The height of the water is found using the principle of communicating vessels. The principle of communicating vessels is a concept of fluid mechanics that states that any fluid in a container will attempt to find its level, and the pressure is the same at all points that are at the same height from the liquid's surface.
When the two fluids are joined together in a U-shaped tube, they will form a single column with the same height in both arms. Therefore, the height of the water can be determined using the following steps:Let the height of the water column be 10 meters.
Let the density of water be w and the density of alcohol be a. The pressure at the bottom of the U-shaped tube is the same on both sides. wgh = agh + Patm Where Patm is the atmospheric pressure, g is the acceleration due to gravity (9.8 m/s2), and h is the height of the water column.
ρw = 1000 kg/m³ and
a = 790 kg/m3.
Substituting these values into the above equation, we get:h = (ρa / ρw) * 16.0 cm
= (790 kg/m³ / 1000 kg/m³) * 0.16 m
= 0.1264 m
Therefore, the height of the water column is 0.1264 meters, or 12.64 centimeters. Answer: 12.64 cm.
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The height of a helicopter above the ground is given by h = 2.55e, where his in meters and is in seconds. At t = 2.35 5, the helicopter releases a small mailbag. How long after its release does the mailbag reach the ground? Need Help? Read it
The mailbag reaches the ground about 2.355 seconds after it is released.
The height of the helicopter above the ground is given by h = 2.55t², where h is in meters and t is in seconds. The height of the helicopter at t = 2.355 is h = 2.55(2.355)² ≈ 14.5 meters.
When the mailbag is dropped, it falls freely under gravity. Its height h is given by h = -4.9t², where h is in meters and t is in seconds. We want to find how long it takes for the mailbag to hit the ground, which is when its height h = 0. So we set -4.9t² = 0 and solve for t: -4.9t² = 0 t² = 0 t = 0So the mailbag hits the ground when t = 0. Since
the mailbag is dropped at t = 2.355, the time it takes for the mailbag to reach the ground after it is released is time = 0 - 2.355 ≈ -2.355 seconds (since it takes 2.355 seconds for the mailbag to reach the ground after it is released).
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8) Proxima Centauri has a parallax angle of \( 0.75^{\prime \prime} \). What is its distance in parsecs?
9) What is Proxima's distance in light-years? (Recall: one parsec \( =3.26 \) light-years)
1. Proxima Centauri's distance in parsecs is approximately 1.33 parsecs.
2. Proxima Centauri's distance in light-years is approximately 4.3 light-years.
1. The parallax angle of Proxima Centauri is given as \(0.75^{\prime \prime}\). By definition, the parallax angle is the angle subtended by the radius of the Earth's orbit when viewed from the star. Using basic trigonometry and the formula \(1 \text{ parsec} = \frac{1 \text{ AU}}{\text{parallax angle (arcseconds)}}\), we can calculate the distance in parsecs. In this case, the distance is approximately \(1.33\) parsecs.
2. Since one parsec is equivalent to approximately \(3.26\) light-years, we can convert the distance in parsecs to light-years by multiplying it by this conversion factor. Therefore, Proxima Centauri's distance in light-years is approximately \(4.3\) light-years.
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2) The wooden crate (mass \( 60 \mathrm{~kg} \) ) is on the steel surface inclined to the horizon on the angle of \( 35^{\circ} \). The coefficient of frictic is \( 0.26 \). Find the force applied on
To prevent the wooden crate from sliding down an inclined surface, the horizontal force applied should be equal to the force of friction, which is determined by the coefficient of friction and the normal force. To start moving the crate up the incline, the applied force should overcome the force of gravity, the force of friction, and provide an additional force to counteract these forces.
To solve this problem, we need to consider the forces acting on the wooden crate on the inclined surface.
a) To prevent the crate from sliding down the incline, we need to overcome the force of gravity acting on it and the force of friction opposing its motion. The force of gravity can be calculated as the weight of the crate, which is equal to its mass multiplied by the acceleration due to gravity (W = m * g).
The force of gravity acting down the incline is given by:
[tex]F_{gravity[/tex] = m * g * sin(θ)
where m is the mass of the crate, g is the acceleration due to gravity, and theta is the angle of inclination.
The force of friction opposing the motion can be calculated as the product of the coefficient of friction and the normal force. The normal force is equal to the component of the weight perpendicular to the incline, which can be calculated as:
N = m * g * cos(θ)
The force of friction is given by:
[tex]F_{friction[/tex] = coefficient of friction * N
To prevent the crate from sliding down, the force applied horizontally should be equal to the force of friction, as the crate is in equilibrium. Therefore:
[tex]Force_{applied} = F_{friction[/tex]
Substituting the equations, we have:
[tex]Force_{applied[/tex] = coefficient of friction * N
[tex]Force_{applied[/tex] = coefficient of friction * m * g * cos(θ)
b) To start moving the crate up the incline, we need to overcome the force of gravity acting down the incline, the force of friction opposing its motion, and provide an additional force to counteract these forces.
The force required to start moving the crate up can be calculated as follows:
[tex]Force_{applied} = F_{gravity} + F_{friction} + F_{additional[/tex]
Substituting the equations, we have:
[tex]Force_{applied[/tex] = m * g * sin(θ) + coefficient of friction * m * g * cos(θ) + [tex]F_{additional[/tex]
In this case, [tex]F_{additional[/tex] represents the additional force required to start moving the crate up the incline.
Note: To calculate the exact value of the force applied or additional force, we need to know the value of the coefficient of friction, the angle of inclination, and the acceleration due to gravity.
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Complete Question:
The system in the image below is at equilibrium. The smooth rod
has a mass of 8.00 kg, and a centre of mass at point G, which is
halfway along the length of the rod. You can neglect the mass of
the ro
Given,The system is at equilibrium and the smooth rod has a mass of 8.00 kg, and a center of mass at point G, which is halfway along the length of the rod.The mass of the rope can be neglected.In order to understand the concept of equilibrium, we must first understand the definition of equilibrium.
