The value of h is approximately 0.0817 meters. The angular speed of the cylinder just before the cheese hits the ground is approximately 2.00 radians per second.
The total energy at the start is just the potential energy of the cheese, so we have:
mgh = (1/2)mv²
Simplifying, we get:
h = (1/2)v²/g = (1/2)(4.00 m/s)²/9.81 m/s²≈ 0.0817 m
B). τ = rF = mg
The moment of inertia of the cylinder is given by I = (1/2)m(R² + r²), where R is the outer radius of the cylinder. Using the values given, we get:
I = (1/2)(2.00 kg)((0.200 m)² + (0.100 m)²) = 0.0100 kg m^2
L = Iω + mvr
where v is the speed of the cheese just before it hits the ground.
Using the values given, we get:
L = (0.0100 kg m²)ω + (0.500 kg)(4.00 m/s)(0.100 m) = 0
Solving for ω, we get:
ω = -(0.500 kg)(4.00 m/s)(0.100 m)/(0.0100 kg m²) ≈ -2.00 rad/s
Since the negative sign indicates that the cylinder is rotating in the opposite direction to the cheese's motion, we take the absolute value to get:
|ω| = 2.00 rad/s
Angular speed is a measure of how quickly an object is rotating about a fixed point or axis. It is defined as the rate of change of the object's angular displacement per unit time. Angular displacement is the angle through which an object rotates, measured in radians, while time is measured in seconds.
The angular speed is typically denoted by the symbol "ω" and is expressed in units of radians per second (rad/s). It is a scalar quantity, meaning it only has a magnitude and no direction. The direction of the angular velocity is given by the right-hand rule, which states that the direction of the angular velocity vector is perpendicular to the plane of rotation and points in the direction that the fingers of the right hand curl when rotated in the direction of rotation.
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Once an answer is submitted, you will be unable to return to this part. Let R1 = {(1, 2), (2, 3), (3, 4)} and R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)} be relations from {1, 2, 3} to {1, 2, 3, 4]. Then, find the indicated relations. (Please enter "null" if the relations consist of no ordered pairs.) Identify the union of the given relations R1 and R2. R1 U R2 iv (Click to select) {(1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)} {(1, 2), (2, 1), (2, 2), (3, 1), (3, 2), (3, 4), (3,4)} {(1, 2), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3), (3, 4), (4,4)} {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3,4)}
the indicated relations are {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)}.
The union of R1 and R2, denoted R1 U R2, is the set of all ordered pairs that belong to either R1 or R2 or both. To find the union, we simply combine the ordered pairs from R1 and R2 without duplication.
R1 = {(1, 2), (2, 3), (3, 4)}
R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)}
R1 U R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)}
Therefore, {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)} is the answer.
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sound waves are group of answer choices the static transmission of particles through the ether the interaction of the processes of our inner ear with those of the outer ear electromagnetic radiation that travels much more slowly than light the waves of pressure changes that occur in the air as a function of the vibration of a source
In the case of sound waves, they are the result of pressure changes in the air as a function of the vibration of the source. Option 4 is right.
Sound waves are a type of mechanical wave known as pressure waves, which occur due to the vibration of a source. These waves involve the transfer of energy through a medium, such as air, water, or solid materials, without the permanent displacement of the medium's particles.
When a vibrating object, such as a speaker or a musical instrument, produces sound, it creates compressions and rarefactions in the surrounding air. These pressure variations then propagate through the medium in the form of sound waves, which travel away from the source at a specific speed, known as the speed of sound.
Upon reaching our ears, these sound waves interact with our outer ear, which collects and funnels the waves into the ear canal. The waves then travel to the eardrum, causing it to vibrate. These vibrations are subsequently transmitted to our inner ear through the ossicles, tiny bones in the middle ear. Finally, the vibrations reach the cochlea, where they are transformed into electrical signals and sent to the brain for processing and interpretation.
In summary, sound waves are the waves of pressure changes that occur in the air as a function of the vibration of a source, and they play a crucial role in our perception of sound through the interaction of the processes of our inner ear with those of the outer ear.
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Full question is:
Sound waves are:
the static transmission of particles through the etherthe interaction of the processes of our inner ear with those of the outer earelectromagnetic radiation that travels much more slowly than light the waves of pressure changes that occur in the air as a function of the vibration of a sourceDerive an expression for the speed the electron must have for the total energy to be equal to zero: E = K +U= 5 mo? +k12 = 0 (5.3) r
To derive an expression for the speed the electron must have for the total energy to be equal to zero, we start with the formula for total energy: E = K + U, where K is the kinetic energy and U is the potential energy. Setting this equal to zero, we get:
E = K + U = 5mo + k12 = 0
where mo is the rest mass of the electron and k12 is the Coulomb constant.
Explanation: Now, we can use the formula for kinetic energy, K = (1/2)mv^2, where m is the mass of the electron and v is its velocity. Substituting this into the total energy equation, we get:
(1/2)mv^2 + U = 0
Solving for v, we get:
v = sqrt((-2U)/m)
Substituting the expression for potential energy, U = -k12/r, we get:
v = sqrt((2k12/r)/m)
This is the expression for the speed the electron must have for the total energy to be equal to zero.
Summary: To find the speed the electron must have for the total energy to be equal to zero, we start with the formula for total energy and set it equal to zero. Using the formula for kinetic energy, we solve for v and substitute the expression for potential energy. The final expression is v = sqrt((2k12/r)/m).
