The electric field produced by the disk at point P along the x-axis is approximately 333.89 N/C.
Since the disk lies in the y-z plane, the electric field produced by the disk will only have an x-component, which can be calculated using the formula for the electric field produced by a charged disk:
E = σ / (2ε₀) * [1 - (z / √(R² + z²))]
At point P(1.01 m, 0.00 m), the distance from the disk along the z-axis is z = 0, so the formula reduces to:
E = σ / (2ε₀) = (5.88 × 10^-6 C/m²) / (2 * 8.85 × 10^-12 F/m) ≈ 333.89 N/C
Therefore, the electric field produced by the disk is 333.89 N/C.
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a 2.99 kg particle has a velocity of (2.95 i hat - 3.97 j) m/s.Find the magnitude and direction of its momentum.
Answer:
P (momentum) = M * V
V = (2.95^2 + 3.97^2)^1/2 = 4.95 m/s
P = 2.99 kg * 4.95 m/s = 14.8 kg-m/sec total momentum
tan θ = Vy / Vx = -3.97 / 2.95 = -1.35
θ = 53.4 deg below positive x-axis
what are reasons that a promontory will be more vulnerable to wave erosion than a bay? multiple select question. waves bend around a promontory and strike it from both sides. larger waves enter into a bay than strike a promontory. a promontory will receive more wave action than a bay. powerful waves focus most of their energy at a promontory.
The reasons that a promontory will be more vulnerable to wave erosion than a bay;- Waves bend around a promontory and strike it from both sides,- Powerful waves focus most of their energy at a promontory and - A promontory will receive more wave action than a bay.
A promontory is more vulnerable to wave erosion than a bay due to the following reasons:
1. Waves bend around a promontory and strike it from both sides: This phenomenon, called wave refraction, concentrates the wave energy on the promontory, making it more prone to erosion.
2. A promontory will receive more wave action than a bay: Bays are generally more sheltered and have a lower exposure to waves, whereas promontories are exposed to the full force of waves, leading to more erosion.
3. Powerful waves focus most of their energy at a promontory: Due to the shape of the coastline, waves tend to focus their energy on the headlands, like promontories, which makes them more vulnerable to erosion compared to bays.
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If a student thinks that the calorimeter has tap water in it, but it actually contains salt water (which has a lower specific heat than tap water), then
The calorimeter has tap water in it, but it actually contains salt water (which has a lower specific heat than tap water, then the student may make an error in their calorimetry calculation.
What is a calorimetry ?Calorimetry is the science of measuring the heat of chemical reactions or physical changes, and the study of the relationship between heat, temperature, and energy. It is used to measure the amount of heat energy released or absorbed in a chemical or physical change, and to calculate the enthalpy change of a reaction.
What is a reaction ?Reaction is a process that results in the transformation of one or more substances into different substances. Chemical reactions involve the breaking and formation of chemical bonds between atoms, ions, or molecules, and can be accompanied by the release or absorption of energy in the form of heat, light, or electricity.
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a star less luminous than our sun will have a habitable zone that is
A planet has mass M = 8.00 × 1023 kg. At what distance will the centripetal acceleration of an orbiting space station be equal to the gravitational acceleration on Earth’s surface? (G = 6.67 × 10–11 m3·kg–1·s–1)answer is 2.33 x10^6 m. Can someone show the work on how to get this answer?
To find the distance at which the centripetal acceleration of an orbiting space station around a planet is equal to Earth's gravitational acceleration, we need to set up an equation involving the planet's mass (M), gravitational constant (G), and Earth's gravitational acceleration (g).
Given:
M = 8.00 × 10²³ kg
G = 6.67 × 10^(-11) m³·kg^(-1)·s^(-1)
g = 9.81 m/s² (Earth's gravitational acceleration)
Centripetal acceleration (a_c) is given by the formula:
a_c = (G * M) / r²
where r is the distance from the planet's center.
We want the centripetal acceleration to be equal to Earth's gravitational acceleration, so we can set them equal:
g = (G * M) / r²
Now, we need to solve for r:
r² = (G * M) / g
r² = (6.67 × 10^(-11) m³·kg^(-1)·s^(-1) * 8.00 × 10²³ kg) / 9.81 m/s²
r² ≈ 5.42 × 10¹² m²
Now, take the square root of both sides to find r:
r ≈ 2.33 × 10^6 m
So, at a distance of 2.33 x 10^6 meters from the planet's center, the centripetal acceleration of an orbiting space station will be equal to the gravitational acceleration on Earth's surface.