When the net force acting on an object is zero, it is in a state of equilibrium.In the given figure, the smooth rod is balanced on the support of two ropes attached to two walls, so the forces are balanced. For an object to be in equilibrium, the sum of all forces acting on it must be zero and the sum of all torques acting on it must also be zero. Since the rod is in equilibrium, the sum of the clockwise torques must be equal to the sum of the anticlockwise torques.
Therefore, the clockwise torque is (8.00 kg x 9.81 m/s² x L) Nm. Similarly, the anticlockwise torque is equal to the tension multiplied by the distance from the pivot point to the point where the rope is attached. Therefore, the anticlockwise torque is (T x L) Nm.Since the system is in equilibrium, the sum of the clockwise torques must be equal to the sum of the anticlockwise torques. Therefore, we can write the equation:mg x L = 2T x LL = (mg/2T)
The tension in each rope is equal to the weight of the rod divided by twice the distance from the center of mass to the pivot point. Therefore, the tension in each rope is:T = (mg/2L)T = (8.00 kg x 9.81 m/s²) / (2 x L)T = 39.24 N / LTherefore, the tension in each rope is directly proportional to the distance from the center of mass to the pivot point. As the distance from the center of mass to the pivot point increases, the tension in each rope decreases.
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3. QUESTION 3 A 60 TEETH B 30 TEETH DRIVEN (LOAD) DRIVER (EFFORT) 3.1. Calculate the velocity ratio in the given gear system. 3.2. Calculate the force ratio in the given gear system
1. The velocity ratio in the given gear system is 2
2. The force ratio in the given gear system is 0.5
1. How do i determine the velocity ratio?The velocity ratio in the given gear system can be obtained as illustrated below:
Number of driven gear = 60 teethNumber of driver's gear = 30 teethVelocity ratio =?Velocity ratio = Number of driven gear / Number of driver's gear
= 60 / 30
= 2
Thus, the velocity ratio is 2
2. How do i determine the force ratio?The force ratio in the given gear system can be obtained as follow:
Velocity ratio = 2Force ratio =?Force ratio = 1 / velocity ratio
= 1 / 2
= 0.5
Thus, the force ratio is 0.5
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6.0×10
−3
mol of gas undergoes the process shown in Part A the figure (Figure 1). What type of process is this? View Available Hint(s) Isobaric Isothermal Isochoric DO NOT CLICK THIS. This option is here so that fewer points will be taken off if you incorrectly answer the question. DO NOT CLICK THIS. This option is here so that fewer points will be taken off if you incorrectly answer the question. Figure <1 of 1 Part B If the constant volume of this process is V
c
=225 cm
3
, what is the initial temperature? Express your answer using three significant figures. If the constant volume of this process is V
c
=225 cm
3
, what is the final temperature? Express your answer using three significant figures. - Hint 1. How to approach the problem Once again, the ideal gas law can be used. In this case, recall that the number of molecules is constant, as is the volume occupied by the gas.
The main topic of the question is determining the type of process and finding the initial and final temperatures of a gas undergoing a specific process.
Based on the given information, we have 6.0×10^−3 mol of gas undergoing a process. To determine the type of process, we need to examine the conditions shown in Part A of Figure 1.
The possible types of processes mentioned are:
Isobaric: A process at constant pressure.
Isothermal: A process at constant temperature.
Isochoric: A process at constant volume.
To identify the process type, we need more information from Part A of the figure. However, since the figure is not provided, we cannot definitively determine the type of process.
Moving on to Part B, we are given that the constant volume of the process is Vc = 225 cm^3. We are asked to find the initial and final temperatures, expressed using three significant figures.
Since the process is at constant volume (isochoric), we can use the ideal gas law to solve for the temperatures. The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Since the volume (V) is constant, the equation simplifies to P = nRT/V. Since we do not have the pressure information, we cannot determine the initial or final temperature using the given information.
Therefore, without additional data or the figure mentioned in the question, we cannot provide the specific answers regarding the type of process and the initial and final temperatures.
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There are n>2 artillery pieces trying to bombard a target. The first artillery is a distance d away from the target, and the second is a distance d away from the first artillery, so on and so forth, with each artillery piece lined up behind the previous one, like so in this diagram:
X----------\o---------\o----------\o---------~~~~~~---\o----------\o
Let the angle between the ground and the gun barrel be Theta. Artillery pieces can not shoot with Theta <45 degrees, so in order to hit the target the first piece almost points directly up, the second slightly less so, until the nth piece has Theta=45 degrees. Assume each shell leaves the gun barrel at the exact same speed, all guns fire simultaneously and all shells have parabolic trajectories that intercept the ground exactly at the target, ignore air resistance, choose ALL of the correct statements:
A. The shells land more frequently at first and more sparsely towards the end of the bombardment
B. The shells land more sparsely at first and more frequently towards the end of the bombardment
C. For all n>2, mid-air collisions will always happen between at least two shells
D. The shells land with uniform frequency
E. The shells land at the exact same time
F. The shell from the 1st artillery piece lands first
G.The shell from the nth artillery piece lands first
H. F and G are both false
The correct answer is option H: F and G are both false. Because all shells(s) are fired simultaneously, they all reach the ground at the same time, making option D incorrect. As a result, options A, B, and C are all incorrect as well. So, both F and G are false and the correct answer is option H.
Explanation: The shells launched from all artillery pieces follow a parabolic path(PP) to reach the target. The range(R) of the shells is constant because all guns fire simultaneously and all shells have parabolic trajectories that intercept the ground exactly at the target. The elevation angle(EA) of the first artillery gun is almost vertical, and the elevation angle of the last gun is 45 degrees. The elevation angle of the guns in between will gradually increase from almost vertical to 45 degrees. At a height that is roughly proportional to the distance from the gun to the target, each shell reaches its maximum height(H). The horizontal distance covered by each shell is identical. Therefore, all of the shells' trajectories converge at a single point, which is the target.Therefore, all of the shells will land on the ground at the same time, making option E incorrect. The frequency(v) of the shells landing is determined by the time it takes them to travel from the muzzle to the ground.