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A soap film (n = 1.33) is 365 nm thick and coats a flat piece of glass (n = 1.52). Thus, air is on one side of the film and glass is on the other side, as the figure illustrates. Sunlight, whose wavelengths (in vacuum) extend from 380 to 750 nm, travels through air and strikes the film nearly perpendicularly. For what wavelength in the range of 380 to 750 nm does constructive interference cause the film to look bright in reflected light?
This value is within the given range, so the wavelength for which constructive interference causes the film to look bright in reflected light is 487 nm.
When light reflects from a soap film, there is a phase change of 180 degrees if the light reflects from the bottom of the film, and no phase change if it reflects from the top of the film. The path length difference between the two reflected beams determines whether they interfere constructively or destructively.
The path length difference is given by:
2nt = mλ
where n is the refractive index of the soap film, t is the thickness of the film, m is an integer, and λ is the wavelength of light in the film.
In this case, we want to find the wavelength for which constructive interference causes the film to look bright in reflected light. This occurs when the path length difference is equal to an integer number of wavelengths, so we can rearrange the equation above to get:
λ = 2nt/m
We need to find the value of m for which λ is in the range of 380 to 750 nm. We can assume that the thinnest part of the film will give the first bright spot.
For m = 1, we get:
λ = 2nt = 2(365 nm)(1.33) = 974 nm
This is outside the range of 380 to 750 nm.
For m = 2, we get:
λ = 2nt/m = 2(365 nm)(1.33)/2 = 487 nm
This value is within the given range, so the wavelength for which constructive interference causes the film to look bright in reflected light is 487 nm.
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a circuit jas an alternating voltage of 100 volts that peaks every 0.5 seconds. write a sinusoidal model for the voltage v as a function of the time t (in seconds)
The sinusoidal model for the voltage V as a function of the time t (in seconds) is V(t) = 100 * sin(4 * π * t).
1. Amplitude (A): This is the maximum value of the voltage, which is 100 volts in this case.
2. Period (T): This is the time it takes for the voltage to complete one cycle, given as 0.5 seconds.
3. Frequency (f): This is the number of cycles per second, calculated as the inverse of the period (f = 1/T).
Given these values, you can now write the sinusoidal model for the voltage V as a function of time t:
V(t) = A * sin(2 * π * f * t)
Substitute the given values:
V(t) = 100 * sin(2 * π * (1/0.5) * t)
Simplify the equation:
V(t) = 100 * sin(4 * π * t)
So, the sinusoidal model for the voltage V as a function of the time t (in seconds) is V(t) = 100 * sin(4 * π * t).
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what do the temperature variations of the cosmic microwave background observed by the planck telescope say about the big bang and inflation?
The temperature variations of the cosmic microwave background observed by the Planck telescope confirms the big bang and inflation.
The temperature variations, or anisotropies, in the CMB, a leftover radiation from the early cosmos, are the result of minute changes in the density of stuff there. Inflation, a brief period of rapid expansion that took place a tiny fraction of a second after the Big Bang, stretched these variations to cosmic sizes.
The precise temperature measurements made by the Planck telescope, which are consistent with the predictions of inflationary models, lend credence to the cosmic inflation theory. The data also supports the flatness, or absence of curvature, of the cosmos.
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You are designing a lever to lift an object that weighs 500N. The lever exerts the output force 1 m from the fulcrum. How far from the fulcrum must an effort force of 250 N be applied to lift the object? Show your work.
A lever to lift an object that weighs 500N. The lever exerts the output force 1 m from the fulcrum.
To solve this problem, we can use the formula for the mechanical advantage of a lever
Mechanical Advantage = Output Force / Input Force
We know that the output force is 500 N and the input force is 250 N. Therefore, the mechanical advantage is
Mechanical Advantage = 500 N / 250 N
Mechanical Advantage = 2
Next, we can use the formula for the distance from the fulcrum to the input force
Distance from fulcrum to input force = Output Force distance / Mechanical Advantage
We know that the output force distance is 1 m. Therefore, the distance from the fulcrum to the input force is
Distance from fulcrum to input force = 1 m / 2
Distance from fulcrum to input force = 0.5 m
Hence, an effort force of 250 N must be applied 0.5 m from the fulcrum to lift the object that weighs 500N.
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a new trend at automobile dealers is to fill tires with pure nitrogen gas rather than air. what mass of nitrogen gas would be needed to pressurize a tire with a volume of 18.0 liters to 32.0 psi at 25 degrees celsius? 14.7 psi
Therefore, about 0.255 grams of nitrogen gas would be needed to pressurize a tire with a volume of 18.0 liters to 32.0 psi at 25 degrees Celsius using pure nitrogen gas.
To solve this problem, we can use the ideal gas law, which states:
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 in Kelvin.
