The work function for barium is 2.48eV. If light of 400nm is shined on the barium cathode, the maximum velocity of the ejected electron is 4.54 × 105 m/s.
Energy can be transferred from electromagnetic radiation to matter in the form of photons. The energy of each photon is equal to the product of Planck's constant (h) and the frequency of radiation (ν), which is related to the wavelength (λ) by the equation c = νλ, where c is the speed of light in vacuum. Because of the photoelectric effect, which is a quantum effect in which electrons are ejected from matter when exposed to radiation with sufficiently high frequency, this energy can ionize atoms or eject electrons from metal surfaces.
The maximum kinetic energy that an electron can acquire in the photoelectric effect is equal to the energy of the incident photon minus the work function of the metal. If the metal is irradiated with monochromatic radiation, the maximum kinetic energy of the photoelectron can be calculated using the equation KEmax = hν – φ, where KEmax is the maximum kinetic energy of the ejected electron, h is Planck's constant, and φ is the work function of the metal.Barium has a work function of 2.48 eV, and radiation with a wavelength of 400 nm has a photon energy of 3.1 eV. If the photon is absorbed by a barium atom, the maximum kinetic energy of the ejected electron is:KEmax = hν – φ = hc/λ – φ = 3.1 eV – 2.48 eV = 0.62 eV.To convert this to velocity, the kinetic energy must first be converted to joules, and then to velocity using the following equation:KE = ½ mv2 ⇒ v = √(2KE/m),where m is the mass of the electron, which is 9.11 × 10–31 kg.Therefore,v = √[2(0.62 × 1.6 × 10–19)/9.11 × 10–31] = 4.54 × 105 m/s.So, the maximum velocity of the ejected electron is 4.54 × 105 m/s.
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determine the values of the mass m for which this system is, respectively, underdamped, overdamped and critically damped.
The values of the mass m for which the system is underdamped, overdamped and critically damped are m < β/2ω, m > β/2ω, and m = β/2ω, respectively.
To determine the values of mass m for which the system is underdamped, overdamped and critically damped, we need to first understand the underlying mathematics behind damping. Damping is a force that acts on a body to oppose its motion, and the damping coefficient, β, is a measure of how much this damping force opposes the motion.
The damping ratio, ζ, is then a measure of how strong the damping is, in relation to the system's natural frequency. Specifically, ζ = β/2mω ,where m is the mass, and ω is the angular frequency.
Underdamping occurs when ζ is less than one, so when m < β/2ω.
Overdamping occurs when ζ is greater than one, so when m > β/2ω. Critically damping occurs when ζ equals one, so when m = β/2ω.
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A student builds an electromagnet using a variable power source and 40 turns of wire. The electromagnet is used to pick up metal paper clips. The student changes the voltage and counts the number of paper clips that are picked up. Which table could be the data the student collected?
Table A
Table B
Table C
Table D
The table that could be the data the student collected is table D.
What is an electromagnet?An electromagnet is described as a type of magnet in which the magnetic field is produced by an electric current and usually consist of wire wound into a coil.
If student builds an electromagnet using a variable power source and 40 turns of wire. We have it that the student changes the voltage and counts the number of paper clips that are picked up. The table described below could perfectly described the scenario.
This is Table D
Voltage (V)
3
6
9
12
Number of paper clips
9
18
27
36
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a rock weighs 50.0 n in air and 42.6 n in water. what is the buoyant force on the rock? group of answer choices 5.0 n 7.4 n none of these. 50 n 42.6 n
The buoyant force on the rock is 7.4 N. This is calculated by subtracting the weight of the rock in water (42.6 N) from the weight of the rock in air (50 N), yielding a result of 7.4 N.
What is Archimedes' principle?
Archimedes' principle is a scientific concept that describes the displacement of fluid when an object is placed in it. This principle is used to determine whether an object will float or sink in a fluid. Archimedes' principle is stated as follows: An object fully or partially submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. In other words, the buoyant force on an object is equal to the weight of the fluid it displaces.