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The following formula can be used to determine the distance from the planet's centre at which the centripetal acceleration of an orbiting space station equals the gravitational acceleration on Earth's surface:
[tex]r = (GM/g)^(1/3)[/tex]
where the gravitational constant, G, equals 6.67 1011 m3 kg-1 s-1.
M is equal to 8.00 1023 kg (the planet's mass).
Gravitational acceleration on Earth's surface is equal to 9.81 m/s2.
When we change the values, we obtain:
[tex]r = [(6.67 × 10^-11) × (8.00 × 10^23) / 9.81]^(1/3)[/tex]
[tex]r = 2.33 × 10^6 m[/tex]
Therefore, 2.33 x 106 m is the necessary distance.
F = G (m1m2 / r2), where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them, can be used to express the gravitational force between two objects. When a planet and a satellite are involved, the centripetal force that holds the satellite in orbit around the planet is produced by the gravitational force. As a result, we may compare the centripetal force to gravity and find r. This results in the formula above, which we can use to calculate the necessary distance.
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catching a wave, a 73.2-kg surfer starts with a speed of 1.44 m/s, drops through a height of 1.84 m, and ends with a speed of 8.89 m/s. how much nonconservative work was done on the surfer?
The nonconservative work done on the surfer is 2845.5 J.
We can use the work-energy theorem to solve this problem. The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. In this case, we can calculate the initial and final kinetic energies of the surfer and find the difference, which will give us the net work done.
The initial kinetic energy of the surfer is:
[tex]K_i = (1/2) * m * v_i^2[/tex]
[tex]K_i = (1/2) * 73.2 kg * (1.44 m/s)^2[/tex]
K_i = 75.7 J
The final kinetic energy of the surfer is:
[tex]K_f = (1/2) * m * v_f^2[/tex]
[tex]K_f = (1/2) * 73.2 kg * (8.89 m/s)^2[/tex]
K_f = 2921.2 J
The change in kinetic energy is:
ΔK = K_f - K_i
ΔK = 2921.2 J - 75.7 J
ΔK = 2845.5 J
According to the work-energy theorem, this change in kinetic energy must be equal to the net work done on the surfer. Therefore, the nonconservative work done on the surfer is:
W_nc = ΔK
W_nc = 2845.5 J
So, the nonconservative work done on the surfer is 2845.5 J.
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a 1.00-m3 object floats in water with 20.0% of its volume above the waterline. what does the object weigh out of the water? the density of water is 1000 kg/m3.
The weight of the object out of water is 800 kg.
To solve this problem, we need to use the principle of buoyancy. When an object is placed in water, it experiences an upward force called buoyant force, which is equal to the weight of the water displaced by the object.
In this case, the object has a volume of 1.00 m³, and 20.0% of its volume is above the waterline. Therefore, the volume of the object submerged in water is:
Vsubmerged = 1.00 m3 - 0.20 x 1.00 m³ = 0.80 m³
We also know the density of water is 1000 kg/m³. Therefore, the weight of the water displaced by the object is:
Wwater = density of water x volume of water displaced
Wwater = 1000 kg/m³ x 0.80 m³
Wwater = 800 kg
This means the buoyant force acting on the object is 800 kg. In order for the object to float, the buoyant force must be equal to the weight of the object. Therefore, we can find the weight of the object as:
Weight of object = Buoyant force = 800 kg
So the object weighs 800 kg out of the water.
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although protons repel each other because each one has a positive charge, protons are stable in a nucleus because of group of answer choices the neutrons, which have a counterbalancing negative charge. the strong force. the weak force. the gravitational force. the electrons, which have a counterbalancing negative charge. neutrons getting between protons, separating the protons from each other.
The stability of the nucleus is maintained through the combined effects of the strong force and neutrons.
Although protons repel each other due to their positive charge, they are stable in a nucleus because of the strong force, which is a fundamental force that binds the particles together.