First, we need to convert the volume to cubic meters and the pressure to Pascals:
V = 18.0 L
= 0.018 m³
P = (32.0 - 14.7) psi
= 17.3 psi
= 119310 Pa
Next, we need to calculate the number of moles of nitrogen gas needed:
n = PV/RT
where R = 8.314 J/mol·K is the gas constant for nitrogen gas, and T = 25 + 273 = 298 K is the temperature in Kelvin.
n = (119310 Pa × 0.018 m³) / (8.314 J/mol·K × 298 K)
= 0.0091 mol
Finally, we can calculate the mass of nitrogen gas using its molar mass:
m = n × M
where M = 28.014 g/mol is the molar mass of nitrogen gas.
m = 0.0091 mol × 28.014 g/mol
= 0.255 g
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The total temperature and total pressure of 50kg/s air-flow entering a compressor are 250K and 0.5atm. respectively. a) Calculate the power that the machine needs to increase the total pressure of te low to 5atm, considering a compressor's efficiency of 90%. Assume ca-100OJ (kg K) and '' : 1.4. b) Calculate the total temperature at the ext of an isentropic turbine that moves the aforementioned compressor if the total temperature downstream of the burner is 1600K and the fuel flow rate is lkg/s. For this calculation assume op -1300J (kg K)
The total temperature needed for the compressor is therefore 2.8722 MW.
a) The first step is to calculate the inlet conditions in terms of specific enthalpy (h) and specific entropy (s), using the given total temperature and total pressure:
T0 = 250 K
P0 = 0.5 atm = 50.6 kPa
Using the ideal gas law, the inlet density (ρ0) can be calculated as:
ρ0 = P0 / (R_air * T0) = 0.5 / (287 * 250) = 0.0022 kg/m³
Using the specific heat ratio (γ = 1.4), the specific gas constant for air (R_air = 287 J/(kg K)), and the isentropic relation between total temperature and pressure:
T0 / P0^((γ-1)/γ) = Tt / Pt^((γ-1)/γ)
where Tt and Pt are the total temperature and pressure at the compressor outlet, respectively, assuming isentropic compression. Rearranging this equation to solve for Tt, we get:
Tt = T0 * (Pt/P0)^((γ-1)/γ) = 250 * (5/0.5)^0.286 = 766.6 K
Using the ideal gas law again, the outlet density (ρt) can be calculated as:
ρt = Pt / (R_air * Tt) = 5 / (287 * 766.6) = 0.0009 kg/m³
The mass flow rate of air (mdot) is given as 50 kg/s, so the volumetric flow rate (Vdot) can be calculated as:
Vdot = mdot / ρ0 = 50 / 0.0022 = 22727 m³/s
The compressor's efficiency (η_comp) is given as 90%, so the actual work input per unit mass of air (w_in) is:
w_in = (h_comp - h_0) / η_comp
where h_comp and h_0 are the specific enthalpies at the compressor outlet and inlet, respectively. Since the compression is assumed to be reversible and adiabatic, the specific enthalpy at the compressor outlet can be calculated using the isentropic relation between temperature and pressure:
Tt / T0 = (Pt/P0)^((γ-1)/γ)
h_comp / h_0 = Tt / T0
Substituting the values, we get:
h_comp / h_0 = 766.6 / 250 = 3.066
The specific enthalpy at the inlet can be calculated using the specific heat at constant pressure (cp) for air, which is approximately constant over the temperature range involved:
cp = 1000 J/(kg K)
h_0 = cp * T0 = 250000 J/kg
Finally, the actual work input per unit mass of air is:
w_in = (h_comp - h_0) / η_comp = (3.066 * 250000 - 250000) / 0.9 = 57444 J/kg
he total power needed for the compressor is therefore:
P = mdot * w_in = 50 * 57444 = 2.8722 MW
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a negatively charged ion moves due north with a speed of 1.6×106 m/s at the earth's equator.What is the magnetic force exerted on this ion?F=?N
The magnitude of the magnetic force exerted on the ion is 1.024 x 10⁻¹³ N. Since the ion is negatively charged, the direction of the force is to the west.
The magnetic force on a charged particle moving in a magnetic field is given by the equation:
F = qvB sin(∅)
where
q is the charge of the particle,
v is its velocity,
B is the magnetic field, and
∅ is the angle between the velocity and the magnetic field.
In this case, the ion is moving due north, so its velocity is perpendicular to the earth's magnetic field at the equator, which is directed horizontally. Therefore, ∅= 90 degrees, and sin(∅) = 1.
The charge on the ion is negative, so q is negative. We can plug in the given values:
F = (-q)(v)(B)sin(∅)
F = (-1.6 x 10⁻¹⁹ C)(1.6 x 10⁶ m/s)(5 x 10⁻⁵ T)(1)
F = -1.024 x 10⁻¹³ N
So the magnitude of the magnetic force exerted on the ion is 1.024 x 10⁻¹³ N. Since the ion is negatively charged, the direction of the force is to the west.
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Consider a giant flat plane that touches the earth at one point and extends out into space. Suppose you slide an iron block along the plane where it makes contact with the Earth. Suppose also that the plate is perfectly frictionless, air resistance is absent and Vo
Consider a giant flat plane that touches the Earth at one point and extends out into space. Now, imagine an iron block is placed on the point where the plane makes contact with the Earth. In this situation, the plane is perfectly frictionless, meaning there is no resistance between the iron block and the plane's surface.
Additionally, air resistance is absent in this scenario.
To slide the iron block along the flat plane, you need to apply a force to it. Let's say that the force is applied, and the iron block has an initial velocity (Vo). Since there is no friction or air resistance, the iron block will continue to move along the flat plane with a constant velocity equal to Vo. It will not slow down or speed up as it moves along the frictionless plane, due to the absence of any opposing forces.
In summary, the iron block will slide along the flat, frictionless plane at a constant velocity Vo, without being affected by any slowing forces.