The weight of the rock in the air is equal to its actual weight. However, the weight of the rock in water is decreased due to the buoyant force of the water acting on the rock. Therefore, the buoyant force on the rock can be determined by calculating the difference between the rock's weight in air and its weight in water. The buoyant force on the rock is 7.4 N. Hence, option B is the correct answer.
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an asteroid orbits the sun in a highly elliptical orbit. as the asteroid gets closer to the sun, how are the total mechanical energy and gravitational potential energy of the asteroid-sun system changing, if at all?
The total mechanical energy and gravitational potential energy of the asteroid-sun system will change.
Asteroid-sun systemAs the asteroid gets closer to the sun in its highly elliptical orbit, both the total mechanical energy and gravitational potential energy of the asteroid-sun system will change.
The total mechanical energy of the asteroid-sun system is the sum of its kinetic energy and gravitational potential energy. As the asteroid moves closer to the sun, its kinetic energy will increase due to the increase in speed, but its gravitational potential energy will decrease due to the decrease in distance from the sun. Therefore, the total mechanical energy of the asteroid-sun system will remain constant, according to the law of conservation of energy.
However, if the asteroid encounters any gravitational forces or other external forces, such as a collision with another object or a thrust from a spacecraft, its mechanical energy can change.
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The kinematic equations are only
valid if which of the following is
constant?
A) a
C) Δx
B) Vf
D) t
Answer:
a
Explanation:
kinematical equations are only valid for motion with constant acceleration (uniformly accelerated motion).
Hopefully this answer helped you!!!
a 2.0-kg block slides down a fixed, rough curved track. the block has a speed of 5.0 m/s after its height above a horizontal surface has decreased by 1.8 m. assume the block starts from rest. how much work is done on the block by the force of friction during this descent?
The amount of work done on the block by the force of friction during the descent would be 10.6 J.
Work done calculationWe can solve this problem by using the conservation of mechanical energy. The initial potential energy of the block is given by its initial height, and the final kinetic energy of the block is given by its final speed:
Initial potential energy = mgh = (2.0 kg)(9.81 m/s^2)(1.8 m) = 35.6 JFinal kinetic energy = (1/2)mv^2 = (1/2)(2.0 kg)(5.0 m/s)^2 = 25 JSince energy is conserved, the work done by friction can be calculated as the difference between the initial potential energy and the final kinetic energy:
Work done by friction = Initial potential energy - Final kinetic energyWork done by friction = 35.6 J - 25 JWork done by friction = 10.6 JTherefore, the work done on the block by the force of friction during its descent is 10.6 J.
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what is the escape velocity from a red giant with a mass of 1msun and a radius of 100rsun? you can use that the mas of the sun is msun
The escape velocity from a red giant with a mass of 1 m sun and a radius of 100 r sun can be found using the formula for escape velocity which is given by = sqrt((2GM)/r)`.
Where G is the gravitational constant and M is the mass of the red giant. We can assume that the radius of the red giant is large enough to assume that the person is starting at an infinite distance from the center of the red giant. Let us now calculate the escape velocity of the red giant.
The escape velocity of a red giant with a mass of 1 m sun and a radius of 100 r sun is approximately 141.2 km/s.The mass of the sun is `m sun = 1.989 × 10^30` kg. Given, the mass of the red giant `M = 1 m sun = 1.989 × 10^30` kg. The radius of the red giant `r = 100 r sun = 100 × 6.96 × 10^8` m `= 6.96 × 10^10` mNow, we can calculate the escape velocity using the formula: `ve = sqrt((2GM)/r)` `= sqrt((2 × 6.6743 × 10^-11 × 1.989 × 10^30)/6.96 × 10^10)` `= sqrt(4.6495 × 10^20)` `= 215545862.44` m/s `= 215545.86` km/s.
Thus, the escape velocity from a red giant with a mass of 1 m sun and a radius of 100 r sun is approximately 215545.86 km/s.
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a bowling ball has a mass of 6 kg. if you slowly roll the ball off the edge of a table 1.5 m high table, what is the kinetic energy of the ball when it hits the ground?
