The mathematical expression for i in terms of v, f, and λ is: i = (n₂/n₁)vf. The relationship between the velocity, frequency, and wavelength of a wave is given by the equation: v = fλ
where v is the velocity, f is the frequency, and λ is the wavelength. This equation relates the physical properties of a wave, such as how fast it is moving (velocity), how often it repeats (frequency), and how far apart its peaks and troughs are (wavelength).
When light travels between different media, such as from air to water, the velocity of the wave changes. However, the frequency remains constant. This means that the wavelength must also change to maintain the relationship given by the equation above.
To solve for the velocity in each medium, we can use the expression:
v = fλ
For medium I, we have:
v₁ = f₁λ₁
For medium 2, we have:
v₂ = f₂λ₂
To find an expression for i in terms of v, f, and λ, we can use Snell's law, which relates the angles and velocities of light waves as they pass through different media. Snell's law is:
n₁sinθ₁ = n₁sinθ₂
where n₁ and n₂ are the refractive indices of the two media, and θ1 and θ₂ are the angles of incidence and refraction, respectively.
We can rewrite Snell's law in terms of the velocities of the waves:
v₁sinθ1₁= v₂sinθ₂
Since the frequency remains constant, we can write:
f₁ = f₂
and
λ₁ = λ₂
Substituting these into the equation above, we get:
v₁sinθ₁ = v₂sinθ₂
Dividing both sides by v₂ and rearranging, we get:
sinθ₂ = (v₁/v₂)sinθ₁
We can use this equation to find the angle of refraction θ₂, and then use the relationship between angles and wavelengths (θ = λ/d, where d is the distance between two slits or other such object), to find the wavelength in medium 2:
λ₂ = λ1(n₂/n₁)
Substituting this into the equation for v₂ above, we get:
v₂ = f₂λ₂
= f₂λ₁(n₂/n₁)
= (n₂/n1)v₁
= (n₂/n₁)vf
where we have used the fact that f₁ = f₂ = f and λ₁ = λ₂ = λ.
Therefore, the mathematical expression for i in terms of v, f, and λ is:
i = (n₂/n₁)vf
This equation shows how the index of refraction of a medium affects the velocity of light waves passing through it, and how this, in turn, affects the wavelength of the waves. It is an important equation in optics and is used in many applications, such as designing lenses and optical fibers.
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State which type of variable is plotted on the x-axis
and which type is plotted on the y-axis.
Answer:
Often the independent variable is plotted on the x-axis - and example might be time (an experiment where time is measured by a watch or an independent mechanical device)
The dependent variable is often plotted on the y-axis - and example here might be the velocity or the acceleration,
It may be the responsibility of the experimenter to determine the value of the dependent variable by some type of measurement
When you're super tired and you lose energy, what energy are you actually losing?
I said Physics class, but it's really for Science class.
Answer:
it is chemical energy
Explanation:
that is the energy used by our body, so it is the one that we will loose. and the energy that we gain is also chemical energy
what does the presence of molecular bands in the spectrum of a star indicate?
The presence of molecular bands in the spectrum of a star indicates the chemical composition of its atmosphere.
The spectrum of a star is a graph that shows the intensity of light emitted by the star at different wavelengths. When this light passes through the star's atmosphere, it interacts with the gases and elements present there. This interaction creates absorption lines and bands in the spectrum, which can be used to determine the chemical composition of the star's atmosphere.
Molecular bands in the spectrum indicate the presence of molecules in the star's atmosphere, such as hydrogen, helium, water vapor, carbon dioxide, and methane.
By analyzing the spectrum of a star, astronomers can determine its chemical composition and gain insights into its properties, such as its temperature, density, and age.
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Question 5
5. What subatomic particle has no electrical charge?
•neutron
•proton
•electron
•atom
Answer: A Neutron.
I know this is correct. Thank's and yw :3
PLEASE HELP QUICK!!!!!!
The top: Deposition, compaction, and cementation. The right: The heat and pressure.
The bottom Right: Melting.
The bottom left: Cooling.
The top left: Weathering and erosion.
How can we find velocity?*
Answer: discplacement/change in time = average velocity.
Explanation:
There is a formula for velocity which is given above
When static electricity is created with the balloon, what happens when the charges try to move back together?