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A light source simultaneously emits photons with two energies, 2. 2 eV and 3. 2 eV. The intensity of the lower-frequency component of the light is twice that of the higher-frequency component. The light source illuminates a metal with a work function of 1. 8 eV. What will be the maximum kinetic energy of the photoelectrons, in electron volts?
The maximum kinetic energy of the photoelectrons is proportional to the intensity of the incident light, with a proportionality constant of 0.61 eV.
The maximum kinetic energy of photoelectrons can be calculated using the equation:
[tex]$K_{max} = h\nu - \phi$[/tex]
where [tex]$h$[/tex] is Planck's constant,[tex]$\nu$[/tex] is the frequency of the incident light, and [tex]$\phi$[/tex] is the work function of the metal. Since we are given the energies of the photons, we can use the relation [tex]$E = h\nu$[/tex] to find the frequencies.
The energies of the photons are:
[tex]E_1 = 2.2$ eV[/tex]
[tex]E_2 = 3.2$ eV[/tex]
The corresponding frequencies are:
[tex]$\nu_1 = \frac{E_1}{h} = \frac{2.2 \text{ eV}}{4.14 \times 10^{-15} \text{ eV s}} \approx 5.31 \times 10^{14} \text{ Hz}$[/tex]
[tex]$\nu_2 = \frac{E_2}{h} = \frac{3.2 \text{ eV}}{4.14 \times 10^{-15} \text{ eV s}} \approx 7.74 \times 10^{14} \text{ Hz}$[/tex]
Since the intensity of the lower-frequency component is twice that of the higher-frequency component, we can calculate the total intensity [tex]$I$[/tex] as:
[tex]$I = 2I_1 + I_2$[/tex]
where [tex]$I_1$[/tex] is the intensity of the lower-frequency component and [tex]$I_2$[/tex] is the intensity of the higher-frequency component.
Since energy is proportional to frequency, we can write:
[tex]$I_1 = 2I_2$[/tex]
[tex]$E_1 I_1 + E_2 I_2 = I$[/tex]
Substituting the values, we get:
[tex]$2.2 \text{ eV} \times 2I_2 + 3.2 \text{ eV} \times I_2 = I$[/tex]
[tex]$8.6 \text{ eV} \times I_2 = I$[/tex]
[tex]$I_2 = \frac{1}{9.6} I$[/tex]
[tex]$I_1 = \frac{2}{9.6} I$[/tex]
The total intensity is not given, but we don't need it to calculate [tex]K_{max}$.[/tex]
Now we can calculate [tex]$K_{max}$[/tex]
[tex]$K_{max} = h\nu_2 - \phi$[/tex]
[tex]$K_{max} = (6.626 \times 10^{-34} \text{ J s}) (7.74 \times 10^{14} \text{ Hz}) - (1.8 \text{ eV})$[/tex]
[tex]$K_{max} \approx 1.67 \text{ eV}$[/tex]
Therefore, the maximum kinetic energy of the photoelectrons is approximately 1.67 eV.
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7. Earth's mantle is cooling off over time as heat is lost from the interior to the atmosphere and space. At what mantle temperature will convection in the mantle cease? Assume the viscosity, 4 = 10%° Pas, g = 10 m/s?, density, p = 3300 kg/m’, thermal diffusivity, k = 10° m?/s, the surface temperature, T; = 273 K, the mantle is 3000 km thick, and the thermal expansion coefficient, a = 3 x 10 1/K. Assume a critical Rayleigh number of 1000.
At a mantle temperature of approximately 1571.75 K, convection in the mantle will cease.
To determine the mantle temperature at which convection will cease, we need to use the given information and the critical Rayleigh number (Ra) formula. The critical Rayleigh number is given as 1000.
The formula for Rayleigh number is:
Ra = (g * α * ΔT * h^3) / (ν * κ)
where
g = 10 m/s² (gravitational acceleration)
α = 3 x 10^(-5) 1/K (thermal expansion coefficient)
ΔT = mantle temperature - surface temperature (temperature difference)
h = 3,000,000 m (mantle thickness, converted from 3000 km)
ν = 10^(20) Pas (viscosity)
κ = 10^(-6) m²/s (thermal diffusivity)
First, we need to solve for ΔT:
1000 = (10 * 3 * 10^(-5) * ΔT * (3,000,000)^3) / (10^(20) * 10^(-6))
Rearranging the equation to solve for ΔT, we get:
ΔT = (1000 * 10^(20) * 10^(-6)) / (10 * 3 * 10^(-5) * (3,000,000)^3)
ΔT ≈ 1298.75 K
Now, we can find the mantle temperature (T_mantle) by adding the surface temperature (T_s = 273 K) to ΔT:
T_mantle = T_s + ΔT
T_mantle ≈ 273 + 1298.75
T_mantle ≈ 1571.75 K
At a mantle temperature of approximately 1571.75 K, convection in the mantle will cease.
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although the matter's identity stays the same its ______ might change
Although the matter's identity stays the same, its physical properties might change. This means that even if a substance remains the same, its characteristics such as shape, size, or state of matter (solid, liquid, gas) may change due to external factors like temperature or pressure.