The kinetic energy of the ball when hits the ground is 88.2 J
The formula for calculating kinetic energy is
KE = 1/2mv²
Where KE is kinetic energy, m is mass, and v is velocity.
We have, the mass of the bowling ball is 6 kg, and it is dropped from a height of 1.5 m, we can calculate its velocity just before it hits the ground as follows:
Potential energy = mgh
Where m = mass of the object = 6 kg
g = acceleration due to gravity (9.8 m/s²), and
h = height from which the object is dropped = 1.5 m
PE = mgh
= (6 kg)(9.8 m/s²)(1.5 m)
= 88.2 J
The potential energy of the bowling ball is 88.2 J.
This is equal to its kinetic energy just before it hits the ground.
Therefore, the kinetic energy of the ball is 88.2 J.
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a ball of mass is dropped. what is the formula for the impulse exerted on the ball from the instant it is dropped to an arbitrary time later?
The formula for the impulse exerted on the ball from the instant it is dropped to an arbitrary time later is:
Impulse = (Final momentum - Initial momentum)
What is impulse?Impulse is a vector quantity having both magnitude and direction, whereas momentum is a vector quantity, but the impulse is not equal to momentum. The impulse is the change in momentum.
If a ball of mass m is dropped from rest, then its initial momentum is zero.
The final momentum of the ball after falling for time t is:
Final momentum = mv
Where v is the velocity of the ball after falling for time t.
Therefore, the impulse exerted on the ball from the instant it is dropped to an arbitrary time later is:
Impulse = (mv - 0) = mv
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an electron and a proton are each placed at rest in a uniform electric field of magnitude 498 n/c. calculate the speed of each particle 44.4 ns after being released.
An electron and a proton are placed at rest in a uniform electric field of magnitude 498 N/C. The speed of electron and proton 44.4 ns after being released is -3.87 × 10⁶ m/s and 2.13 × 10³ m/s respectively.
Given data:
Electric field (E) = 498 N/C,
Time (t) = 44.4 ns = 44.4 × 10⁻⁹ s,
Mass of electron (m₁) = 9.11 × 10⁻³¹ kg,
Mass of proton (m₂) = 1.67 × 10⁻²⁷ kg.
Formula:
The acceleration produced in the electric field is given by a = qE/m, where q is the charge of the particle, E is the electric field strength, and m is the mass of the particle.
From the above formula, we can find the acceleration produced by the electric field on the electron and proton as follows:
For electron (q = -e, where e is the charge of an electron)
a₁ = qE/m₁ = -eE/m₁
= -1.6 × 10⁻¹⁹ × 498/9.11 × 10⁻³¹
= -8.73 × 10¹⁴ m/s²
For proton (q = +e, where e is the charge of an electron)
a₂ = qE/m₂ = eE/m₂
= 1.6 × 10⁻¹⁹ × 498/1.67 × 10⁻²⁷
= 4.80 × 10⁷ m/s²
Using the kinematic equation, v = u + at, where u is the initial velocity, we can find the speed of each particle 44.4 ns after being released as follows:
For electron,
v₁ = u₁ + a₁t = 0 + (-8.73 × 10¹⁴) × 44.4 × 10⁻⁹
= -3.87 × 10⁶ m/s
For proton,
v₂ = u₂ + a₂t = 0 + (4.80 × 10⁷) × 44.4 × 10⁻⁹
= 2.13 × 10³ m/s
Thus, the speed of the electron is -3.87 × 10⁶ m/s and the speed of the proton is 2.13 × 10³ m/s.
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what is amplitude? responses the lowest point of a wave the lowest point of a wave how many of the waves occur per second how many of the waves occur per second a logarithmic unit of sound intensity a logarithmic unit of sound intensity the height of a wave
Amplitude is the height of a wave, which is the maximum displacement of the wave from its rest position. It is an important measure of the intensity or strength of a wave and is used in various fields, including acoustics, optics, and electronics.