The strong force is the strongest force in nature and overcomes the electromagnetic force that causes the protons to repel each other. Neutrons, which have no charge, also play a significant role in stabilizing the nucleus.
The neutrons act as a buffer between the positively charged protons, separating them from each other and reducing the electrostatic repulsion. Electrons, which have a negative charge, are not involved in stabilizing the nucleus as they are located outside the nucleus in orbitals around the nucleus.
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when does a star become a main-sequence star? when the rate of hydrogen fusion within the star's core is high enough to maintain gravitational equilibrium when hydrogen fusion is occurring throughout a star's interior when the protostar assembles from a molecular cloud when a star becomes luminous enough to emit thermal radiation the instant when hydrogen fusion first begins in the star's core
Answer: hope it helps
Explanation:
A protostar becomes a main sequence star when its core temperature exceeds 10 million K. This is the temperature needed for hydrogen fusion to operate efficiently.
a wire of length 4.35 m and mass 137 g is under a tension of 125 n. a standing wave has formed which has seven nodes including the endpoints. a. draw the wave pattern b. what is the frequency of this wave? c. which harmonic is it? d. what is the fundamental frequency
The standing wave's fundamental frequency is the frequency of the first harmonic, which has one node and two antinodes, whereas the number of nodes determines the standing wave's harmonic number.
A 4.35 metre long, 137 gramme wire is being pulled at 125 newtons of force. With seven nodes total, including the endpoints, a standing wave has developed.
A collection of dots and dashes can be used to represent the wave pattern. The relationship between wave speed and wavelength is used to compute the standing wave's frequency. The tension in the wire and its linear mass density are used to calculate the wave speed.
The standing wave's fundamental frequency is the frequency of the first harmonic, which has one node and two antinodes, whereas the number of nodes determines the standing wave's harmonic number.
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the reason that evaporation is a cooling process is group of answer choices due to conduction and convection. the more energetic molecules escape the liquid. radiation of heat during the process. all of the above none of the above
Evaporation is a cooling process because more energetic molecules escape the liquid, carrying away heat through radiation. Answer: "None of the above".
The release of more energising molecules from the liquid during evaporation causes cooling. The heat energy that these molecules bring with them when they go lowers the liquid's temperature. Not conduction or convection, but heat radiation throughout the operation is mostly to blame for this cooling impact.
Therefore, "none of the above" is the appropriate response. In general, the energy needed to break the intermolecular bonds in the liquid, which lowers the temperature overall, is responsible for the cooling impact of evaporation.
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How can we tell if a collision is elastic or inelastic?
Answer:
The type of collision, whether elastic or inelastic, can be determined by observing the behavior of the colliding objects before and after the collision. Here are some key characteristics that can help identify whether a collision is elastic or inelastic:
Conservation of Kinetic Energy: In an elastic collision, kinetic energy is conserved, while in an inelastic collision, some of the kinetic energy may be converted into other forms of energy.
Objects' Motion After Collision: In an elastic collision, objects bounce off each other and move independently, while in an inelastic collision, objects may stick together, deform, or move as a single mass.
Restitution Coefficient: In an elastic collision, the restitution coefficient is close to 1, indicating high bounce-back, while in an inelastic collision, the restitution coefficient is less than 1, indicating less bounce-back.
Conservation of Momentum: In both elastic and inelastic collisions, momentum is conserved, but the change in velocity of the objects after the collision can indicate whether the collision is elastic or inelastic.
all of the stars we see at night with our unaided eyes are within
All of the stars we see at night with our unaided eyes are within our own Milky Way galaxy.
Most of these stars are relatively close, within a few thousand light-years from Earth.
Due to the limitations of human vision, we cannot see stars outside our galaxy without the aid of telescopes or other equipment.
The Milky Way is a barred spiral galaxy that contains hundreds of billions of stars, including our own sun. It is about 100,000 light-years in diameter and is located in the Local Group of Galaxies, which includes several other small galaxies. Our solar system is located in one of the spiral arms of the Milky Way, about 25,000 light-years from the center. The Milky Way is believed to have formed about 13.6 billion years ago and is still actively forming new stars today. The exact shape and structure of the Milky Way have been difficult to determine due to our position within the galaxy, but ongoing studies and observations are helping to improve our understanding of our galactic home.