Any substance with mass and volume is considered matter in classical physics and generic chemistry. In everyday as well as scientific usage, "matter" includes atoms and anything made of them, as well as any particles (or combination of particles) that act as if they have both rest mass and volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic particles. However, it excludes other energy phenomena or waves, such as light or heat, as well as massless particles like photons. There are different states of matter.
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When 3.5 g of liquid water is cooled from 90c to 20c how much energy is lost?
(Choose only one answer)
The amount of heat or energy that is lost when the water is cooled is 1,024.1 J.
What is the amount of heat lost?
The amount of heat lost is calculated by applying the formula for heat capacity of water as shown below;
Q = mcΔT
where;
m is the mass of the waterc is the specific heat capacityΔT is the change in temperature of the waterThe amount of heat or energy that is lost when the water is cooled is calculated as follows;
Q = 3.5 g x 4.18 J/gC x (90 C - 20 C)
Q = 1,024.1 J
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steam enters an adiabatic nozzle steadily at 3 mpa , 670 k , 50 m/s and exits at 2 mpa , 200 m/s .
The final outlet state when the steam enters an adiabatic nozzle is found to be 2 MPa, 478.6 K, and 200 m/s.
The problem involves calculating the outlet state of steam passing through an adiabatic nozzle from a given inlet state.
The steady flow energy equation is used here.
Using the steam tables, the specific enthalpy of steam at the inlet state is found, and the specific enthalpy at the outlet state is calculated using the given velocity and the steady flow energy equation.
Using the steam tables again, the temperature and specific entropy at the outlet state are then determined.
Thus, the final outlet state is found to be 2 MPa, 478.6 K, and 200 m/s.
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Complete Question:
Steam Enters An Adiabatic Nozzle Steadily At 3 MPA, 670 K, 50 M/S And Exits At 2 MPA, 200 M/S. If The Nozzle Has An Inlet Area Of 7 Cm^2, A) Determine The Exit Area Of The Nozzle B) What Must The Exit Area Be For The Exit Velocity To Be 400 M/S?
Steam enters an adiabatic nozzle steadily at 3 MPA, 670 K, 50 m/s and exits at 2 MPA, 200 m/s. If the nozzle has an inlet area of 7 cm^2,
A) Determine the exit area of the nozzle
B) What must the exit area be for the exit velocity to be 400 m/s?
A proton is going with a velocity of v = v,i + vyj, where vx = 71 m/s and vy = 66 m/s. The proton comes into a magnetic field B = Byj, where By = 7.1 T. B L 2011 ©theexpertta.com A 25% Part (a) Express the magnetic force F in terms of the proton charge e, velocity v and the magnetic field B. Grade Summary Deductions 0 % Potential 100% F = eở x B F = eB x ✓ F = eŨ. B F = eB · Ū Submissions Attempts remaining: 3 33% per attempt) detailed view Submit Hint Feedback I give up! Hints: 0% deduction per hint. Hints remaining: 1 Feedback: 0% deduction per feedback. HA 25% Part (b) In this particular case, express the magnitude of the force, IFI, in terms of e, vx, Vy and By A 25% Part (c) Calculate the numerical value of Fl in N. A 25% Part (d) What's the direction of the force?
The magnetic force on the proton is F = -e vx By k. The numerical value of F is 1.2 × [tex]10^{-15[/tex] N. The force is in the -k direction, which means it is directed downward perpendicular to the plane containing the velocity and magnetic field vectors.
Part (a) - The magnetic force F on a charged particle moving through a magnetic field is given by the equation:
F = q(v x B)
For a proton with charge e and velocity v = vx i + vy j, and a magnetic field B = By j, we have:
F = e(v x B) = e[(vx i + vy j) x (By j)]
Taking the cross product of the velocity and magnetic field vectors:
(v x B) = (vx i + vy j) x (By j)
= (vx By) i x j + (vy By) j x j
= -vx By k
where i, j, and k are the unit vectors in the x, y, and z directions, respectively.
Substituting this into the expression for the magnetic force, we get:
F = e(v x B) = -evxBy k
Therefore, the magnetic force on the proton is F = -e vx By k.
Part (b) - Expressing the magnitude of the force, IFI, in terms of e, vx, vy, and By:
The magnitude of the magnetic force on a charged particle is given by:
|F| = q|v||B| sin(θ)
where θ is the angle between v and B.
In this case, the angle between v and B is 90 degrees, so sin(θ) = 1. Therefore:
|F| = e|v||B|
Substituting in the given values, we get:
|F| = e √(vx² + vy²) |By| = e √(71² + 66²) (7.1) = 2.34 × [tex]10^{-16[/tex] N
Part (c) - Calculating the numerical value of F in N:
Substituting the given values into the expression for the magnetic force, we get:
F = -e vx By k = -1.6 × [tex]10^{-19[/tex] C × 71 m/s × 7.1 T k = -1.2 × [tex]10^{-15[/tex] N k
Therefore, the numerical value of F is 1.2 × [tex]10^{-15[/tex] N.
Part (d) - Determining the direction of the force:
The force is in the -k direction, which means it is directed downward perpendicular to the plane containing the velocity and magnetic field vectors.
Magnetic force is the force exerted by a magnetic field on a moving charge or a magnet. It is one of the fundamental forces of nature and is responsible for many phenomena that we observe in our everyday lives, such as the behavior of compasses and the attraction and repulsion of magnets.