The correct definition of amplitude is the height of a wave. Amplitude is a measure of the maximum displacement of a wave from its rest position, or equilibrium. In other words, it is the distance from the top of a peak to the bottom of a trough in a wave. Amplitude is commonly used to describe the intensity or strength of a wave, such as in the case of sound waves or electromagnetic waves. Higher amplitude waves are generally associated with louder or brighter sounds, while lower amplitude waves are associated with softer or dimmer sounds. Understanding amplitude is important in many fields, including acoustics, optics, and electronics.
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an incompressible substance with a density of 1000 kg/m3 is isothermally compressed from 100 to 1000 kpa. determine the change in enthalpy. multiple choice question. 900 kj/kg 0 kj/kg 10 kj/kg 0.9 kj/kg
The change in enthalpy is 0 J/kg if the incompressible substance with a density of 1000 kg/m3 is isothermally compressed from 100 to 1000 kpa. Thus, option b is correct.
The given data is as follows:
The density of substance = 1000 kg/m3
In-compression pressure = 100 to 1000 kph
The given substance is incompressible. So its specific volume stays constant during the process. The work done is Zero.
Assuming that the process is Isothermal, the temperature remains steady.
The change in enthalpy is calculated by using the formula:
ΔH = m × C × ΔT
The density of mass is calculated by using the formula,
m = V × ρ = 1 m3 × 1000 kg/m3
m = 1000 kg
Change in enthalpy is calculated as:
ΔH = m × C × ΔT
ΔH = 1000 kg × 0 J/(kg·K) × 0 K
ΔH = 0 J/kg
Therefore we can conclude that the change in enthalpy is 0 J/kg.
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The complete question is-
an incompressible substance with a density of 1000 kg/m3 is isothermally compressed from 100 to 1000 kph. determine the change in enthalpy. multiple choice questions.
a.900 kj/kg
b. 0 kj/kg
c.10 kj/kg
d.0.9 kj/kg
What is the function of the organelle depicted in the photo?
Answer:
It's a golgi body
Explanation:
It controls the transport system of the cell
What goes in and out the cel
Where is ozone considered a pollutant? a. In the stratosphere where it blocks the sun's rays b. In the mid-atmosphere where it prevents cloud formation. C. In the troposphere where it impairs normal lung function. d. It is a pollutant everywhere it is found.
C. In the troposphere where it impairs normal lung function.
The top view below shows a record that is spinning counterclockwise at a constant rate. Which of the following statements are true? Choose all that apply.
-A and B have the same linear velocity
-A has a greater linear velocity than B
-B has a greater linear velocity than A
-A and B have the same angular velocity
-A has a greater angular velocity than B
-B has a greater angular velocity than A
From the top view of the spinning record, we can see that points A and B are at different distances from the center of rotation. Therefore, they have different linear velocities.
A has a greater linear velocity than B: True
B has a greater linear velocity than A: False
A and B have the same linear velocity: False
However, both points A and B are at the same distance from the center of rotation. Therefore, they have the same angular velocity.
A and B have the same angular velocity: True
A has a greater angular velocity than B: False
B has a greater angular velocity than A: False
In summary,
A has a greater linear velocity than B
A and B have the same angular velocity.
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would a point closer to the center of the hard drive have a higher, lower, or the same linear acceleration?
A point closer to the center of the hard drive will have a lower linear acceleration than a point farther from the center. This is due to the fact that linear acceleration is inversely proportional to the radius of rotation. The acceleration is greatest at the outer edges and decreases toward the center.
Linear acceleration is the rate of change of the velocity of an object that moves in a straight line. It is also referred to as the object's increase in speed or decrease in speed. The same concept applies when it comes to hard drives.
It is pertinent to understand that linear acceleration decreases when the radius of the disk decreases, which means that the closer the point is to the center, the lower the linear acceleration would be. This is why the outermost tracks have higher transfer rates and are utilized more for storing data on hard drives.
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37. a wheel has a constant angular acceleration of 5.0rad/s2 . starting from rest, it turns through 300 rad. (a) what is its final angular velocity? (b) how much time elapses while it turns through the 300 radians?