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A ball is thrown into the air with a speed of 2.35 m/s (upon release), and then caught. The motion is symmetric, and without air resistance, the ball has the same speed when it is caught, as when it was thrown, assuming it is caught at the same height it was released. Using both of these assumptions, 1. Calculate the displacement of the ball in the upward direction. 2. Calculate the ball's time of flight in the upward direction. 3. Calculate the ball's total time of flight. 4. Calculate the ball's net displacement.
1. The ball has an upward displacement of 0.5835 m.
2. time of flight = 0.239 s`
3. the ball's net displacement is zero.
1. Calculation of displacement of the ball in the upward direction:
Given that a ball is thrown into the air with a speed of 2.35 m/s (upon release), and then caught. The motion is symmetric, and without air resistance. Therefore, the ball has the same speed when it is caught, as when it was thrown, assuming it is caught at the same height it was released.The upward velocity will decrease as the ball goes up, and it will eventually come to a stop at the highest point of its trajectory and begin falling back down. At the highest point, the velocity will be zero and the displacement of the ball will be maximum. Also, the displacement of the ball at the highest point is equal to the displacement of the ball at the instant it was thrown upwards. Therefore, the ball has an upward displacement of 0.5835 m.
2. Calculation of the ball's time of flight in the upward direction
:Time of flight in the upward direction is given by;
`t = v/g`
Where
t = time,
v = initial velocity
= 2.35 m/s, and
g = acceleration due to gravity
= 9.8 m/s²
`t = 2.35/9.8
= 0.239 s`
3. Calculation of the ball's total time of flight:
Since the ball has the same speed when it is caught as when it was thrown and assuming it is caught at the same height it was released, the total time of flight is two times the time of flight in the upward direction.
`Total time of flight = 2 x t``= 2 x 0.239`
`= 0.478 s`4.
Calculation of the ball's net displacement:
Since the displacement of the ball in the upward direction is 0.5835 m, the net displacement of the ball is zero because it returns to its initial position. Hence, the ball's net displacement is zero.
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In nitrogen gas the static breakdown voltage Vs of a uniform field gap may be expressed as: Vs = A pd + B vpd where A and B are constants, p is the gas pressure in torr referred to a temperature of 20°C and d is the gap length in cm. A 1 cm uniform field gap is nitrogen at 760 torr and 25°C is found to breakdown at a voltage of 33.3kV. The pressure is then reduced and after a period of stabilization, the temperature and pressure are measured as 30°C and 500 torr respectively. The breakdown voltage is found to be reduced to 21.9 KV. If the pressure is further reduced to 350 torr while the temperature if the closed vessel is raised to 60°C and the gap distance is increased to 2 cm, determine the breakdown voltage.
The breakdown voltage at a pressure of 350 torr, a temperature of 60°C, and a gap distance of 2 cm is 30.66 kV. The answer is 30.66.
In nitrogen gas, the static breakdown voltage Vs of a uniform field gap may be expressed as:
Vs = A pd + B vpd
where A and B are constants, p is the gas pressure in torr referred to a temperature of 20°C and d is the gap length in cm. A 1 cm uniform field gap is nitrogen at 760 torr and 25°C is found to breakdown at a voltage of 33.3 kV.
The pressure is then reduced and after a period of stabilization, the temperature and pressure are measured as 30°C and 500 torr, respectively. The breakdown voltage is found to be reduced to 21.9 KV.
The voltage equation,
Vs = A pd + B vpd, may be rewritten as
Vs = p (Ad + Bvd)
where Ad and Bvd are the constant values.
Ad + Bvd is known as the Paschen product or the breakdown product.
Therefore, the Paschen product for nitrogen gas at 760 torr and 25°C can be determined using the given values as follows;
Paschen product = Ad + Bvd
= Vs / p
= 33.3 / 760
= 0.0439 KV/torr
From the information given, the temperature and pressure are reduced to 30°C and 500 torr, respectively, and the voltage drops to 21.9 kV. This is the result of a change in the Paschen product. A new Paschen product must be calculated before the voltage can be calculated.
The new Paschen product can be calculated using the new pressure and temperature values as follows;
New Paschen product = Ad + Bvd
= Vs / p
= 21.9 / 500
= 0.0438 KV/torr
Therefore, there is a slight reduction in the Paschen product. This is expected since the pressure has decreased, which would lead to an increase in the breakdown voltage. The new voltage can be calculated using the new Paschen product and the new gap length as follows;
New voltage = Paschen product x p x d
= 0.0438 x 350 x 2
= 30.66 KV
Therefore, the breakdown voltage at a pressure of 350 torr, a temperature of 60°C, and a gap distance of 2 cm is 30.66 kV. The answer is 30.66.
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A single-stage, single-cylinder compressor is rated at 425 m³/min (7.0833 m³/s) of air. Suction conditions are 101.325 kPa and 27 °C and compresses it to 1034 kPa. The compression follows PV1.35 = C. The Gas constant R for air = 0.287 kJ/kg-K. Determine the mass flow rate of air, m' = kg/s. 7.694 8.054 8.336 7.985
We can calculate the mass flow rate of air as,m = PAV/RT = P2 × A2 × V2 / R × T2 = 1034 × π / 4 × (0.25)^2 × 0.6284 / (0.287 × 300) = 8.054 kg/s Therefore, the mass flow rate of air is 8.054 kg/s.
Given,The volume flow rate of air is 7.0833 m³/sThe suction conditions are 101.325 kPa and 27 °C The air is compressed to 1034 kPa.The compression follows PV1.35
= C The Gas constant R for air
= 0.287 kJ/kg-K.To find, the mass flow rate of air, m'
= kg/s.The formula to calculate mass flow rate is:m
= PAV/RTWhere,P
= absolute pressure of the gasA
= cross-sectional area of the pipe V
= volume flow rate of the gasR
= gas constant of the gasT
= absolute temperature of the gas From the given data, we have,Initial Pressure P1
= 101.325 k Pa Final Pressure P2
= 1034 k Initial Temperature T1
= 27 °C
= 300 K Compression follows PV 1.35
= CSo, P1V1.35
= P2V2.35
=> V2
= (P1/P2)^{1/1.35} × V1
= (101.325/1034)^{1/1.35} × 7.0833
= 0.6284 m³/s. We can calculate the mass flow rate of air as,m
= PAV/RT
= P2 × A2 × V2 / R × T2
= 1034 × π / 4 × (0.25)^2 × 0.6284 / (0.287 × 300)
= 8.054 kg/s Therefore, the mass flow rate of air is 8.054 kg/s.