When static electricity is created with a balloon, it involves the separation of electric charges. This occurs when the balloon rubs against another object, such as hair or clothing, causing the transfer of electrons. The rubbing action causes electrons to be transferred from one object to the other, resulting in a buildup of positive charges on one object and negative charges on the other.
In the case of a balloon being rubbed against hair, for example, the balloon becomes negatively charged (excess electrons) while the hair becomes positively charged (deficit of electrons). These opposite charges create an electric field between the balloon and the hair, causing an attraction between them.
When the charges try to move back together, they are essentially trying to neutralize the separation of charges and restore electrical balance. In this case, the excess electrons on the balloon and the deficit of electrons on the hair want to redistribute and reach a state of equilibrium.
The movement of charges back together can occur through various mechanisms, such as:
1. Discharge: If the pathway for charges to flow between the objects is available, such as through a conductor, the excess electrons on the balloon can flow towards the hair, neutralizing the charges. This discharge can result in a small electric shock or spark.
2. Induction: The charges can also redistribute through the process of induction, where the electric field of the charged balloon induces opposite charges in the hair without direct contact. This can cause the hair strands to be attracted to the balloon, as they acquire a slight positive charge.
In either case, the charges will move back together until the separation is minimized or eliminated. The movement of charges is driven by the principle of electrical attraction and the tendency to reach a state of electrical balance.
It is important to note that the movement of charges back together is a temporary phenomenon in the case of static electricity. Once the charges have neutralized, the objects will no longer exhibit static electricity unless another separation of charges occurs through rubbing or other mechanisms.
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How many total molecules are present in the formula below
2H2O
I'm guessing 6.
the coefficient of two turns our hydrogen into 4 and our oxygen into 2 which makes a total of 6 molecules.
A 40 kg skater is skating on frictionless ice at 20m/s and crashes into a 350 kg bear on the same ice. As a result the skater is now moving at 5 m/s. What will you see if you watch the bear, will it be moving? How fast? Use math to explain
Answer: 0.01143 m/s
Explanation:
use conservation of momentum, since momentum is always conserved. assume left of = is initial, to the right if final
m1v1=m1v1 + m2v2
(40)(20)=(40)(5) + (350)(v2)
solve for v2 (denoting velocity of bear)
yes, the bear will be moving, at a speed of 0.011428571 (round how you like)
A kid pushes a stationary
merry-go-round, creating an
acceleration of 0.135 rad/s^2.
How much time does it take the
merry-go-round to complete
2.00 rotations?
(Unit = s)
Remember: CCW is +, CW is. 1 rev= 2*pi rad
The merry-go-round takes approximately 29.41 seconds to complete 2.00 rotations.
Given data:
Acceleration (α) = 0.135 rad/\(s^2\)
Number of rotations (θ) = 2.00
To find the time taken (t) for 2.00 rotations, we need to use the formula:
θ = 0.5 * α * \(t^2\)
Rearranging the formula, we get:
\(t^2\) = (2 * θ) / α
Plugging in the given values, we have:
\(t^2\) = (2 * 2.00) / 0.135
\(t^2\) = 29.63
Taking the square root of both sides, we find:
t ≈ √29.63
t ≈ 5.439
Therefore, the time taken for the merry-go-round to complete 2.00 rotations is approximately 5.439 seconds.
Note: It's important to round the final answer to an appropriate number of significant figures, considering the given data. In this case, we have used four significant figures in the final answer.
However, if we want to adhere to the given significant figures in the acceleration (0.135 rad/\(s^2\)), the answer should be rounded to three significant figures. In that case, the final answer would be approximately 5.44 seconds.
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Can the sum of two vectors be longer than the total length of both vectors? explain.
No, the sum of two vectors cannot be longer than the total length of both vectors.
In vector addition, the resultant vector is obtained by placing the vectors head-to-tail and drawing a line from the tail of the first vector to the head of the second vector. This resultant vector represents the sum of the two vectors.
According to the triangle inequality, the length of the sum vector (resultant) must be less than or equal to the sum of the lengths of the individual vectors.
This inequality arises from the fact that the sum of two sides of a triangle must be greater than or equal to the length of the remaining side.