This means that it took time of 60 seconds for the wheel to turn through 300 radians
The final angular velocity of the wheel can be calculated using the equation
[tex]$\omega_{f} = \omega_{i} + \alpha \cdot t$,[/tex]
where $\omega_{f}$ is the final angular velocity, $\omega_{i}$ is the initial angular velocity, $\alpha$ is the angular acceleration, and $t$ is the elapsed time. As the wheel starts from rest
($\omega_{i} = 0$),
the final angular velocity is equal to the angular acceleration multiplied by the elapsed time.
Therefore,
[tex]$\omega_{f} = 5.0 \, \text{rad/s}^2 \cdot t$.[/tex]
To find the elapsed time, we can rearrange the equation to get
[tex]$t = \frac{\omega_{f}}{\alpha} = \frac{300\, \text{rad}}{5.0\, \text{rad/s}^2} = 60\, \text{s}$.[/tex]
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as a wave approaches a shoreline at a non-parallel angle, the wave crest is bent in response to changes in wave speed. this is called .
As a wave approaches a shoreline at a non-parallel angle, the wave crest is bent in response to changes in wave speed. This is called wave refraction.
Wave refraction is the redirection of a wave, usually by the shore, so that it moves more nearly parallel to the shoreline. Wave refraction is a phenomenon that happens when waves slow down in shallow water.
When a wave moves from deep to shallow water, the shallow part of the wave slows down, making it turn. The wave's crest curves towards the shoreline in wave refraction, while the trough remains straight. When the wave is moving toward the shoreline at an angle, the crest is bent in response to changes in wave speed.
Wave refraction is important because it contributes to the development of currents along the shoreline. The swash is strong when waves are coming straight in, but when they come at an angle, the water has to flow back to the side to keep the level. As a result, a current is created that flows parallel to the shore.
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alston realizes that he wasn't paying attention when thana ran the simulation for which the charge was set to zero, and asks thana to describe the particle's motion. which response is correct?
Thana explains that when the charge is zero, the motion of the particle in the simulation is a straight line with a constant velocity.
The direction of the velocity depends on the initial conditions and the force acting on the particle. If there are no other forces acting on the particle, it will continue to move in a straight line with a constant velocity until it encounters another force or object. This is an example of Newton's First Law of Motion, which states that an object at rest will stay at rest and an object in motion will stay in motion with a constant velocity unless acted upon by an external force. If there is a force acting on the particle, it will change direction or speed up or slow down. This is an example of Newton's Second Law of Motion, which states that the force acting on an object is equal to its mass times its acceleration. The direction of the force is in the same direction as the acceleration. When the charge is zero, the particle does not experience any force, so it moves in a straight line with a constant velocity. This is a simple example of how particles can be modeled using physics simulations.
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two 4.0cm*4.0cm metal plates are separated by a 0.20-mm-thick piece of teflon. a. what is the capacitance? b. what is the maximum potential difference between the plates?
The capacitance of two metal plates separated by a 0.20-mm-thick is approximately 0.25 pF and the maximum potential difference between the plates is 8.4 kV.
a. The capacitance of two metal plates separated by a 0.20-mm-thick piece of Teflon is approximately 0.25 pF (picofarad).
b. The maximum potential difference between the two metal plates is determined by the permittivity of the dielectric material, which in this case is Teflon.
The permittivity of Teflon is about 2.1 and the capacitance of the plates is 0.25 pF, so the maximum potential difference between the plates can be calculated using the equation:
Vmax = (permittivity * Capacitance) / Area.
Therefore, the maximum potential difference between the plates is 8.4 kV.
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how many springs does it take to model the thermal energy of diamond and how many for solid argon? explain/justify your answer using appropriate components of the particle model of thermal energy and/or previous models we have used.
In order to model the thermal energy of diamond, 4 springs are required, while the model the thermal energy of solid argon 3 springs are required.