The strength of the magnetic force depends on the strength of the magnetic field and the velocity of the moving charge or magnet. The direction of the force is perpendicular to both the magnetic field and the direction of motion of the charged particle. The magnetic force has many important applications in technology, such as in electric motors, generators, and magnetic resonance imaging (MRI) machines. It is also used in particle accelerators to manipulate and control the motion of charged particles.
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radiation is a(n) when it produces leukemia in radiologists and survivors of atomic bomb explosions.
Radiation is a significant risk factor when it produces leukemia in radiologists and survivors of atomic bomb explosions.
Ionizing radiation, such as that emitted from radioactive materials, medical equipment, and atomic bombs, has enough energy to remove tightly bound electrons from atoms, causing them to become charged particles or ions. These ions can damage cellular structures, including DNA, which can lead to mutations and ultimately cause cancer, such as leukemia. Radiologists, who are regularly exposed to ionizing radiation during their work with diagnostic imaging equipment, are at an increased risk of developing leukemia. Similarly, survivors of atomic bomb explosions have been exposed to high levels of ionizing radiation, which can also result in the development of leukemia, this increased risk is due to the mutagenic nature of ionizing radiation, which directly influences the genetic material of cells.
In both scenarios, safety measures and guidelines should be in place to minimize the exposure to ionizing radiation. For radiologists, this may include wearing protective gear and limiting the duration of their exposure to radiation sources. For survivors of atomic bomb explosions, monitoring and assessing long-term health risks become vital for early detection and treatment of radiation-induced leukemia. In conclusion, radiation is a significant risk factor for leukemia development in both radiologists and survivors of atomic bomb explosions due to the damage it causes to the cellular structures, particularly DNA.
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if the rocket has traveled 350 350 feet horizontally since it was launched, what is the rocket's height above the ground? incorrect feet
Using the projectile principle, the slope of the rockets path, height above the ground and the distance traveled at a height of 313 yards would be 2.57, 218.63, 121.69 respectively.
Given the Parameters :
Angle of inclination = 1.2 radian
Converting to degree :
θ = 1.2 rads × 180/π = 68.755°
A.)
The slope of the rocket's path :
Slope = tanθ
Slope = tan(68.755) = 2.57
B.)
Horizontal distance, = distance along the x-axis = 85 yards
Vertical distance = height = distance along y-axis, y
y = tanθ × x
y = slope × x
y = tan(68.755) × 85
y = 218.63 yards
C.)
Vertical distance, y = 313 yards
From : x = 121.69 yards
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Full Question ;
A rocket is launched from the ground and travels in a straight path. The angle of inclination of the rocket's path is 1.2 radians. (That is, the rocket's path and the ground form an angle with a measure of 1.2 radians.)]
Required:
a. What is the slope of the rocket's path?
b. If the rocket has traveled 85 yards horizontally since it was launched, how high is the rocket above the ground? _____yards.
c. At some point in time, the rocket is 313 yards above the ground. How far has the rocket horizontally (since it was launched) at this point in time? _____yards
2. How many instrument players are needed to form each ensemble? Are their
instruments made of wood or metal?
The number of players in an ensemble and the materials used in instruments vary depending on the type of ensemble and instrument being played, as well as the preferences and traditions of the musicians involved.
The number of instrument players needed to form an ensemble depends on the type of ensemble being formed. For example, a string quartet typically consists of two violins, a viola, and a cello, while a symphony orchestra can have over 100 musicians playing a wide variety of instruments.
As for whether the instruments are made of wood or metal, it again depends on the type of instrument. String instruments such as violins, violas, cellos, and double basses have wooden bodies, while their bows are made of wood and horsehair. Brass instruments such as trumpets, trombones, and tubas are typically made of brass, while woodwind instruments such as flutes, clarinets, and oboes can have bodies made of wood or metal, depending on the specific instrument.
In general, the materials used to make instruments can affect their sound and tone quality. For example, wooden instruments are often favored for their warmth and richness of tone, while brass instruments are prized for their bright and powerful sound. Ultimately, the specific materials used in an instrument depend on factors such as the instrument's intended use, the preferences of the musician playing it, and the traditions of the musical genre in which it is used.
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a whistle of frequency 587 hz moves in a circle of radius 76.9 cm at an angular speed of 16.2 rad/s. what are (a) the lowest and (b) the highest frequencies heard by a listener a long distance away, at rest with respect to the center of the circle? (take the speed of sound in air to be 343 m/s.)
The lowest frequency heard by the listener is 578.4 Hz and the highest frequency heard is 620.4 Hz. These frequencies are due to the Doppler effect caused by the movement of the whistle in a circle.
We can start by finding the velocity of the whistle as it moves in a circle. This can be found using the formula v = rω, where v is the velocity, r is the radius, and ω is the angular speed. Plugging in the given values, we get:
v = (0.769 m)(16.2 rad/s) = 12.448 m/s
Now, let's think about the sound waves that the whistle is producing. As the whistle moves in a circle, it is constantly emitting sound waves in all directions. However, some of these waves are compressed (higher frequency) and some are stretched out (lower frequency) depending on the direction of their motion relative to the listener.
To find the highest and lowest frequencies heard by a listener at rest with respect to the center of the circle, we need to consider the Doppler effect. This is the phenomenon where the frequency of a sound wave appears to change for an observer if the source of the sound is moving relative to the observer.