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An industrial load consumes 10 kW at a power factor of 0.80 lagging from a 240-V, 60- Hz, single phase source. A bank of capacitors is connected in parallel to the load to raise the power factor to 0.95 lagging. Find the current drawn from the source. Find the reactive power drawn from the source. Find the apparent power drawn from the source. Find the required reactive power in KVAR to raise the Power factor to 0.95 lagging. Find the required capacitance of the capacitor bank in uF.
An industrial load consumes 10 kW at a power factor of 0.80 lagging from a 240-V, 60- Hz, single phase source. the current drawn 33.33 A. reactive power is 6,000 VAR, apparent power is 10,000 VA, reactive power to raise the power is 1,250 VAR, and capacitor bank is approximately 28.96 μF.
Given:
Real power (P) = 10 kW = 10,000 W
Power factor before correction (pf) = 0.80
Voltage (V) = 240 V
Frequency (f) = 60 Hz
Power factor after correction (pfreq) = 0.95
Now one can substitute the given values into the formulas to find the required values:
Step 1:
P = S × pf
P = 10,000 W × 0.80
P = 8,000 W
Step 2:
S = P / pf
S = 8,000 W / 0.80
S = 10,000 VA
Step 3:
Q = √([tex]S^2[/tex] - [tex]P^2[/tex])
Q = √((10,000 VA[tex])^2[/tex] - (8,000 W[tex])^2[/tex])
Q ≈ 6,000 VAR
Step 4:
I = P / V
I = 8,000 W / 240 V
I ≈ 33.33 A
Step 5:
Qreq = P ×tan(acos(pf) - acos(pfreq))
Qreq = 8,000 W × tan(acos(0.80) - acos(0.95))
Qreq ≈ 1,250 VAR
Step 6:
C = Qreq / (2πf[tex]V^2[/tex])
C = 1,250 VAR / (2π × 60 Hz × (240 V[tex])^2[/tex])
C ≈ 28.96 μF (capacitance of the capacitor bank in uF.)
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The current in a 100 watt lightbulb is 0.880 A. The filament inside the bulb is 0.150 mm in diameter. You may want to review (Pages 750 - 752) Part A What is the current density in the filament? Express your answer to three significant figures and include the appropriate units. μA A ? Value Units Submit Previous Answers Request Answer X Incorrect; Try Again; 2 attempts remaining Part B What is the electron current in the filament? Express your answer using three significant figures.
The electron current in the filament is 1.41 μA.
Given values,
Current in a 100 W
light bulb = 0.880 A
Filament diameter = 0.150 mm
Let's determine the current density in the filament.
The current density in the filament is given by the relation;
J= I/A
Where,
J = Current density
I = Current flowing through the filament
A = Cross-sectional area of the filament
The area of the filament can be calculated by the formula for the area of a circle.
Area of the filament = πr²
Where r is the radius of the filament.
Radius of the filament = 0.150 mm / 2
= 0.075 mm
= 0.075 × 10^-3 m
Area of the filament = π(0.075 × 10^-3)²
= 1.7669 × 10^-8 m²
Now, the current density in the filament
J= I/A
= 0.880 A / 1.7669 × 10^-8 m²
= 4.9759 × 10^7 A/m²
Therefore, the current density in the filament is 4.98 × 10^7 A/m².
The electron current in the filament is given by the formula;
I = nAve
Where,
I = Current in the filament
n = Number of electrons passing through the filament per second
v = Drift velocity of electrons in the filament
A = Cross-sectional area of the filament
From Ohm's law,
V = IR
⇒ I = V/R
Since P = VI,
Power of the light bulb is 100 W,
V = IR, and
R = V/I100
= V × I,
V = 100/0.880
= 113.64
VE = V/N
where N is the energy per electron.
E = eV
where e is the electron charge.
E = (1.6 × 10^-19 C)(113.64 V)
= 1.818 × 10^-17 Jn
= P/E
= 100/1.818 × 10^-17
= 5.5 × 10^18 electrons/s
Electron current = nAve
= 5.5 × 10^18 (1.7669 × 10^-8) (113.64 × 1.6 × 10^-19)
= 1.41 × 10^-6 A
= 1.41 μA
Therefore, the electron current in the filament is 1.41 μA.
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The structural diversity of carbon-based molecules is based upon which of the following properties?
A. the ability of those bonds to rotate freely
B. the ability of carbon to form four covalent bonds
C. None of these choices is correct.
D. All of these choices are correct.
E. the orientation of those bonds in the form of a tetrahedron
The ability of carbon to form four covalent bonds: Carbon has four valence electrons, allowing it to form up to four covalent bonds with other atoms.
This versatility in bonding allows for the formation of complex and diverse carbon-based molecules.E. The orientation of those bonds in the form of a tetrahedron: Carbon atoms bonded to four different groups tend to adopt a tetrahedral geometry. This arrangement contributes to the three-dimensional shape and structural diversity of carbon-based molecules.Therefore, all of these choices contribute to the structural diversity of carbon-based molecules.
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When the switch on the left circuit is closed, a maximum EMF of
9V is induced in the right circuit
(b) If the number of turns in the left and right coils are both doubled, what is the maximum EMF induced in the right circuit when the switch is closed?
Therefore, if the number of turns in the left and right coils are both doubled, the maximum EMF induced in the right circuit when the switch is closed will be 18V.
(a)When the switch on the left circuit is closed, a maximum EMF of 9V is induced in the right circuit
EMF stands for Electromotive Force and is defined as the potential difference across the terminals of a cell when no current is flowing in the circuit. When the switch on the left circuit is closed, the circuit becomes complete and a maximum EMF of 9V is induced in the right circuit. This happens because the magnetic field lines of the left circuit cut across the coils of the right circuit and induce an EMF across it.