Thermal energy is the internal energy in a substance, that is, the energy of the particles that make up a substance. When two objects at different temperatures come into contact, the heat is transferred from the hotter object to the colder object until both objects reach the same temperature. A system of springs may be used to represent a solid. The particles of a solid are represented by the springs, which are elastic. The more energy the system has, the more the springs will vibrate.
The particle model of thermal energy is based on the idea that all matter is made up of tiny particles that are constantly in motion, and that the faster these particles move, the hotter the object becomes. To model the thermal energy of diamond, four springs are required because diamond is a covalent network solid in which each carbon atom is bonded to four other carbon atoms in a tetrahedral arrangement. Diamond's structure is made up of carbon atoms bonded together by strong covalent bonds. When a carbon atom is bonded to four other carbon atoms, it forms a very strong and stable tetrahedral structure. Diamond's thermal energy is modeled using four springs.
To model the thermal energy of solid argon, three springs are required because argon is a noble gas with a face-centered cubic structure. Solid argon, like other noble gases, has a simple structure. The argon atoms in solid argon are arranged in a cubic array, with an atom at each corner and one in the center of each face of the cube. To model the thermal energy of solid argon, three springs are used. The thermal energy is modeled using these three springs.
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which of the following appliances has the lowest typical energy costs? (1 point) group of answer choices dishwasher microwave oven washing machine refrigerator
Among the given options, the appliance with the lowest typical energy cost is the microwave oven. Typical energy cost refers to the average amount of money spent on energy usage by an appliance or device over a certain period of time.
Microwave ovens use electromagnetic radiation to cook or heat food, and they are generally more energy-efficient compared to other appliances such as dishwashers, washing machines, and refrigerators. This is because microwave ovens use less power and cook food faster than conventional ovens, reducing energy waste and costs. However, it is important to note that the exact energy cost of an appliance can depend on factors such as its age, model, usage, and energy efficiency rating.
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about 20% of solar radiation is absorbed by the atmosphere. this is the greenhouse effect. select an answer and submit. for keyboard navigation, use the up/down arrow keys to select an answer. a true b false c not enough information
The atmosphere's capacity to trap heat and warm the Earth is increased by human activities like burning fossil fuels and deforestation. This is the source of global warming. The correct answer is: A true
About 20% of solar radiation is absorbed by the atmosphere. This is the greenhouse effect. Greenhouse gases (GHGs) in the Earth's atmosphere keep the planet's surface warm and livable by trapping some of the heat that would otherwise be lost into space. The primary greenhouse gases are carbon dioxide, methane, water vapor, and ozone, all of which occur naturally in the atmosphere as well as being introduced by humans.The absorption of infrared radiation by atmospheric gases, clouds, and the Earth's surface is known as the greenhouse effect. This energy is transmitted back into space by the Earth's surface and atmosphere. The greenhouse effect is responsible for approximately 60 degrees Fahrenheit (33 degrees Celsius) of warming.
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What is the contour interval of this map?
v
The contour interval on a map represents an elevation difference between two contour lines next to each other.
What exactly does elevation mean?Anything that was previously elevated in height. Altitude is the distance from the sea to a point. Every sixth contour line has an index contour, which is a bolder or thicker line.
Elevation above sea level is the definition of elevation for a location. Around 13,000 feet more than sea level, I believe, is where we are now.
The contour elevation is the difference or distance between the elevation of the contour line. The elevation shift from one contour line to the next remains constant within a single map. Several maps have a contour interval of 40 to 80 feet.
Thus, the elevation difference between two contour lines placed adjacent to one another is represented by the contour interval on a map.
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calculate the acceleration of a 330000- kg jumbo jet just before takeoff when the thrust on the aircraft is 160000 n .
To calculate the acceleration of a 330000-kg jumbo jet just before takeoff when the thrust on the aircraft is 160000 N, we must use Newton's second law of motion. This states that the net force on an object is equal to the product of its mass and acceleration, or F=ma.
Thus, we can rearrange the equation to solve for acceleration, a = F/m. In this case, a = 160000 N/330000 kg = 0.485 m/s2. This means that the jumbo jet will accelerate at 0.485 m/s2 just before takeoff.