The formula for the Doppler effect is:
f' = f (v + v_obs) / (v + v_source)
where f is the frequency of the sound wave, f' is the perceived frequency, v is the velocity of the sound wave (which is the speed of sound in air, given as 343 m/s), v_obs is the velocity of the observer (which is 0 since they are at rest), and v_source is the velocity of the source (which is the velocity of the whistle, found earlier as 12.448 m/s).
(a) The lowest frequency heard will occur when the whistle is moving directly away from the listener. In this case, the sound waves will be stretched out (lower frequency) due to the Doppler effect. The velocity of the sound wave relative to the listener is v - v_obs = 343 m/s. The velocity of the source relative to the listener is v_source - v_obs = 12.448 m/s. Plugging these values into the Doppler formula, we get:
f' = f (v + v_obs) / (v + v_source)
f' = 587 Hz (343 m/s) / (343 m/s + 12.448 m/s)
f' = 578.4 Hz
So the lowest frequency heard by the listener is 578.4 Hz.
(b) The highest frequency heard will occur when the whistle is moving directly towards the listener. In this case, the sound waves will be compressed (higher frequency) due to the Doppler effect. The velocity of the sound wave relative to the listener is v + v_obs = 343 m/s. The velocity of the source relative to the listener is v_source + v_obs = 12.448 m/s. Plugging these values into the Doppler formula, we get:
f' = f (v + v_obs) / (v + v_source)
f' = 587 Hz (343 m/s + 0 m/s) / (343 m/s - 12.448 m/s)
f' = 620.4 Hz
So the highest frequency heard by the listener is 620.4 Hz.
Lowest frequency heard by the listener is 578.4 Hz and the highest frequency heard is 620.4 Hz. These frequencies are due to the Doppler effect caused by the movement of the whistle in a circle.
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a runner whose mass is 49 kg accelerates from a stop to a speed of 8 m/s in 3 seconds. (a good sprinter can run 100 meters in about 10 seconds, with an average speed of 10 m/s.) (a) what is the average horizontal component of the force that the ground exerts on the runner's shoes? average force
The average horizontal component of the force that the ground exerts on the runner's shoes is 130.83 N.
Average horizontal component of the force that the ground exerts on the runner's shoes can be calculated using the equation F = ma, where F is the force, m is the mass, and a is the acceleration.
First, we need to find the acceleration of the runner using the equation a = (v - u)/t, where v is the final velocity, u is the initial velocity (which is 0 in this case since the runner starts from a stop), and t is the time taken.
a = (8 m/s - 0 m/s)/3 s
a = 2.67 m/s²
Next, we can use the formula F = ma to find the average horizontal component of the force:
F = 49 kg x 2.67 m/s²
F = 130.83 N
Therefore, the average horizontal component of the force that the ground exerts on the runner's shoes is 130.83 N.
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if the circular conductor shown below undergoes thermal expansion while it is in a uniform magnetic field, a current is induced clockwise around it. is the magnetic field directed into or out of the page?
When a circular conductor undergoes thermal expansion in a uniform magnetic field and induces a clockwise current, the magnetic field is directed into the page. This is in accordance with Lenz's Law, which predicts the direction of the induced current based on the change in magnetic flux.
To determine whether the magnetic field is directed into or out of the page when a circular conductor undergoes thermal expansion in a uniform magnetic field and induces a clockwise current, we can use Lenz's Law.
Step 1: Understand Lenz's Law. Lenz's Law states that the direction of the induced current is such that it opposes the change in the magnetic flux that caused it.
Step 2: Identify the change in the magnetic flux. In this case, the change in magnetic flux is due to the thermal expansion of the circular conductor, which increases the area within the loop.
Step 3: Determine the direction of the induced current. Since the magnetic flux is increasing within the loop, the induced current will act in a way to oppose this increase. The current is induced clockwise, which means it will create a magnetic field directed into the page.
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a mass weighing 4 pounds is attached to a spring whose spring constant is 36 lb/ft. what is the period of simple harmonic motion?
As per the given variables, the period of the simple harmonic motion is 2.09 seconds
Mass = (m) = 4 pounds
Spring constant = (k)= 36lb/ft
Simple harmonic motion includes an item moving cyclically and periodically around a central point or equilibrium position as a result of the action of a restoring force, with the object experiencing the same maximum displacement on each side of the equilibrium point.
Calculating the time period of Simple harmonic motion -
t = 2π√m/k
Substituting the values -
t = 2 x 3.14 x √4/36
t = 6.28 x √1/9
t = 6.28/3
t = 2.09
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the blind spot refers to the region of the eye at where the ________ exits the eye.
The blind spot refers to the region of the eye where the optic nerve exits the eye. The optic nerve is responsible for transmitting visual information from the eye to the brain, but where it exits the eye, it creates a small gap in the visual field that is not perceived by the brain.
This is because there are no photoreceptor cells (rods or cones) at the location where the optic nerve exits the eye, which means that no visual information can be detected and transmitted to the brain from that point. However, the brain is able to compensate for this gap by using information from surrounding areas of the visual field to fill in the missing information. This is known as the brain's "filling-in" mechanism, which allows us to perceive a seamless visual field even though there is a blind spot present.