The EMF induced across the right circuit can be calculated using Faraday's law of electromagnetic induction which states that the EMF induced is directly proportional to the rate of change of magnetic flux through a surface. Mathematically, this can be expressed as: EMF = -dΦ/dt, where dΦ/dt is the rate of change of magnetic flux through a surface.
(b)If the number of turns in the left and right coils are both doubled, what is the maximum EMF induced in the right circuit when the switch is closed?
When the number of turns in the left and right coils are both doubled, the magnetic field strength of the left circuit also doubles. This is because the magnetic field strength is directly proportional to the number of turns of the coil. As a result, the rate of change of magnetic flux through the surface of the right circuit also doubles and hence, the EMF induced in the right circuit is also doubled.
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A force of 9 N is applied to an object. The moment arm for the force is 0. 21 m. What is the torque produced by the force?
The work done on the object by the applied force is 1500 J, and the power developed is 8000 W.
The torque produced by the force can be determined by multiplying the force by the moment arm. This can be represented using the formula:Torque = Force × Moment armGiven that a force of 9 N is applied to an object with a moment arm of 0.21 m, the torque produced by the force can be calculated as follows:Torque = 9 N × 0.21 m= 1.89 N·mTherefore, the torque produced by the force is 1.89 N·m.Answer in 200 words.Torque is the tendency of a force to rotate an object around an axis or pivot. The torque produced by a force is proportional to the force applied and the moment arm.The moment arm is the shortest distance between the line of action of the force and the axis of rotation. It is the perpendicular distance from the axis of rotation to the line of action of the force. The moment arm is an important factor in determining the torque produced by a force.A torque of 1 N·m is produced when a force of 1 N is applied perpendicular to a moment arm of 1 m. This is known as the moment of force or the turning effect of a force.The torque produced by a force is measured in newton-metres (N·m) in the SI system of units. In order to calculate the torque produced by a force, the magnitude of the force and the moment arm need to be known.The formula for calculating the torque produced by a force is:Torque = Force × Moment armWhere torque is measured in N·m, force is measured in newtons (N), and moment arm is measured in metres (m).
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A 25 cm x 25 cm circuit board uniformly dissipating 40 W of power is cooled by air, which
approaches the circuit board at 15°C with a velocity of 4 m/s. Disregarding any heat transfer
from the back surface of the board, determine the surface temperature of the electronic
components at the end of the board. Assume the flow to be turbulent since the electronic
components are expected to act as turbulators. Assume a film temperature of 30°C. Discuss the
validity of assumptions made to solve this problem. How does the analysis change if the film
temperature was initially assumed to be 80°C?
A higher film temperature would likely lead to a lower convective heat transfer rate and higher surface temperature for the electronic components at the end of the board.
To determine the surface temperature of the electronic components at the end of the circuit board, we can analyze the convective heat transfer between the board and the surrounding air.
Given the power dissipation (40 W), board dimensions (25 cm x 25 cm), air temperature (15°C), air velocity (4 m/s), and assuming a film temperature of 30°C, we can calculate the surface temperature.
First, we calculate the convective heat transfer coefficient (h) using empirical correlations for forced convection.
Once we have the heat transfer coefficient, we can apply Newton's law of cooling to calculate the surface temperature.
To validate the assumptions made:
Turbulent flow assumption: This assumption is reasonable since the electronic components act as turbulators, promoting turbulence in the air flow around the board.
Uniform power dissipation: Assuming uniform power dissipation across the board is common, especially if the dissipated power is evenly distributed.
If the film temperature was initially assumed to be 80°C instead of 30°C, it would affect the convective heat transfer coefficient.
Higher film temperatures usually result in lower heat transfer coefficients due to reduced temperature differences between the surface and the air.
Therefore, assuming a higher film temperature would likely lead to a lower convective heat transfer rate and higher surface temperature for the electronic components at the end of the board.
It is important to accurately estimate the film temperature to ensure accurate predictions of the surface temperature.
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A spherical balloon of volume 3.93 * 10 ^ 3 * c * m ^ 3 contains hellum at a pressure of 1.21 * 10 ^ 5 * g . How many moles of hellum are in the balloon if the average kinetic energy of the hellum atoms is 3.6 * 10 ^ - 22 J?
The number of moles of helium in the balloon is approximately 0.065 moles.
To calculate the number of moles of helium in the balloon, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Convert the given pressure to Pascals.
Given pressure = 1.21 * 10^5 g
1 g = 9.8 m/s^2 (acceleration due to gravity)
1 kg = 1000 g
1 Pascal = 1 Newton/m^2 = 1 kg/(m * s^2)
Converting the pressure to Pascals: 1.21 * 10^5 g * 9.8 m/s^2 * 1 kg/(1000 g) = 1.186 * 10^6 Pa
Convert the given volume to cubic meters.
Given volume = 3.93 * 10^3 cm^3
1 cm^3 = (1/100)^3 m^3 = 1/1,000,000 m^3
Converting the volume to cubic meters: 3.93 * 10^3 cm^3 * (1/1,000,000) m^3 = 3.93 * 10^3 * 10^-6 m^3 = 3.93 * 10^-3 m^3
Calculate the number of moles of helium.
R is the ideal gas constant, which is approximately 8.314 J/(mol * K).
The average kinetic energy of helium atoms (KE) is given as 3.6 * 10^-22 J.
The average kinetic energy of a gas particle is directly proportional to its temperature (T) in Kelvin. Therefore, we can equate KE = (3/2) * k * T, where k is the Boltzmann constant (1.38 * 10^-23 J/K).
From the equation, we have:
(3/2) * k * T = 3.6 * 10^-22 J
Solving for T: T = (3.6 * 10^-22 J) / [(3/2) * (1.38 * 10^-23 J/K)] = 8.695 K
Now we can rearrange the ideal gas law equation and solve for the number of moles:
n = PV / (RT)
n = (1.186 * 10^6 Pa) * (3.93 * 10^-3 m^3) / [(8.314 J/(mol * K)) * 8.695 K] ≈ 0.065 moles
Therefore, the number of moles of helium in the balloon is approximately 0.065 moles.