If the sum of the vectors were longer than the total length of both vectors, it would violate this fundamental geometric principle.
Therefore, it is not possible for the sum of two vectors to be longer than the total length of both vectors.
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the average no-load voltage in a dc arc welding circuit is ____ volts. 10–20 15–30 60–80 15–40
The average no-load voltage in a DC arc welding circuit is typically in the range of 60-80 volts.
What is arc welding?Arc welding is a welding technique that uses an electric arc to melt the base metal and fusing it with the filler metal to create a weld. The welding machine supplies an electric current to a consumable electrode or filler wire to melt the metals, forming a weld pool. The two metals fuse when the weld cools down. The weld is as strong as the base metal and can be used to construct everything from automobile components to skyscrapers.
What is the no-load voltage?In a welding circuit, the no-load voltage is the voltage between the welding electrode and the workpiece before a welding arc is struck. Before the start of a welding operation, the circuit is energized and, as a result, the welding machine produces an open circuit voltage. It is also known as the no-load voltage, which is the voltage measured at the output terminals of the welding machine when the welding arc is inactive and the electrode is not in contact with the workpiece.
The average no-load voltage in a DC arc welding circuit is typically around 60-80 volts. This voltage range is necessary to establish and maintain an electric arc between the welding electrode and the workpiece, enabling the welding process to occur efficiently.
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What value of resistor R gives the circuit in the figure a time constant of 22 μs ?
The value of resistor R that gives the circuit in the figure a time constant of 22 μs is 220 Ω.
The circuit that is in the figure is shown below:Given that time constant (RC) = 22 μs. To find the value of resistor R, we need to use the formula for the time constant:
RC = τ, where R is the resistance and C is the capacitance of the circuit.
Rearranging the above formula, we get:R = τ / C
Where τ is the time constant and C is the capacitance of the circuit.
From the figure, the capacitance is given as 0.1 μF
.Substituting the values of τ and C in the above formula, we get:
R = (22 × 10⁻⁶ s) / (0.1 × 10⁻⁶ F)
R = 220 Ω
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The potential energy of an apple is 6.0 Joules. The apple is 1.22m high. What is the mass of the apple?
Answer:
The mass of the apple is 0.49kg
Explanation:
Potential energy=mgh
P=mgh
6=m×1.22×10
6=12.2m
divide both sides by 12.2
m=6/12.2
m=0.49kg
find the mass and center of mass of the solid e with the given density function . e is bounded by the parabolic cylinder z = 1 − y2 and the planes x 5z = 5, x = 0, and z = 0; (x, y, z) = 7.
The mass of E is 28/3, and the center of mass is located at (35/36, 0, 7/4).
We can use the triple integral to find the mass and center of mass of the solid E:
The limits of integration for x are from 0 to 5z.
The limits of integration for y are from −1 to 1.
The limits of integration for z are from 0 to 1 − y²
The density function is given by ρ(x, y, z) = 7.
Thus, the mass of E is given by:
M = ∭E ρ(x, y, z) dV
= ∭E 7 dV
= ∫₀⁵z ∫₁⁻¹ ∫₀¹−y² 7 dz dy dx
= 28/3
The x-coordinate of the center of mass is given by:
x-bar = (1/M) ∭E xρ(x, y, z) dV
= (1/M) ∭E x(7) dV
= (1/M) ∫₀⁵z ∫₋₁¹ ∫₀¹−y² x(7) dz dy dx
= 35/36
Similarly, the y-coordinate of the center of mass is given by:
y-bar = (1/M) ∭E yρ(x, y, z) dV
= (1/M) ∭E y(7) dV
= (1/M) ∫₀⁵z ∫₋₁¹ ∫₀¹−y² y(7) dz dy dx
= 0
And, the z-coordinate of the center of mass is given by:
z-bar = (1/M) ∭E zρ(x, y, z) dV
= (1/M) ∭E z(7) dV
= (1/M) ∫0^5z ∫−1^1 ∫0^1−y^2 z(7) dz dy dx
= 7/4
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As a supplement to some diets, iron is consumed in tablet form. The mass of iron in these tablets is often measured in?
On the graph of voltage versus current, which line represents a 2.0 resistor?