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a merry-go-round accelerates from rest to 0.63 rad/s in 27 s . assuming the merry-go-round is a uniform disk of radius 7.5 m and mass 29000 kg , calculate the net torque required to accelerate it.
The net torque required to accelerate is 28496 Nm.
What is the net torque required to accelerate it?The net torque required to accelerate a uniform disk of radius 7.5 m and mass 29000 kg from rest to 0.63 rad/s in 27 s is needed.
The problem is asking for the net torque required to accelerate a merry-go-round from rest to a final angular velocity of 0.63 rad/s in 27 seconds. The merry-go-round is assumed to be a uniform disk, which means that its mass is evenly distributed across its entire radius. We are also given the radius of the merry-go-round (7.5 m) and its mass (29000 kg).
To solve the problem, we can use the formula:
[tex]τ = Iα[/tex]
where τ is the net torque applied to the merry-go-round, I is its moment of inertia, and α is its angular acceleration. Since the merry-go-round is initially at rest, its initial angular velocity is zero. Using the formula for angular acceleration, we can find that:
[tex]α = Δω/Δt = (0.63 rad/s - 0 rad/s) / 27 s = 0.0233 rad/s^2[/tex]
To find the moment of inertia of the merry-go-round, we can use the formula for the moment of inertia of a uniform disk:
[tex]I = (1/2)mr^2[/tex]
where m is the mass of the disk and r is its radius. Substituting the given values, we get:
[tex]I = (1/2)(29000 kg)(7.5 m)^2 = 1220625 kg m^2[/tex]
Finally, we can use the formula [tex]τ = Iα[/tex] to find the net torque required to accelerate the merry-go-round:
[tex]τ = (1220625 kg m^2)(0.0233 rad/s^2) = 28496 Nm[/tex]
Therefore, the net torque required to accelerate the merry-go-round is 28496 Nm.
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the gibbs energy change (symbolized by δ ) is a measure of the spontaneity of a process, and of the useful energy available from it.
The Gibbs energy change (ΔG) is indeed a measure of the spontaneity of a process and the useful energy available from it.
Explanation:
1. Gibbs energy (G) is a thermodynamic potential that combines enthalpy (H) and entropy (S) to predict whether a process will be spontaneous or not at a constant temperature (T) and pressure (P).
2. The change in Gibbs energy (ΔG) is calculated using the formula: ΔG = ΔH - TΔS, where ΔH is the change in enthalpy and ΔS is the change in entropy.
3. If ΔG is negative, the process is spontaneous, meaning it will proceed on its own without the need for external energy input. A negative ΔG also indicates that the system releases useful energy.
4. If ΔG is positive, the process is non-spontaneous and will require external energy to proceed. The useful energy in this case is not available, as it must be supplied from an external source.
5. If ΔG is equal to zero, the process is at equilibrium, meaning the forward and reverse processes occur at the same rate, and there is no net change in the system.
In summary, the Gibbs energy change (ΔG) is an important parameter that helps determine the spontaneity of a process and the amount of useful energy that can be obtained from it.
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after a sci a patient may experience all of the following except: a. spasticity b. resting tremor c. autonomic dysreflexia d. orthostatic hypotension
The right response is resting tremor (option b). A patient may have spasticity, autonomic dysreflexia, and orthostatic hypotension following a spinal cord injury (SCI). SCI is not often linked to resting tremor.
SCI can interfere with the body's ability to communicate with the brain, leading to a variety of physical symptoms. Spasticity, which manifests as stiffness, muscle spasms, and increased muscle tone, is a frequent consequence. Patients with SCI at or above the T6 level may develop autonomic dysreflexia, a potentially fatal illness that is characterised by an abrupt rise in blood pressure. When someone stands up, their blood pressure drops, causing lightheadedness and dizziness. This condition is known as orthostatic hypotension.
While essential tremor, Parkinson's disease, and other neurological illnesses are frequently linked to resting tremor, SCI is not typically one of them.
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The right response is resting tremor (option b). A patient may have spasticity, autonomic dysreflexia, and orthostatic hypotension following a spinal cord injury (SCI). SCI is not often linked to resting tremor.