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Q No.2 Apply Voltage and Current Divider Formulae to find Vo
In a circuit, the voltage divider rule and current divider rule are frequently used to find the output voltage and current. These laws are extremely helpful in designing circuits, and they may be used in numerous scenarios.
The formula for the voltage divider rule is as follows:
V1 = Vt (R1 / R1 + R2)
V2 = Vt (R2 / R1 + R2)
Where Vt is the total voltage of the circuit.
The formula for the current divider rule is as follows:
I1 = It (R2 / R1 + R2)
I2 = It (R1 / R1 + R2)
Where It is the total current of the circuit.
In this circuit, we want to find the voltage Vo across resistor R3. To do this, we must first calculate the total resistance of the circuit:
RT = R1 + R2 + R3 || R4
RT = (R1 + R2) || (R3 + R4)
RT = (2kΩ + 1kΩ) || (4kΩ + 2kΩ)
RT = 1.33kΩ
Now that we know the total resistance of the circuit, we can use the voltage divider rule to find the voltage across resistor R3:
V3 = Vt (R3 / RT)
V3 = 12V (4kΩ / 1.33kΩ)
V3 = 36V
We can now use the current divider rule to find the current through resistor R3:
I3 = It (R4 / RT)
I3 = 3mA (2kΩ / 1.33kΩ)
I3 = 4.5mA
Finally, we can use Ohm's law to find the voltage Vo across resistor R3:
Vo = R3 I3
Vo = 4kΩ × 4.5mA
Vo = 18V
Therefore, the output voltage Vo across resistor R3 is 18V.
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You work as an electronic tech responsible for the maintenance and modification of a manufacturing line. Your company is experiencing quality problems on a line that assembles cabinets with magnets to hold the doors closed. Workers are having a high rate of not installing the magnets. Your job is to design a circuit that will sense when a magnet is missing on a cabinet and stop the conveyor line and turn on an LED that signals the defect. General Instructions: • Design the circuit simulation to operate with the Speed/Power Control panel on the left-hand side of the trainer and Discrete Sensor Panel on the right. • Use the Hall Effect sensor to sense the existence of the magnet. This is the only sensor that will sense a magnet. Use the motor on the Speed/Power Control Panel as the conveyor motor.
In order to design a circuit that senses when a magnet is missing on a cabinet and stops the conveyor line and turn on an LED that signals the defect, the circuit simulation must operate with the Speed/Power Control panel on the left-hand side of the trainer and Discrete Sensor Panel on the right, and the Hall Effect sensor must be used to sense the existence of the magnet.
This is the only sensor that will sense a magnet. The motor on the Speed/Power Control Panel must be used as the conveyor motor. Here is how the circuit can be designed:Step 1: Start by connecting a voltage source (VCC) to a resistor (R1) and then to the base of an NPN transistor (Q1). The collector of Q1 is then connected to the positive terminal of the motor and the emitter is connected to ground.Step 2: Connect the Hall Effect sensor to the same voltage source (VCC) and add a pull-up resistor (R2) to the output of the sensor. Connect the output of the sensor to a transistor (Q2) base.
The collector of Q2 is then connected to a second resistor (R3) and then to ground. The emitter of Q2 is connected to the base of Q1 and to an LED. Finally, connect the other end of the LED to ground. Step 3: Turn on the trainer and set the speed of the conveyor motor to the desired value. Place a magnet on a cabinet and run the conveyor to ensure that the magnet is detected and that the conveyor continues to run. Remove the magnet from the cabinet and run the conveyor to ensure that the motor stops and the LED turns on.
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(4) A transformer has 500 primary turns, the primary power & voltage are 480W and 120V (rms). (a) We want the secondary voltage to be 300 V (rms) how many secondary turns are needed? (b) What is the input current and output current (rms)?
The input current is 4 A (rms) and the output current is 10 A (rms).
a. The transformer has a ratio of primary to secondary voltage of 120 / 300 = 2 / 5.
The turns ratio will be the same as the voltage ratio, then:
N1 / N2 = 120 / 300N1 / N2 = 2 / 5N2
= (5/2) N1N2 = (5/2) * 500
= 1250 turns (rounded to the nearest integer).
Therefore, 1250 secondary turns are required.
b. The input power is equal to the output power since the transformer is ideal.
Then:Input power = Output power480 W = (120 V) (I1)I1 = 4 A (rms)
The turns ratio is equal to the ratio of the output to the input current.
Then:N1 / N2 = I2 / I1N1 / N2 = I2 / 4 AI2 = (N2 / N1) (4 A)I2 = (1250/500) (4 A)I2 = 10 A (rms)
Therefore, the input current is 4 A (rms) and the output current is 10 A (rms).
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In close analog to the half-lives of U-235 and U-238, let's say two 80 elements have half-lives of 4.5 billion years and 750 million years. If we start out having the same number of each (1:1 ratio), what will the ratio be after 4.5 billion years? Express as x:1, where x is the larger of the two.
The ratio of element B to element A after 4.5 billion years will be approximately 234:1.
Two 80 elements have half-lives of 4.5 billion years and 750 million years.
If we start out having the same number of each (1:1 ratio), the ratio after 4.5 billion years would be x:1, where x is the larger of the two.
The decay equation can be expressed as A = A₀ e^(-kt)where A₀ is the initial amount of the substance, A is the amount of substance left after time t,k is the rate constant of the decay process,t is the time in which the decay occurred.
In the given case, the two elements have the following half-lives: Element A has a half-life of 4.5 billion years, so kA = ln(2) / (4.5 billion)Element B has a half-life of 750 million years, so kB = ln(2) / (750 million)
Let the initial amount of both element A and element B be 1.
The amount of element A left after 4.5 billion years will be given as A = A₀ e^(-kA × 4.5 billion)
Similarly, the amount of element B left after 4.5 billion years will be given as B = A₀ e^(-kB × 4.5 billion)
So, the ratio of element B to element A will be B / A = e^(-kB × 4.5 billion) / e^(-kA × 4.5 billion)B / A = e^(-[kB - kA] × 4.5 billion)
Therefore, the ratio of element B to element A after 4.5 billion years will be x:1, where x is the larger of the two.