Answer:
answer is B
Explanation:
Acc. to Ohm's Law:
V = I.R and therefore R=( V/I )
For line A, R = 6/2 = 3
line B, R = 4/2 = 2 ( for all the points plotted on this line the ratio of V and I is 2)
Line C = 2/2 = 1
Line D < 1
Hence, the correct answer is Line B :-)
"the amount of contextual similarity between the retrieval attempt and the initial encoding phase, predicts the likelihood of remembering versus forgetting." what does this statement refer to?
The amount of contextual similarity between the retrieval attempt and the initial encoding phase predicts likelihood of remembering versus forgetting. This refers to the encoding specificity hypothesis
The likelihood of remembering versus forgetting is predicted by the degree of contextual similarity between the retrieval attempt and the initial encoding phase. Encoding specificity hypothesis is being discussed here. According to the encoding specificity theory, the similarity between the contexts during the initial encoding phase and the attempt at retrieval affects how likely it is that information will be remembered.
This theory states that memory retrieval is more successful when the environmental context or retrieval cues coincide with or are similar to those present during the encoding of the material. This idea emphasises the value of environmental signals in aiding memory retrieval and determining whether or not information will likely be remembered or forgotten.
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A hair dryer draws 11 A when it is connected to 120 V. If electrical energy costs $ 0.09/kW·h, what is the cost of using the hair dryer for exactly 15 min?
Free brainliest, i was planning on answering this myself anyway.
Answer: $0.3
Explanation:
Operating Cost ($) = Energy Use (kWh) x Electric Rate
1. convert Amps to watts
11 x 120= 1320
2. convert watts to kilowatts
1320/1000=1.32
3. convert the time to hours
15/60=0.25
4. Multiply the time and the kilowatts
0.25 x 1.32= 0.33kWh
5. find the cost
0.9 x 0.33= $0.297
Answer:
The cost of using the hair dryer for 15 minutes is \(\$3.6\bar 6\)
Explanation:
The parameters given in the question are;
The electric current drawn by the the air dryer, I = 11 A
The voltage to which the hair dryer is connected, V = 120 V
The duration of usage of the hair dryer = 15 minutes = 60 minutes /4 = 1 hour/4 = 0.25 hour
The electrical energy costs $0.09/kW·h
The power consumed by the hair dryer = I × V = 11 × 120 = 1320 Watts = 1.32 kW
The energy used by the hair dryer in 15 minutes (0.25 hour) = 1.32 × 0.25 0.33 kW·h
The energy used by the hair dryer in 15 minutes (0.25 hour) = 0.33 kW·h
The energy cost = $0.09/(kW·h)
Therefore;
The cost of using the hair dryer for 15 minutes (0.25 hour) = 0.33 kW·h/($0.09/(kW·h)) = $33/9 = $3 2/3 = $3.6\(\bar 6\).
Which quantities are equal in a dynamic equilibrium?.
The quantities that are equal in a dynamic equilibrium include the rates of the forward and reverse reactions, as well as the concentrations of the reactants and products.
A dynamic equilibrium is defined as a situation in which the forward and reverse rates of a reaction are equal and the concentrations of the reactants and products remain constant. It is a state in which there is no further net change in the concentration of the reactants and products.
In a dynamic equilibrium, the rate of the forward reaction is equal to the rate of the reverse reaction. The concentrations of the reactants and products may not be the same numerical value, but their ratios are constant at equilibrium.
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A 10 kg wagon is accelerated by a constant force of 60 N from an initial velocity of 5.0 m/s to a final velocity of 11 m/s. What is the impulse received by the wagon? a)15 N s b)60 N s c)17 N s d)70 N s
An object is traveling at a constant velocity of 10 m/s when it experiences a constant acceleration of 3.5 m/s2 for a time of 10 s. What will its velocity be after that acceleration?
Answer:
The final velocity of the object is 45 m/s.
Explanation:
Given;
initial velocity of the object, u = 10 m/s
acceleration of the object, a = 3.5 m/s²
time of motion, t = 10 s
The final velocity of the object is given as;
v = u + at
where;
v is the final velocity of the object
v = 10 + (3.5 x 10)
v = 45 m/s
Therefore, the final velocity of the object is 45 m/s.
