
Stator current formula is defined as follows:
Iph = S / √3 × Vph
Iph = 4,500,000 / √3 × 13,000
Iph = 254.12 Amps
Excitation voltage
Excitation voltage formula is defined as follows:
Vf = E + Ia × (ra cos Øa + Xs cos Øs) / √3 × Iph × Xs
Vf = √(13,000² - 254.12²) + 254.12 × (0.5 cos 36.87 + 8 cos 75.31) / √3 × 254.12 × 8
Vf = 757.1 Volts
Voltage regulation
The formula for voltage regulation is defined as follows:
VR = (Vnl - Vfl) / Vfl × 100%
VR = (13,000 - 12,308.5) / 12,308.5 × 100%
VR = 5.60%
Efficiency of the generator
The formula for the efficiency of the generator is defined as follows:
η = S / (S + Loss)
η = 4,500,000 / (4,500,000 + 30,000 + 3 × 254.12² × 0.5 + 3 × 254.12² × 8)
η = 0.944 or 94.4%
Therefore, the values are:
i) Stator current = 254.12 Amps
ii) Excitation voltage = 757.1 Volts
iii) Voltage regulation = 5.60%
iv) Efficiency of the generator = 94.4%.
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Write a differential equation of the RC circuit relating Vi(t)
to Vo(t).
The RC circuit consists of a resistor R and a capacitor C connected in series to a voltage source Vi(t) and a load Vo(t). The differential equation of the RC circuit is given by:
V_i(t) - V_o(t) = RC dV_o(t)/dtwhere V_i(t) is the input voltage, V_o(t) is the output voltage, R is the resistance, C is the capacitance, and dV_o(t)/dt is the derivative of the output voltage with respect to time t. This equation relates the input voltage V_i(t) to the output voltage V_o(t) in the RC circuit.The term RC in the equation is known as the time constant of the circuit and determines the rate at which the capacitor charges or discharges. If RC is small, the capacitor charges or discharges quickly, whereas if RC is large,
the capacitor charges or discharges slowly. This property of the RC circuit makes it useful in many applications, such as in filters, oscillators, and timers.The above differential equation can be solved to obtain the output voltage V_o(t) as a function of time t, given the input voltage V_i(t) and the initial condition of the capacitor voltage V_o(0). The solution depends on the nature of the input voltage and the circuit parameters R and C, and can be obtained using various techniques such as Laplace transforms, Fourier series, or numerical methods.
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The magnetic flux in a core is continuous in the core and gap. Is the magnetic field intenisty (H) also continous in the core and gap?
Yes, the magnetic field intensity (H) is continuous in the core and gap. The magnetic flux (φ) in a core is continuous throughout the core and gap.
The magnetic field intensity (H) is also constant throughout the core and gap of a ferromagnetic material where the core can be seen as a magnetic circuit.
A magnetic circuit consists of a ferromagnetic material in the core and a non-ferromagnetic material in the gap which provides a path for the magnetic flux to flow.
H is equal to the flux density (B) divided by the permeability (μ) of the core and gap.
The magnetic field intensity H is produced due to the flow of current in a conductor. H is the most widely used parameter in the analysis of magnetic circuits because it is simple to calculate and is directly proportional to the current in a conductor.
The magnetic field intensity H is also a measure of the magnetic field strength in a material.
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e. 5 4. Living matter has an activity of 450 dps due to carbon 14. If a sample of wood from a burial site has an activity of 340 dps, estimate the age of the site. Half-life of carbon 14 is 5730 years. Around (years) a. 2317 b. 3922 c. 5371 d. 7128 e. 9652
the estimated age of the burial site is approximately 5371 years. Option (c) is the closest match to this estimate.
To estimate the age of the burial site, we can use the concept of radioactive decay and the known half-life of carbon-14.
The activity of carbon-14 in living matter decreases over time due to radioactive decay. The formula for the activity of a radioactive substance is given by:
A = A₀ * (1/2)^(t/t₁/₂)
Where:
A = Current activity
A₀ = Initial activity
t = Time elapsed
t₁/₂ = Half-life of the radioactive substance
In this case, the initial activity (A₀) is 450 dps (decays per second), and the current activity (A) is 340 dps. The half-life of carbon-14 is 5730 years.