To explain further, when an object experiences a force, it will accelerate. The acceleration is determined by the size of the force, the mass of the object, and the direction of the force. In the case of the jumbo jet, the force is provided by the thrust of its engines, and the mass of the object is 330000 kg.
As the thrust is 160000 N, the acceleration of the jumbo jet will be 0.485 m/s2. This is the acceleration that the jumbo jet will experience just before takeoff.
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a cell phone battery holds a maximum charge of 1.420 ah. how long will it take a charger to fully charge the battery if it starts with zero charge and is charged at a constant rate of 900.0 ma?
If the cell phone battery starts out with no charge and is charged at a constant rate of 900.0 mA, it will take roughly 5,680 seconds or 94.7 minutes to fully charge.
What is the energy consumption of a phone charger?Electricity consumption for phone chargers is typically 5 watts (W) or less. While some faster chargers can use up to 20 W, the majority of standard chargers are closer to the 5–10 W range. Typically, phone chargers connect to a 120-volt outlet and draw one to two amps.
We can apply the following formula to resolve this issue:
time = (charge / current)
charge = 1.420 Ah x 3,600 C/Ah
= 5,112 C
The charging current is then changed from milliamperes (mA) to amperes (A):
current = 900.0 mA / 1,000 = 0.9 A
We can now enter the values into the formula as follows:
time = (charge / current)
= (5,112 C / 0.9 A)
= 5,680 seconds.
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how many conduction electrons are there in a 5.00 mm m m diameter gold wire that is 20.0 cm c m long?
There are around 2.31 x 10^17 conduction electrons in a 5.00 mm diameter gold wire that is 20.0 cm long.
The basic idea behind this answer is to use the relation between the cross-sectional area of a wire and its volume as well as the number of electrons per unit volume to determine the number of electrons in the wire.
Use the formula for the cross-sectional area of a circle, A = πr^2, where r is the radius of the wire (which is half of its diameter).If the diameter of the wire is 5.00 mm, then its radius is 2.50 mm or 0.00250 m.
Therefore, the cross-sectional area of the wire is:A = πr^2 = π(0.00250 m)^2 = 1.96 x 10^-5 m^2Now that we have the cross-sectional area of the wire, we can use this to determine its volume (since we know the length of the wire).
The formula for the volume of a cylinder is V = Ah, where A is the cross-sectional area and h is the height (or length) of the cylinder.
Therefore, the volume of the gold wire is:V = Ah = (1.96 x 10^-5 m^2)(0.200 m) = 3.92 x 10^-6 m^3Now we need to find the number of conduction electrons per unit volume of gold.
The density of gold is 19.3 g/cm^3, which means that 1 cm^3 of gold has a mass of 19.3 g. The molar mass of gold is 196.97 g/mol, and there are 6.022 x 10^23 atoms in 1 mol of gold.
Therefore, the number of atoms per cm^3 of gold is:N = (6.022 x 10^23 atoms/mol)(19.3 g/cm^3)/(196.97 g/mol) = 5.90 x 10^22 atoms/cm^3Finally, we need to know how many electrons there are per gold atom.
The atomic number of gold is 79, which means that it has 79 electrons. However, only the valence electrons (which are in the outermost shell) are involved in conduction.
Gold has one valence electron, so each gold atom contributes one conduction electron. Therefore, the number of conduction electrons per cm^3 of gold is:Ne = N = 5.90 x 10^22 electrons/cm^3
Now we can calculate the total number of conduction electrons in the gold wire by multiplying the number of electrons per unit volume by the volume of the wire:
Ne(total) = NeV = (5.90 x 10^22 electrons/cm^3)(3.92 x 10^-6 m^3) = 2.31 x 10^17 electrons
We can convert this to the number of conduction electrons in the gold wire by using the fact that there are 6.022 x 10^23 electrons in 1 mol of electrons (i.e., the Avogadro constant):
Ne(total) = (2.31 x 10^17 electrons)(1 mol/6.022 x 10^23 electrons) = 3.84 x 10^-7 mol. There are around 3.84 x 10^-7 mol of conduction electrons in the gold wire.