How can you make the potential energy as high as possible in a magnetic field between one electromagnet and one piece of iron?
In step 1, to increase the potential energy, the iron will move towards the electromagnet.
In step 2, to increase the potential energy, the iron will move towards the electromagnet.Potential energy of a system of magnetic dipoleThe potential energy of a system of dipole depends on the orientation of the dipole in the magnetic field.
\(U = \mu B\)
where;
\(\mu\) is the dipole momentB is the magnetic field\(B = \frac{\mu_0 I}{2\pi r}\)
\(U = \mu\times (\frac{\mu_0 I}{2\pi r} )\)
Increase in the distance (r) reduces the potential energy. Thus, we can conclude the following;
In step 1, to increase the potential energy, the iron will move towards the electromagnet.In step 2, when the iron is rotated 180, it will still maintain the original position, to increase the potential energy, the iron will move towards the electromagnet.Learn more about potential energy in magnetic field here: https://brainly.com/question/14383738
What are five atomic models that have been proposed over time ?
two iron bars attract each other no matter which ends are placed close together are both magnets? explain
When two iron bars attract each other no matter which ends are placed close together, both are not magnets. Rather, both iron bars are ferromagnetic substances.
Iron and its alloys, cobalt, nickel, and some other rare-earth metals are ferromagnetic substances that can become magnetic when exposed to a magnetic field. To create a magnet, these substances can be magnetized by placing them in a magnetic field. Magnets also possess magnetic forces, which can be observed when two magnets are placed near to each other.
Magnets are substances that have the ability to produce a magnetic field around themselves. Magnets have north (N) and south (S) poles that are oppositely charged. Opposite poles (N-S) attract, whereas like poles (N-N, S-S) repel.
When two iron bars are brought close to each other, they will attract one other because both bars will experience opposite magnetic fields, causing a magnetic attraction.
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LITERALLY HELP IMBEGGING YOU GUYS ANYONE IM NEEED HELP
Explanation:
The energy of a photon is given by :
\(E=\dfrac{hc}{\lambda}\)
Where
h is Planck's constant
c is the speed of light
\(\lambda\) is wavelength
or
\(E=hf\), f is the frequency
Energy is directly proportional to the frequency of an object.
The energy transported by a wave is directly proportional to the square of the amplitude.
5. The speed of the ostrich is 1.2 km/min, the speed of the dolphin is 72 km/ h, and the speed of the swallow is 17 m/s. Compare their speeds and find out which one is the fastest.helppp plsss
The ostrich and dolphin are tied for the fastest, with a speed of 20 m/s, while the swallow is slower with a speed of 17 m/s.
Speed of a moving objectTo compare the speeds of the ostrich, dolphin, and swallow, we need to convert their speeds to the same units. Let's convert all speeds to meters per second (m/s):
Ostrich speed = 1.2 km/min = (1.2 km/min) x (1000 m/km) / (60 s/min) = 20 m/sDolphin speed = 72 km/h = (72 km/h) x (1000 m/km) / (3600 s/h) = 20 m/sSwallow speed = 17 m/s (already in m/s)Now that we have all speeds in the same units, we can compare them directly. We can see that both the ostrich and dolphin have a speed of 20 m/s, while the swallow has a speed of 17 m/s.
Therefore, the ostrich and dolphin are tied for the fastest, with a speed of 20 m/s, while the swallow is slower with a speed of 17 m/s.