We can rearrange the formula to solve for time (t):
t = t₁/₂ * (log(A/A₀) / log(1/2))
Substituting the given values:
t = 5730 * (log(340/450) / log(1/2))
Using a calculator, we find:
t ≈ 5371 years
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A block of an unknown material is floating in a fluid, half-submerged. If the specific gravity of the fluid is 1.5, what is the block's density? (Use specifie gravity Pud/Pe and density of water P 1,000 k/m
A. 350kg/m
B. 8oO kgm
C. 900 kgm
D. 1,250 kg/m
The correct option is D, If the specific gravity of the fluid is 1.5, the block's density will be 1,500 kg/m.
The specific gravity (SG) of a substance is the ratio of the density of that substance to the density of another substance (usually water).
Given data:
Specific gravity (SG) = 1.5
Density of water (P) = 1,000 kg/m
We can use the formula for specific gravity to find the density of the unknown material:
SG = Density of unknown material/Density of water
Density of unknown material = SG x Density of water
Density of unknown material = 1.5 x 1,000
Density of unknown material = 1,500 kg/m
Therefore, the block's density is 1,500 kg/m.
Hence, the density of the block is 1,500 kg/m. Therefore, the correct option is D.
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Explanation:
Since specific gravity is 1.5
the unknown fluid has density of 1500 kg / m^3
Now...for convenience , let's assume the block is 1 m^3
the submerged half of it displaces 1/2 m^3 , so it would have a buoyancy of 750 kg from the fluid....but the OTHER half of the block is above the fluid level....so the entire buoyancy of 750 kg supports the entire 1 m^3 block
so the block density is 750 kg/ 1 m^3 = 750 kg/m^3 <===but this is not an answer provided as a choice <==== maybe choose answer B
1) Describe by means of sketches, the three different types of combustion chambers in direct injection engines? 2) Plot the heat release versus crank angle showing the four phases of combustion? 3) What does fuel cetane number refer to? 4) What is the effect of load (fuel quantity) on ignition delay period? Explain your answer? (clarify your answer by using diagrams) 5) What is function of lift pump in fuel injection system? What are the main types of lift pumps? \ 6) Explain with the help of sketches, how could the accelerator pedal change the fuel quantity in both in-line and axial distributer fuel pumps? 7) For a hollow cone injector, sketch the spray pattern showing different spray regimes?
The three types of combustion chambers in direct injection engines are i) spherical, ii) toroidal, and iii) bathtub. The spherical chamber is entirely spherical and has the smallest surface-area-to-volume ratio, whereas the bathtub chamber is similar to the spherical chamber.
It shows the typical heat release rate curve for a diesel engine in a four-phase mode of combustion. 3) The cetane number is an indicator of the diesel fuel's ignition characteristics. The higher the number, the shorter the delay between the injection of fuel into the cylinder and the start of combustion, resulting in less ignition lag and a shorter delay period.4)
The axial distributor pump has an accelerator linkage that operates the metering valve and alters the fuel flow rate through the fuel delivery valve.7) In the figure below, the spray pattern of a hollow cone injector is shown. A hollow cone injector produces two spray regions: the inner and outer spray regions. The inner spray region's diameter and penetration are lower than the outer spray region.
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Give the schematic arrangement of an impulse voltage divider with an oscilloscope connected for measuring impulse voltages. Explain the arrangement used to minimize errors.
The schematic arrangement of an impulse voltage divider with an oscilloscope connected for measuring impulse voltages typically involves several components and connections. The arrangement is designed to minimize errors and ensure accurate measurement of the impulse voltages.
Impulse Voltage Divider: The impulse voltage divider is a high-voltage divider network that is capable of attenuating the high magnitude of the impulse voltage to a measurable level. It consists of resistors and capacitors connected in a specific configuration to achieve the desired voltage division ratio.Voltage Probe: A high-voltage probe is connected to the output of the impulse voltage divider. This probe is designed to withstand high voltage levels and accurately measure the attenuated voltage.Oscilloscope: The oscilloscope is connected to the voltage probe to visualize and measure the attenuated impulse voltage waveform. It provides a graphical representation of the voltage waveform over time.
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A cylindrical container with a cross-sectional area of 69.2 cm
2
holds a fluid of density 836 kg/m
3
. At the bottom of the container the pressure is 117kPa. Assume P
at
=101 kPa What is the depth of the fluid? Find the pressure at the bottom of the container after an additional 255×10
−3
m
3
of this ficid is added to the container. Assume that no fild spils out of the container:
The pressure at the bottom of the container after additional fluid is added is approximately 18 kPa.