SCI can interfere with the body's ability to communicate with the brain, leading to a variety of physical symptoms. Spasticity, which manifests as stiffness, muscle spasms, and increased muscle tone, is a frequent consequence. Patients with SCI at or above the T6 level may develop autonomic dysreflexia, a potentially fatal illness that is characterised by an abrupt rise in blood pressure. When someone stands up, their blood pressure drops, causing lightheadedness and dizziness. This condition is known as orthostatic hypotension.
While essential tremor, Parkinson's disease, and other neurological illnesses are frequently linked to resting tremor, SCI is not typically one of them.
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a merry-go-round rotates from rest with an angular acceleration of 1.50 rad/s2. how long does it take to rotate through (a) the first 4.19 rev and (b) the next 4.19 rev?
a merry-go-round rotates from rest with an angular acceleration of 1.50 rad/s2. 8.67 seconds & 20.4 seconds it take to rotate through (a) the first 4.19 rev and (b) the next 4.19 rev.
To solve this problem, we need to use the equations of rotational motion. The equation we need to use is:
θ = ωi*t + 1/2*α*t^2
where θ is the angle rotated (in radians), ωi is the initial angular velocity (in radians per second), α is the angular acceleration (in radians per second squared), and t is the time (in seconds).
For part (a), we want to find the time it takes to rotate through the first 4.19 rev, which is equivalent to 4.19*2π radians. We know that the merry-go-round starts from rest (ωi = 0) and has an angular acceleration of 1.50 rad/s^2. Substituting these values into the equation above, we get:
4.19*2π = 0*t + 1/2*1.50*t^2
Simplifying, we get:
t = √(4.19*2π / 0.75) = 8.67 seconds
Therefore, it takes 8.67 seconds to rotate through the first 4.19 rev.
For part (b), we want to find the time it takes to rotate through the next 4.19 rev. At this point, the merry-go-round is already rotating with some angular velocity, which we need to find first. Using the equation:
ωf = ωi + α*t
where ωf is the final angular velocity, we get:
ωf = 0 + 1.50*8.67 = 13.00 rad/s
Now we can use the same equation as before to find the time it takes to rotate through the next 4.19 rev, but with ωi = 13.00 rad/s:
4.19*2π = 13.00*t + 1/2*1.50*t^2
Simplifying, we get a quadratic equation:
0.75t^2 + 13.00t - 26.17π = 0
Using the quadratic formula, we get:
t = (-13.00 ± √(13.00^2 + 4*0.75*26.17π)) / 1.50
t ≈ 20.4 seconds or t ≈ -34.4 seconds
We can discard the negative solution since time cannot be negative. Therefore, it takes approximately 20.4 seconds to rotate through the next 4.19 rev.
So, the answers are:
(a) 8.67 seconds
(b) 20.4 seconds
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a flat, square coil of 16 turns that has sides of length 16.0 cm is rotating in a magnetic field of strength 0.060 t. if the maximum emf produced in the coil is 28.0 mv, what is the angular velocity of the coil (in rad/s)? (enter the magnitude.)
The angular velocity of the coil is approximately 7.27 rad/s.
The formula for the maximum emf induced in a rotating coil is given by: emf = NABw, where N is the number of turns in the coil, A is the area of the coil, B is the strength of the magnetic field, and w is the angular velocity of the coil.
Solving for w, we get: w = emf/(NAB)
Substituting the given values, we get: w = (28.0 x 10^-3)/(16 x 16 x 16 x 0.060 x 2π) ≈ 7.27 rad/s.
Therefore, the angular velocity of the coil is approximately 7.27 rad/s.
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The melting of methane hydrates on the seafloor can lead to a sharp rise in global temperatures because methane is a powerful greenhouse gas (true or false)
The melting of methane hydrates on the seafloor can lead to a sharp rise in global temperatures because methane is a powerful greenhouse gas. The statement is true.
Methane is a powerful greenhouse gas, with a global warming potential that is estimated to be about 25 times greater than that of carbon dioxide over a 100-year time horizon. Methane hydrates are solid, crystalline compounds that contain a large amount of methane gas trapped within water molecules. These hydrates are stable under certain temperature and pressure conditions, but if they become destabilized, they can release large amounts of methane into the atmosphere.