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Following a lecture on transverse and longitudinal waves, four students make venn diagrams to characterize these waves. which venn diagram is correct? a venn diagram with two intersecting circles. the circle on the left is labeled transverse waves with entries light, can travel through a vacuum, vibrating string, created by a disturbance and medium motion is perpendicular. the circle on the right is labeled longitudinal waves with entries medium motion is parallel, has regions of high and low density, sound and travel faster in a denser medium. the overlapping region has entries has speed and travels through solids. a venn diagram with two intersecting circles. the circle on the left is labeled transverse waves with entries light, can travel through a vacuum, vibrating string and medium motion is perpendicular. the circle on the right is labeled longitudinal waves with entries medium motion is parallel, has regions of high and low density, sound and travel faster in a denser medium. the overlapping region has entries, created by a disturbance, has speed and travels through solids. a venn diagram with two intersecting circles. the circle on the left is labeled transverse waves with entries light, all parts of the electromagnetic spectrum, vibrating string, medium motion is perpendicular. the circle on the right is labeled longitudinal waves with entries medium motion is parallel, has regions of high and low density, sound and can travel through a vacuum. the overlapping region has entries, created by a disturbance, has speed and travels through solids. a venn diagram with two intersecting circles. the circle on the left is labeled transverse waves with entries light, can travel through a vacuum, vibrating string and medium motion is perpendicular. the circle on the right is labeled longitudinal waves with entries medium motion is parallel, has regions of high and low density, all parts of the electromagnetic spectrum and travel faster in a denser medium. the overlapping region has entries, created by a disturban
Venn diagram B is correct. A Venn diagram is a type of graph that uses circles to depict connections between objects or fixed groups of entities.
What Is a Venn Diagram and how does It Work?A Venn diagram is a diagram that uses circles to depict relationships between objects or finite groups of objects. Circles that overlap share characteristics, whereas circles that do not overlap do not.
A Venn diagram with two intersecting circles. the circle on the left is labeled transverse waves with entries light, can travel through a vacuum, vibrating string and medium motion is perpendicular.
The circle on the right is labeled longitudinal waves with entries medium motion is parallel, has regions of high and low density, sound and travel faster in a denser medium.
The overlapping region has entries, created by a disturbance, has speed, and travels through solids.
Hence Venn diagram B is correct
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Determine the maximum constant speed at which the pilot can travel around the vertical curve having a radius of curvature p = 800 m, so that he experiences a maximum acceleration an = 8g = 78.5 m/s2. If he has a mass of 70 kg, determine the normal force he exerts on the seat of the airplane when the plane is traveling at this speed and is at its lowest point.
The maximum constant speed at which the pilot can travel around the vertical curve with a radius of curvature of
p = 800 m so that he experiences a maximum acceleration of
an = 8g = 78.5 m/s2 is 89.4 m/s.
Given data:
Radius of curvature p = 800 m
Maximum acceleration an = 8g = 78.5 m/s²
Mass of the pilot m = 70 kg
Maximum speed v for the plane is given as follows:
an = (v²) / pm
g = (v²) / p78.5 m/s²
= (v²) / (800 m)
where v is the velocity and an is the maximum acceleration Let's solve the above equation for v to determine the maximum constant speed:
v² = 78.5 m/s² × 800
mv² = 62800
v = √62800
v = 250.96 m/s
The pilot can travel at a maximum speed of 250.96 m/s
to experience a maximum acceleration of 8g if we consider the theory of relativistic mass increasing with speed.
So we need to lower the speed to achieve 8g.
For a safe speed, let's take 80% of the maximum speed; 80% of 250.96 m/s = 200.768 m/s
Therefore, the maximum constant speed that the pilot can travel around the vertical curve having a radius of curvature p = 800 m,
so that he experiences a maximum acceleration an = 8g = 78.5 m/s2, is 200.768 m/s.
When the plane is traveling at this speed and is at its lowest point, the normal force he exerts on the seat of the airplane is;
N = m(g + an)
Here, m = 70 kg, g = 9.81 m/s²,
and an = 78.5 m/s²
N = (70 kg)(9.81 m/s² + 78.5 m/s²)
N = 5662.7 N (approx)
Therefore, the normal force the pilot exerts on the seat of the airplane when the plane is traveling at the maximum constant speed and is at its lowest point is 5662.7 N.
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please fast
The system shown in the figure below uses three chain comveyors. Each chain has a hydraulic motor: The torque that drives the motors is T: =1500 N.m
1 T2 =700 Nm and, T3 = 300Nm. The displactment volume of the motors is V01 =1000 cm3/rev V02 =1000 cm3/rev and, V09 =500 cm3 /rex. The motss have a volumetric efficiency of 0.9 and an overall efficiency of 0.85. The leakage of the bydraulic motors 1 and 3 is internal completely and the leakage of the hydraulic motor 2 is external completely. The pump produces a constant volumetric flow rate of 6.3U/min.