Given data:
Area of cross-section = 69.2 cm²
Density of fluid = 836 kg/m³
Pressure at the bottom of the container = 117 kPa
Pat = 101 kPa
Using the formula,
P = ρgh
Where,
P = pressure
ρ = density
g = acceleration due to gravity
h = height
From the above formula, the height of the fluid can be calculated as:
h = P/ρg
Substituting the given values, we get;
h = (117000 Pa - 101000 Pa)/(836 kg/m³ × 9.8 m/s²)
= 1.96 m
Pressure at the bottom of the container after additional fluid is added: Volume of fluid added = 255 × 10⁻³ m³
Since the fluid is not overflowing, it means the increase in the height of the fluid will be 255 × 10⁻³ m.
Therefore, the new height of the fluid will be (1.96 + 0.255) m = 2.215 m.
Hence, the pressure at the bottom of the container after additional fluid is added can be calculated as:
P = ρgh
P = 836 kg/m³ × 9.8 m/s² × 2.215 m
= 18096.69 Pa
≈ 18 kPa
Therefore, the pressure at the bottom of the container after additional fluid is added is approximately 18 kPa.
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a quantity of steam (350 g) at 106 C is condensed and the resulting water is frozen into ice at 0 C. how much heat was removed?
2. How much heat in joules is neexed to raise the temperature of 8.0 L of water from 0 C to 75.0 C (hint recall the original definition of liter)
Answer: A) total heat removed is 907,900 J.
B) heat needed to raise the temperature of 8.0 L of water from 0°C to 75.0°C is 2,508,000 J.
Part 1, we need to consider the different phase changes and the specific heat capacities of water and ice.
Step 1: Calculate the heat removed during the phase change from steam to water.
- The heat removed during the phase change from steam to water is given by the equation: q = m * ΔH_vaporization.
- The specific heat of vaporization for water is 2260 J/g.
- The mass of steam is given as 350 g.
- Therefore, the heat removed during the phase change from steam to water is: q1 = 350 g * 2260 J/g = 791,000 J.
Step 2: Calculate the heat removed during the phase change from water to ice.
- The heat removed during the phase change from water to ice is given by the equation: q = m * ΔH_fusion.
- The specific heat of fusion for water is 334 J/g.
- The mass of water is still 350 g.
- Therefore, the heat removed during the phase change from water to ice is: q2 = 350 g * 334 J/g = 116,900 J.
Step 3: Calculate the total heat removed.
- To find the total heat removed, we need to add q1 and q2 together.
- Therefore, the total heat removed is: q_total = q1 + q2 = 791,000 J + 116,900 J = 907,900 J.
Part 1: The total heat removed is 907,900 J.
Part 2: To answer this question, we need to use the specific heat capacity of water.
Step 1: Convert the volume of water from liters to grams.
- The density of water is approximately 1 g/mL or 1000 g/L.
- Therefore, the mass of 8.0 L of water is: 8.0 L * 1000 g/L = 8000 g.
Step 2: Calculate the heat needed to raise the temperature of water.
- The equation to calculate the heat needed is: q = m * c * ΔT.
- The specific heat capacity of water is approximately 4.18 J/g°C.
- The mass of water is 8000 g.
- The change in temperature is 75.0°C - 0°C = 75.0°C.
- Therefore, the heat needed to raise the temperature of 8.0 L of water from 0°C to 75.0°C is:
q = 8000 g * 4.18 J/g°C * 75.0°C = 2,508,000 J.
Part 2: The heat needed to raise the temperature of 8.0 L of water from 0°C to 75.0°C is 2,508,000 J.
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The New River Gorge bridge in West Virginia is a 518-m-long
steel arch. How much will its length change between temperature
extremes
−15°C and 35°C? __________cm
Superman leaps in front of Lois La
The thermal expansion of a steel archbridge between
temperature
extremes −15°C and 35°C can be found out by using the formula;ΔL = LαΔTWher
e;L = Length of steel arch bridg
eα = Coefficient of linear expansion of steelΔ
T = Change in temperature of steel arch bridgeHere, the
length
of the New River Gorge bridge in West Virginia is L
= 518 m.
The
coefficient
of linear
expansion
of steel, α = 1.20 × 10⁻⁵ /°C.Δ
T = (35°C) - (-15°C)
= 50°C
Substituting the given values in the above equation,ΔL = LαΔ
T= (518 m) (1.20 × 10⁻⁵ /°C) (50°C)≈ 0.311 mTherefore, the length of the steel arch bridge would change by approximately 0.311 m between temperature extremes −15°C and 35°C.
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