In other words, the larger amount of substance will be element B, since it has a shorter half-life.
The ratio will be given as: B / A = e^(-[kB - kA] × 4.5 billion)B / A = e^(-[ln(2) / (750 million) - ln(2) / (4.5 billion)] × 4.5 billion)B / A = e^(5.465)B / A = 234.05
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how much force is needed to accelerate a 29 kg block at 5.8 m/s2?
Explanation:
Use this equation:
F = m * a
F = 29 kg * 5.8 m/s^2 = 168.2 N
Given the standard form filter transfer function, below, calculate the corner frequency (Hz). Vo/V1 = 1+ ST Assume T= 12.02 ms Give your answer to 2 d.p.
The corner frequency (fc) of the given filter transfer function is approximately 83.19 Hz.
To calculate the corner frequency (fc) from the given transfer function, we need to determine the value of S at the corner frequency.
The standard form transfer function is Vo/V1 = 1 + ST, where T represents the time constant of the filter.
At the corner frequency (fc), the magnitude of the complex variable S is equal to 1/T. Therefore, we can equate S = 1/T and solve for fc.
Given T = 12.02 ms (milliseconds), we need to convert it to seconds by dividing by 1000:
T = 12.02 ms = 12.02 × [tex]10^{-3[/tex] s
Now, substitute T into the equation:
S = 1/T
S = 1 / (12.02 × [tex]10^{-3[/tex])
S = 83.194 Hz
Therefore, the corner frequency (fc) is approximately 83.19 Hz (rounded to 2 decimal places).
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Draw a diagram showing how current varies along a half-wavelength Hertz antenna anwarnthanteona
A half-wave Hertz antenna is one whose length is half that of the wavelength of the signal to be transmitted. Such an antenna is a resonant device that requires no matching network.
It provides a maximum radiation in the horizontal plane with a sharp vertical cutoff. To achieve such an antenna, the ratio of length to the wavelength of the signal must be equal to one-half. It is efficient and is capable of radiating energy in all directions equally.
Let's look at the diagram of how the current varies along a half-wavelength Hertz antenna:
An antenna is typically fed by an RF voltage. This RF voltage applied to the antenna terminals causes an RF current to flow in the antenna. As the RF current moves through the antenna, it produces the radiation that propagates into space.
The diagram shows the sinusoidal current that flows through the antenna. It's important to note that the current is zero at both ends of the antenna. The current reaches its maximum value at the center of the antenna, where the voltage is the highest.
The current in the antenna is sinusoidal, which means that the radiation pattern of the antenna is also sinusoidal. This radiation pattern has a maximum in the direction perpendicular to the antenna and a minimum in the direction parallel to the antenna.
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Review Concept Simulation 9.2 and Conceptual Example 7 as background material for this problem. A jet transport has a weight of 1.32 x 106 N and is at rest on the runway. The two rear wheels are 15.0 m behind the front wheel, and the plane's center of gravity is 12.7 m behind the front wheel. Determine the normal force exerted by the ground on (a) the front wheel and on (b) each of the two rear wheels.
We know that force is mass times acceleration, i.e. F = ma. In this case, we know that the force is weight, and since the aircraft is stationary, we know that the acceleration is zero.
Thus:
F = ma = 0, where F = weight of the aircraft = 1.32 x 106 N (given)
Since the aircraft is stationary, the force acting downwards on the wheels by the ground is equal to the force acting upwards on the wheels by the aircraft.
For the front wheel, the force is:
Ffront = weight of the aircraft x (distance between the rear wheels/total distance from the front wheel to the center of gravity)
Ffront =[tex]20 √3/2 × 10= 100√3 m[/tex]
Ffront = 623680.79 N
Each of the two rear wheels carries an equal weight, i.e. half of the total weight of the aircraft. The force on each rear wheel is:
Frear = weight of half the aircraft x (distance from the front wheel to the center of gravity/total distance from the front wheel to the center of gravity)
Frear = [tex](1.32 x 106 N / 2) x (12.7 m / (12.7 m + 15 m))[/tex]
Frear = 347052.55 N
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while a variety of factors can produce redshifts in the spectrum, the one associated with the expansion of the universe is called:\
The one associated with the expansion of the universe is called cosmological redshift.
Cosmological redshift is the increase in the wavelength of photons as they travel through space due to the expansion of the universe. This redshift occurs as the universe expands, causing the galaxies and other celestial objects to move away from each other.
The term redshift refers to the fact that as light moves away from us, its wavelength becomes longer, and it appears redder. The amount of redshift observed for distant galaxies is directly proportional to their distance from us and is due to the expansion of the universe.
Cosmological redshift is caused by the expansion of the universe and is one of the most important discoveries of modern cosmology. It provides evidence that the universe is expanding and has been doing so for billions of years.
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The angular position of a point on a rotating wheel is given by theta = 7.85t * 2.85t ^ 2 + 1.77t ^ 3 where is in radians and t is in seconds. At t = 0, what are (a) the point's angular position and (b) its angular velocity? (c) What is its angular velocity at t = 6.29s ? (d) Calculate its angular acceleration at t=2.13 s.(e) its angular acceleration constant?
Therefore, the point's angular acceleration when t = 2.13s is 99.589 rad/s2.(e) Angular acceleration constantSince the angular acceleration is not constant, the question of angular acceleration constant does not apply.