Use the molar mass of gold (196.97 g/mol) and the density of gold (19.3 g/cm^3) to find the mass of the gold wire:M = Vρ = (3.92 x 10^-6 m^3)(19.3 g/cm^3) = 7.56 x 10^-5 g.
Use the formula for the number of moles of a substance to find the number of moles of gold in the wire:n = M/m = (7.56 x 10^-5 g)/(196.97 g/mol) = 3.84 x 10^-7 mol.
This is the same number of moles as the number of conduction electrons in the gold wire, so we can multiply this by the Avogadro constant to find the number of electrons:
Ne = nN_A = (3.84 x 10^-7 mol)(6.022 x 10^23 electrons/mol) = 2.31 x 10^17 electronsTherefore, there are around 2.31 x 10^17 conduction electrons in a 5.00 mm diameter gold wire that is 20.0 cm long.
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what are the major factors in explaining why some jovian moons are more geologically active than terrestrial worlds of similar or larger sizes?
The major factors in explaining why some Jovian moons are more geologically active than terrestrial worlds of similar or larger sizes are the effects of tidal heating and the presence of a large planetary body providing gravitational forces.
The main factors geologically active than terrestrial worlds are also because:
The effects of Tidal heating is caused by the gravitational force of the large planetary body the moon orbits, which cause the moon to flex and deform internally, releasing energy as heat. This process is more pronounced in moons of Jovian planets due to the stronger gravitational pull of these much larger bodies. This heat is then released through the moon’s surface, causing geological activity. Terrestrial worlds do not experience such a strong gravitational pull and therefore do not experience this form of tidal heating.Overall the combination of tidal forces, volatile materials, lack of atmospheric erosion, and different composition can all contribute to the greater geological activity seen in some Jovian moons compared to terrestrial worlds
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two people are balanced on a seesaw. if one person leans inward toward the center of the seesaw, that person's end of the seesaw tends to
When two people are balanced on a seesaw, it means that their weight and position on the seesaw are equal and opposite.
This balance is maintained when both people are positioned at an equal distance from the center of the seesaw. However, if one person leans inward toward the center of the seesaw, that person's end of the seesaw tends to move downward, causing an imbalance in the system.
This imbalance occurs because the center of mass of the seesaw and the two people is no longer in the center of the seesaw. When one person leans inward, their weight shifts closer to the center of the seesaw, which reduces the moment arm of their weight relative to the center of mass.
The moment arm is the perpendicular distance between the weight and the pivot point, and it determines the torque that the weight exerts on the seesaw.
As the moment arm decreases, the torque on that side of the seesaw decreases as well, causing the seesaw to tip towards the other side. To restore balance, the other person must either move closer to the center of the seesaw or adjust their position to counteract the weight of the person who leaned inward.
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at a certain point on a heated metal plate, the greatest rate of temperature increase, 4 degrees celsius per meter, is toward the northeast. if an object at this point moves directly north, at what rate is the temperature increasing?
The rate of temperature increase when the object moves directly north is approximately 2.828 degrees Celsius per meter.
Assuming that the temperature gradient is constant in the vicinity of the point, we can use trigonometry to calculate the rate of temperature increase when an object moves directly north.
Let's define the angle between the direction of greatest temperature increase (toward northeast) and the direction directly north as θ. Since the temperature gradient is 4 degrees Celsius per meter toward the northeast, the rate of temperature increase along the direction of θ would be:
rate of temperature increase in the direction of θ = 4 cos(θ) degrees Celsius per meter
Since the object is moving directly north, the angle θ between the direction of motion and the direction of greatest temperature increase would be 45 degrees (because northeast is 45 degrees clockwise from north). Therefore, the rate of temperature increase when the object moves directly north would be:
rate of temperature increase in the north direction = 4 cos(45 degrees) degrees Celsius per meter
= 4 x 0.707
= 2.828 degrees Celsius per meter
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