The melting of methane hydrates on the seafloor is a concern because it has the potential to release vast amounts of methane into the atmosphere, which could significantly contribute to global warming and climate change. This process could be triggered by rising ocean temperatures, changes in ocean currents, or other factors that alter the stability of the hydrates. While the exact extent and impact of this phenomenon are still uncertain, it is an area of active research and concern among climate scientists.
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a magnifying lens with a focal length of 10 cm has what magnification when the viewing eye is relaxed?
Which of the following causes air pollution?
A. All of the above.
B. burning fossil fuel.
C. volcanic eruptions
D.forest fiers
5. Explain the law of conservation of energy using a relevant example from every day life.
The law of conservation of energy states that energy is neither created nor destroyed but is transformed from one form to another.
What is law of conservation of energy?The law of conservation of energy is the law that states that energy is neither created nor destroyed but is transformed from one form to another.
Examples of activities of everyday life that shows the conservation of energy include the following:
For loudspeaker, electrical energy is converted into sound energy.For a microphone, sound energy is converted into electrical energy.For a generator, mechanical energy is converted into electrical energy.When fuels are burnt, chemical energy is converted into heat and light energyLearn more about energy here:
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An example of the law of conservation of energy is a roller coaster.
What is the law of conservation of energy?The law of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed from one form to another. This means that the total amount of energy in a closed system remains constant over time.
A roller coaster car gains kinetic energy as it moves down the track, but it also loses potential energy. At the bottom of the track, the car has the most kinetic energy and the least potential energy, while at the top of the track, it has the most potential energy and the least kinetic energy. However, the total amount of energy in the system remains constant.
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calculate the period of a horizontal mass-on-a-spring system where the stiffness of the spring is 500 n/m and the mass of the system is 25.7 kg.
The period of the horizontal mass-on-a-spring system with a stiffness of 500 N/m and a mass of 25.7 kg is approximately 1.424 seconds.
We'll use the following terms in our calculation: stiffness of the spring (k), mass of the system (m), and period (T).
The formula to calculate the period of a mass-on-a-spring system is:
T = 2π √(m/k)
where:
T = period (in seconds)
m = mass of the system (25.7 kg)
k = stiffness of the spring (500 N/m)
Now, we'll plug in the values:
T = 2π √(25.7 kg / 500 N/m)
To calculate the square root:
T = 2π √(0.0514)
T = 2π × 0.2266
Finally, multiply by 2π:
T ≈ 1.424 seconds
So, the period of the horizontal mass-on-a-spring system is approximately 1.424 seconds.
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if the car rolls down the hill ( with engine off) with negligible friction and air resistance what will its kinetic energy be
Answer:
falling iirc
Explanation:
the threshold frequency (minimum frequency) of aluminum for the photoelectric effect is in the ultraviolet range. what will happen if infrared light shines on the aluminum surface?
Any electromagnetic radiation with a frequency lower than 9.84 x 10¹⁴ Hz (infrared, microwave, radio waves) will not cause the photoelectric effect in aluminum.
If infrared light shines on the aluminum surface, no electrons will be emitted via the photoelectric effect because the frequency of infrared light is lower than the threshold frequency of aluminum. The photoelectric effect occurs when a photon with enough energy (frequency) is absorbed by an electron in a metal, causing the electron to be emitted from the metal.
The minimum frequency or threshold frequency ([tex]f_{t}[/tex]) of a metal can be calculated using the equation:
[tex]f_{t}[/tex] = Φ ÷ h
where Φ is the work function of the metal (the minimum energy required to remove an electron from the metal) and h is Planck's constant. For aluminum, Φ = 4.08 eV.
Converting Φ to joules and using h = 6.626 x 10⁻³⁴ J s, we get:
Φ = 4.08 eV x 1.6 x 10⁻¹⁹ J/eV
Φ = 6.528 x 10⁻¹⁹ J
[tex]f_{t}[/tex] = 6.528 x 10⁻¹⁹ J ÷ 6.626 x 10⁻³⁴ J s
≈ 9.84 x 10¹⁴ Hz
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The most popular grip in tennis is
the western grip
the eastern grip
the double handed grip
the continental grip
Answer:
The answer is Continental Grip
A highway curve is banked (inclined) in such a way that a car travelling at a speed of 18.0m/s can round the curve without skidding, in the absence of friction. If the banking angle is 37°, what is the radius of the curve?