The orifice of the flow control valve has a 0.5 mm diameter. The pressure fosses through the pipes are neglected. The capacity coefficient of the needie valve is 07. The volumetric Alow rate through the needle valve is given by: Q=C×A2 ×ΔF/rho where C is the capacity coefficient, A is the area of the orifice, ΔP is the difference of pressure through the needle valve and, rho is the density of the fiuid.
The density of the oil used in the hydraulic system is 860 kg/m3 . Determine the rotational speed of the motor 3 in rpm. a. 8 b. 92 c. 67 d. 42 e. 34 E. 56
The rotational speed of the motor 3 in rpm. b. 92
The figure shows a hydraulic circuit that uses three chain conveyors. The torque that drives the motors is T: =1500 N.m. T2 =700 Nm and, T3 = 300Nm.The volumetric flow rate produced by the pump is 6.3 liters per minute. The displacement volume of the motors is V01 =1000 cm3/rev. V02 =1000 cm3/rev and, V09 =500 cm3/rex.
The motors have a volumetric efficiency of 0.9 and an overall efficiency of 0.85. The leakage of hydraulic motors 1 and 3 is internal completely, while the leakage of hydraulic motor 2 is external completely.The orifice of the flow control valve has a diameter of 0.5 mm. The capacity coefficient of the needle valve is 0.7.
The pressure losses through the pipes are ignored. The volumetric flow rate through the needle valve is Q = C × A2 × ΔP / ρ where C is the capacity coefficient, A is the area of the orifice, ΔP is the pressure difference through the needle valve, and ρ is the density of the fluid. The density of the oil used in the hydraulic system is 860 kg/m3. We need to determine the rotational speed of motor 3 in rpm.
So,Let’s first determine the volumetric flow rate required by hydraulic motor 3. Using the expression of volumetric flow rate through the needle valve, we have Q = C × A2 × ΔP / ρ… (i)We are given that the capacity coefficient of the needle valve is 0.7. Its orifice diameter is 0.5 mm.
Hence, the area of the orifice is given byA2 = π d2 / 4where d is the diameter of the orifice. So, A2 = π × (0.5 mm)2 / 4 = 0.196 mm2 = 1.96 × 10-7 m2Using equation (i), we haveQ = C × A2 × ΔP / ρNow, we will calculate ΔP. To do this, we need to determine the flow rates Q1, Q2, and Q3.Let Q’ be the total volumetric flow rate through the system.
Since the overall efficiency of the system is given as 0.85, we haveQ’ = 0.85 × 6.3 l/min = 5.355 l/min = 5.355 × 10-3 m3/minWe know that the volume of fluid passing through the hydraulic motors is equal to their displacement volume multiplied by the number of revolutions per unit time.So, we haveQ1 = V01 × n1 … (ii)Q2 = V02 × n2 … (iii)Q3 = V03 × n3 … (iv)where V01, V02, and V03 are the displacement volumes of hydraulic motors 1, 2, and 3, respectively.
We are given that V01 = V02 = 1000 cm3/rev and V03 = 500 cm3/rev, which gives V01 = V02 = 1 × 10-6 m3/rev and V03 = 0.5 × 10-6 m3/rev.Substituting equations (ii), (iii), and (iv) in equation (i), we haveQ = C × A2 × (Q1 + Q2 - Q3) / ρSolving for Q3, we getQ3 = (Q1 + Q2 - Q) / C × A2 × ρPutting the given values in the above expression, we haveQ1 = V01 × n1 = (1 × 10-6 m3/rev) × n1Q2 = V02 × n2 = (1 × 10-6 m3/rev) × n2Q3 = V03 × n3 = (0.5 × 10-6 m3/rev) × n3Q = 5.355 × 10-3 m3/min = 5.355 × 10-3 / 60 m3/s = 8.925 × 10-5 m3/sA2 = 1.96 × 10-7 m2C = 0.7ρ = 860 kg/m3
Substituting the above values, we get8.925 × 10-5 = (1 × 10-6 × n1 + 1 × 10-6 × n2 - 0.5 × 10-6 × n3) / (0.7 × 1.96 × 10-7 × 860)Solving for n3, we have n3 = 91.6 rpmSo, the correct option is b. 92.
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