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Problem 2.A(1 pnt) The Thevenin-equivalent for a section of an AC circuit absorbs (-50) watts and (+30) VARs. The power factor angle in degrees for the Thevenin equivalent section is Problem 2 B (9 pnts) A balanced 3-phase source is directly connected to two parallel 3-phase Δ-connected loads. The 3-phase source is supplying a total of60 kVA at 0.96 pf(leading) to the two loads. The magnitude ofthe line voltage at the load is 630 Vrms . The first Δ- connected load is purely resistive and absorbs 45 kW. Determine the impedance of the 2nd Δ-connected load. MS
So the impedance of the second Δ-connected load is approximately 81.6 ohms.
Problem 2.A:
To find the power factor angle, we need to use the formula:
cos(θ) = P / S
where P is the real power (in watts), S is the apparent power (in VA), and θ is the power factor angle.
Here, P = -50 W (since the circuit absorbs power), and S = √((-50)^2 + 30^2) VA (using the Pythagorean theorem).
Therefore, cos(θ) = -50 / √((-50)^2 + 30^2) = -0.8
Taking the inverse cosine, we get θ ≈ 143.13 degrees.
So the power factor angle for the Thevenin equivalent section is approximately 143.13 degrees.
Problem 2.B:
The total apparent power supplied by the 3-phase source is:
S = 60 kVA / 0.96 = 62.5 kVA
Since the first Δ-connected load is purely resistive, its apparent power is also its real power:
S1 = P1 = 45 kW
The total apparent power absorbed by the two loads is:
S = S1 + S2
S2 = S - S1 = 62.5 kVA - 45 kW = 43.3 kVAR
The apparent power of the second Δ-connected load is the magnitude of its impedance times the square of the line voltage:
S2 = (|Z2| * Vline^2) / 3
where Vline = 630 / √3 ≈ 364.2 Vrms is the line voltage (for a balanced 3-phase system), and the factor of 3 in the denominator is because we are dealing with line quantities (not phase quantities).
Solving for |Z2|, we get:
|Z2| = (3 * S2) / Vline^2 ≈ 81.6 ohms
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Which scenario describes humans helping renewable resources renew?
An oyster company only harvests and sells oysters that are fully grown.
A farmer plants only one kind of crop in the same field until the soil turns bad.
An oil company moves to a new area once its existing wells quit producing oil.
A lumber company cuts down the trees in a forest, then moves to the next forest.
An oyster company only harvests and sells oysters that are fully grown. The correct answer is: 1.
By only harvesting fully grown oysters, the company allows the juvenile oysters to grow and mature, which ensures the long-term sustainability of the oyster population. This practice is a form of selective harvesting, which allows the oysters to reproduce and replenish their population, helping to maintain a healthy and sustainable oyster population. It is an example of responsible management of renewable resources, which aims to balance human exploitation of resources with the need to preserve and protect them for future generations. Hence option: 1 is correct.
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we can measure the radii of stars in an eclipsing binary system, in addition to the masses.
T/F
This statement is True. In an eclipsing binary system, we can observe the periodic eclipses of the two stars as they orbit each other. By measuring the changes in the light and duration of the eclipses, we can calculate the radii of the stars as well as their masses.
In an eclipsing binary system, we can indeed measure both the radii and masses of the stars involved. This is achieved by analyzing the light curves and radial velocity data of the system, which provide information on the stars' sizes and orbital motion.
Combining these measurements allows for the accurate determination of both the radii and masses of the stars.
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What single change to the experimental system would reduce the electric field strength necessary to maintain the oil drop in static equilibrium?
To reduce the electric field strength necessary to maintain the oil drop in static equilibrium, the experimental system could be modified by increasing the distance between the plates, reducing the voltage applied, using a different oil with a higher dielectric constant and reducing the size of the oil drop.
Increasing the distance between the plates: If the distance between the plates is increased, the electric field strength between them will decrease. This will reduce the force acting on the charged oil drop, requiring a lower electric field strength to maintain the drop in static equilibrium.
Reducing the voltage applied to the plates: If the voltage applied to the plates is reduced, the electric field strength between them will also decrease. As a result, the force acting on the charged oil drop will be reduced, requiring a lower electric field strength to maintain the drop in static equilibrium.
Using a different oil with a higher dielectric constant: The dielectric constant of the oil used in the experiment can also affect the electric field strength required to maintain the drop in equilibrium. If a different oil with a higher dielectric constant is used, the electric field strength required to maintain the drop in equilibrium will be reduced.
Reducing the size of the oil drop: The force acting on the charged oil drop is directly proportional to the charge on the drop. Therefore, if the size of the oil drop is reduced, the force acting on it will also decrease, requiring a lower electric field strength to maintain the drop in static equilibrium.
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a young's double-slit experiment is performed using light that has a wavelength of 629 nm. the separation between the slits is 5.25e-5 m. calculate the angle that locates the first-order bright fringes on the screen.
The angle that locates the first-order bright fringes on the screen is 6.88 degrees.
To calculate the angle that locates the first-order bright fringes on the screen in a young's double-slit experiment using light with a wavelength of 629 nm and a slit separation of 5.25e-5 m, we can use the formula:
sin θ = mλ/d
where θ is the angle, λ is the wavelength, d is the slit separation, and m is the order of the bright fringe.
For the first-order bright fringe, m = 1. Plugging in the values we have:
sin θ = (1)(629 nm)/(5.25e-5 m)
Simplifying:
sin θ = 0.1196
Taking the inverse sine:
θ = 6.88 degrees
Therefore, the angle that locates the first-order bright fringes on the screen is 6.88 degrees.
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