In order for a vehicle travelling at 18.0 m/s to negotiate highway bend without sliding, curve must be banked (inclined). The radius of curve approximately 33.1 metres.
What is the formula for the radius of a road curve?The coefficient of side friction is found to be 0.10, and the superelevation at one horizontal curve has been set at 6.0%.the formula for calculating a road curve's radiusFind the shortest curve radius necessary to ensure safe vehicle operation.
speed of the car v = 18.0 m/s
angle of banking of the curve θ = 37°
acceleration due to gravityg = 9.81 m/s²
radius of the curve = r
N = mg * cos(θ).........1
also
N = mv² / r...........2
from equation 1 and 2 we get
mg * cos(θ) = mv² / r
r = v² / (g * cos(θ))
r = (18.0 m/s)² / (9.81 m/s² * cos(37°)) ≈ 33.1 m
Therefore, radius of the curve is approximately 33.1 meters.
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a wave has a wavelength of 5.0 meters and a frequency of 3.0 hertz. what is the wave speed? a wave has a speed of 4.5 m/s and a frequency of 2.0 hertz. what is the wavelength? a wave has a speed of 6.9 m/s and a wave;ength of 3.0 meters. what is the frequency?answer key
The wave speed in the first question is 15 m/s, the wavelength in the second question is 2.25 meters, and the frequency 2.3 Hz.
For the first question, we can use the formula v = λf, where v is the wave speed, λ is the wavelength, and f is the frequency. Substituting the given values[tex]v = 5.0 m * 3.0 Hz = 15 m/s[/tex].
For the second question, we can rearrange formula to solve for wavelength: λ = v/f. Substituting the given values λ = 4.5 m/s ÷ 2.0 Hz = 2.25 meters. For the third question, we can again rearrange the formula to solve for frequency: f = v/λ. Substituting the given values, f = 6.9 m/s ÷ 3.0 meters = 2.3 Hz.
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If L α M3.5, what happens to the luminosity if we increase M by a factor of 5?A. Increases by factor 17.5B. decreases by factor of 17.5C. increases by factor 79D. increases by factor of 280E. decreases by factor of 79
The luminosity of the star will increase by a factor of 125. Therefore, the correct answer is (D) increases by a factor of 280.
If L α M3.5, this means that the luminosity of a star is proportional to the mass raised to the power of 3.5.
If we increase the mass of the star by a factor of 5, the new mass will be 5M, and the luminosity will be:
L' = k(5M)3.5, where k is a constant of proportionality.
Expanding this expression, we get:
L' = k(5³ × M3.5)
L' = k(125 × M3.5)
L' = 125kM3.5
Thus, the luminosity of the star will increase by a factor of 125. Therefore, the correct answer is (D) increases by a factor of 280.
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A) increases by a factor of 17.5
Solution - Hi! Based on the given relationship, L α M^3.5, if we increase M by a factor of 5, we need to calculate the new luminosity (L') using the formula:
L' α (5M)^3.5
To find the factor by which the luminosity increases, we can divide L' by the original L:
(L' / L) = ((5M)^3.5) / (M^3.5)
Since both expressions are proportional, we can focus on the numeric part:
Factor = 5^3.5 ≈ 17.5
So, the luminosity increases by a factor of 17.5, which corresponds to option A.
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18. what do we mean when we say that two light rays striking a screen are in phase with each other? a) when the electric field due to one is a maximum, the electric field due to the other is also a maximum, and this relation is maintained as time passes. b) they are traveling at the same speed. c) they have the same wavelength. d) they alternately reinforce and cancel each other.
The correct option is option a) "When the electric field due to one is a maximum, the electric field due to the other is also a maximum, and this relation is maintained as time passes.".
When we say that two light rays striking a screen are in phase with each other, we mean that their electric fields are synchronized, and the electric field due to one is a maximum when the electric field due to the other is also a maximum, and this relation is maintained as time passes.
This synchronization occurs because they have the same wavelength and are traveling at the same speed.
As a result, they alternately reinforce and cancel each other, creating a pattern of light and dark bands on the screen. Therefore, the correct answer is a) when the electric field due to one is a maximum, the electric field due to the other is also a maximum, and this relation is maintained as time passes.
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