Given equation: $$\theta = 7.85t * 2.85t^2 + 1.77t^3$$where $\theta$ is in radians and t is in seconds.(a) The point's angular position when t = 0.Substitute t = 0 in the above equation,$$\theta = 7.85(0) * 2.85(0)^2 + 1.77(0)^3$$$\theta = 0$ radians(b) The point's angular velocityTo find the angular velocity, differentiate the equation with respect to time.$$ \begin{aligned} \frac{d\theta}{dt} &= \frac{d}{dt}(7.85t * 2.85t^2 + 1.77t^3) \\ &= 7.85 * 2.85t^2 + 7.08t^2 \\ &= 7.08t^2(1 + 2.85) \\ &= 23.352t^2 \end{aligned} $$Substitute t = 0 to find the point's angular velocity at t = 0.$$ \begin{aligned} \frac{d\theta}{dt} &= 23.352t^2 \\ &= 23.352(0)^2 \\ &= 0 \end{aligned} $$Therefore, the point's angular velocity when t = 0 is zero.(c) The point's angular velocity when t = 6.29sSubstitute t = 6.29 in the equation for angular velocity.$$ \begin{aligned} \frac{d\theta}{dt} &= 23.352t^2 \\ &= 23.352(6.29)^2 \\ &= 926.089 \ rad/s \end{aligned} $$Therefore, the point's angular velocity at t = 6.29s is 926.089 rad/s.(d) The point's angular acceleration when t = 2.13sTo find the angular acceleration, differentiate the angular velocity with respect to time.$$ \begin{aligned} \frac{d^2\theta}{dt^2} &= \frac{d}{dt}(23.352t^2) \\ &= 46.704t \\ &= 46.704(2.13) \\ &= 99.589 \ rad/s^2 \end{aligned} $$
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A proton travels along the x-axis through an electric potential V=(250 V/m)x. Its speed is 3.5×10 5
m/s, as it passes the origin, moving in What is the proton's speed at x=1.0 m ? the +x-direction. Express your answer with the appropriate units.
The proton's speed at x = 1.0 m is approximately 3.499 × 10⁵ m/s. This is based on the given electric potential V = (250 V/m)x and the initial speed of the proton at the origin of 3.5 × 10⁵ m/s.
The electric potential is given by V = (250 V/m)x, which means the electric potential increases linearly with x along the x-axis. Since the proton is moving in the +x-direction, its potential energy (PE) is decreasing as it moves away from the origin.
The change in potential energy (ΔPE) can be calculated by multiplying the electric potential (V) by the displacement (Δx) from the origin to x = 1.0 m:
ΔPE = V * Δx
Δx = 1.0 m (given)
Substituting the given electric potential:
ΔPE = (250 V/m) * (1.0 m)
ΔPE = 250 V
The change in potential energy (ΔPE) is equal to the change in kinetic energy (ΔKE) for a conservative force field.
Therefore, we can equate the change in potential energy to the change in kinetic energy:
ΔKE = ΔPE
The change in kinetic energy (ΔKE) is given by:
ΔKE = (1/2) * m * (v² - u²)
Where m is the mass of the proton, v is the final speed at x = 1.0 m, and u is the initial speed at the origin (3.5 × 10⁵ m/s).
Substituting the values:
ΔKE = (1/2) * m * (v² - (3.5 × 10⁵ m/s)²)
Since the proton is positively charged, its potential energy is decreasing, which means its kinetic energy is increasing.
Therefore, the change in kinetic energy is positive, and we can write:
ΔKE = -ΔPE
Substituting the values:
(1/2) * m * (v² - (3.5 × 10⁵ m/s)²) = -250 V
Simplifying the equation, we find:
(v² - (3.5 × 10⁵ m/s)²) = -500 V / m * (2 / m)
(v² - (3.5 × 10⁵ m/s)²) = -1000 V / m
Now, to find the speed (v) at x = 1.0 m, we solve for v:
v² = (3.5 × 10⁵ m/s)² - 1000 V / m
v = √((3.5 × 10⁵ m/s)² - 1000 V / m)
Calculating the value, we find:
v ≈ 3.499 × 10⁵m/s
Therefore, the proton's speed at x = 1.0 m is approximately 3.499 × 10⁵ m/s.
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(6 marks) Q2) Design a Low pass filter with cut frequency of \( 10 \mathrm{KHz} \)
The low-pass filter is designed using the resistance of 10kΩ and capacitance of 15.9nF.
A Low Pass Filter (LPF) allows low-frequency signals to pass through while blocking high-frequency signals. The cut-off frequency, also known as the -3dB point, is the frequency at which the amplitude of the signal is reduced by 50% of its original value. This 50% value is also known as the power level. The cut-off frequency of a filter is the point where the filter transitions from a passband to a stopband.
For a low-pass filter with a cutoff frequency of 10kHz, the following is the design:
Let C be the capacitance value, and R be the resistance value. The cutoff frequency (f_c) formula for a first-order low-pass filter is:
f_c = 1/(2πRC)
We can rearrange this formula to solve for either R or C. Assume R = 10kΩ, then
C = 1/(2πf_cR)
= 1/(2π × 10 × 10³)
= 1/(62.83 × 10³)
= 15.9nF (approximately)
Thus, the low-pass filter is designed using the resistance of 10kΩ and capacitance of 15.9nF.
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10. A woman is draining her fish tank by siphoning the water into an outdoor drain as shown in the figure. The rectangular tank has dimensions / 1 m, w = 0.5 m, and / = 0.5 m. The drain is located a distanced = 4 m below the surface of the water in the tank. The cross sectional area of the siphon tube is 1 cm? Model the water as flowing without friction, How long does it take to completely empty the fish tank?
It takes about 2.82 seconds to completely empty the fish tank.
The volume of water in the tank is given by:
V = lwh = (1 m)(0.5 m)(0.5 m) = 0.25 m³
The cross-sectional area of the siphon tube is 1 cm², and since there is no friction, Bernoulli's principle is used to find the speed of the water as it flows through the siphon tube.
ρgh = 1/2ρv²v = sqrt(2gh)whereρ is the density of water, g is the acceleration due to gravity, h is the distance between the surface of the water in the tank and the drain, and v is the speed of the water as it flows through the siphon tube.
v = sqrt(2 × 9.81 m/s² × 4 m) = 8.85 m/sThe volume of water that flows through the siphon tube per second is given by: Q = where A is the cross-sectional area of the siphon tube and v is the speed of the water as it flows through the tube. Q = (1 cm²)(8.85 m/s) = 0.0885 m³/sThe time taken to completely empty the tank is therefore given by:
T = V/Q = 0.25 m³/0.0885 m³/s = 2.82 s.
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