The new angular speed of the student is 0.592 rad/s.
StepsWe can use the conservation of angular momentum to solve this problem:
Initial angular momentum = final angular momentum
The initial angular momentum is given by:
L1 = I1ω1
where I1 is the moment of inertia of the student plus stool plus extended objects, and ω1 is the initial angular speed.
The final angular momentum is given by:
L2 = I2ω2
where I2 is the moment of inertia of the student plus stool plus objects with the objects pulled in, and ω2 is the final angular speed.
Since the moment of inertia changes when the objects are pulled in, we need to use the parallel axis theorem to calculate I2:
I2 = I1 + 2mr2
where m is the mass of each object (2.9 kg), and r is the distance from the rotation axis to the objects (0.26 m).
Plugging in the numbers, we get:
I2 = 3.4 kg m² + 2(2.9 kg)(0.26 m)²
I2 = 3.4 kg m² + 0.644 kg m²
I2 = 4.044 kg m²
Now we can solve for ω2:
L1 = L2
I1ω1 = I2ω2
(3.4 kg m² )(0.7 rad/s) = (4.044 kg m² )ω2
ω2 = (3.4 kg m² )(0.7 rad/s)/(4.044 kg m² )
ω2 = 0.592 rad/s
Therefore, the new angular speed of the student is 0.592 rad/s.
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in a sealed container with rigid walls, what happens to the pressure inside the container when the temperature is tripled?
According to the ideal gas law (PV = nRT), the pressure within the container will rise by a factor of three if the container's volume stays constant.
When the temperature is tripled, what happens to the pressure?The pressure rises as the Kelvin temperature rises. The relationship between the two amounts is direct proportionality. The pressure of the gas will treble when the Kelvin temperature is tripled.
How does rising temperature affect pressure?The average kinetic energy and the velocity of the gas particles striking the container walls both rise as the temperature rises. As the temperature rises, the pressure must as well since pressure is the force the particles per unit of area exert on the container.
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if a meteor passing by the earth has more kinetic energy then potential energy, what type of orbit will it follow?
Answer: Because energy is conserved an object can’t be “captured” into orbiting a larger object unless there is a way to transfer energy to some third thing. It has to collide, either mechanically or gravitationally, with something and transfer energy to it: another body, a cloud of gas or dust, or something.
The kinetic energy of a body gravitationally interacting changes all the time, regardless of “capture”, as it get closer to another gravitating body it speeds up because energy is conserved and the loss of gravitational potential is compensated by increase in kinetic energy. The closer a comet comes to the Sun the faster it goes. The further away it gets, the slower it goes.
in an earthquake, it is noted that a footbridge oscillated up and down in a one loop (fundamental standing wave) pattern once every 2.0 s. what other possible resonant periods of motion are there for this bridge? what frequencies do they correspond to?
In an earthquake, it is noted that a footbridge oscillated up and down in a one loop (fundamental standing wave) pattern once every 2.0 s. Other possible resonant periods of motion for this bridge include periods in multiples of 2 seconds.
Resonance refers to the condition where an external force or frequency causes an object to oscillate with a larger amplitude at a specific frequency, referred to as its resonant frequency. In general, any object has many resonant frequencies, and when excited with sufficient energy, each of these frequencies will create a resonance where the object will oscillate with a large amplitude.
The resonant frequency is affected by several factors, including an object's size and shape, and its material composition. When an object is excited at its resonant frequency, it can absorb a large amount of energy, and this can cause damage or even destruction of the object. Therefore, it is crucial to know the resonant frequencies of an object to avoid exciting it with similar frequencies.
Here, the footbridge oscillated up and down in a one loop (fundamental standing wave) pattern once every 2.0 s. This means that the footbridge oscillates at a frequency of 0.5 Hz. Therefore, other possible resonant frequencies of the bridge can be determined by multiplying this frequency by an integer (whole number) to obtain its harmonics.
For instance, the first harmonic is two times the fundamental frequency, i.e., 1 Hz, and its period is 0.5 s. The second harmonic is three times the fundamental frequency, i.e., 1.5 Hz, and its period is 0.33 s. The third harmonic is four times the fundamental frequency, i.e., 2 Hz, and its period is 0.25 s. The fourth harmonic is five times the fundamental frequency, i.e., 2.5 Hz, and its period is 0.2 s, and so on.
The above resonant frequencies correspond to the first few harmonics of the footbridge oscillation. The footbridge will respond most strongly to vibrations of these frequencies. In conclusion, the footbridge oscillates at a frequency of 0.5 Hz with a period of 2 seconds. Other possible resonant frequencies can be determined by multiplying this frequency by an integer (whole number) to obtain its harmonics. These harmonics correspond to various frequencies with corresponding periods. The footbridge will respond most strongly to vibrations of these frequencies.
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A food worker has cooled a pot of soup from 136*F to 70*F within 2 hours.What is the maximum amount of time she should take to cool the soup from 70*F to 41*F
A. 2 hours
B. 4 hours
C. 6 hours
D. 8 hours
The maximum amount of time a food worker should take to cool the soup from 70*F to 41*F is 4 hours.The correct answer is b.
According to the FDA's Food Code, potentially hazardous foods must be cooled from 135°F to 70°F within two hours, and from 70°F to 41°F within an additional four hours.Foodborne illnesses can be prevented by the following measures: Cook meat to the correct temperature.
Bacteria that cause foodborne illness can be killed by cooking food to the correct internal temperature. For example, ground beef should be cooked to an internal temperature of at least 160°F. The internal temperature should be checked with a food thermometer.
Take steps to keep the kitchen clean. It's critical to keep the kitchen clean to avoid the spread of bacteria. Countertops, utensils, and cutting boards should all be cleaned with hot soapy water.Routinely rinse fruits and vegetables. Vegetables and fruits should be thoroughly rinsed before consuming to remove any germs or dirt that might be present.
You should wash the produce under running water before cutting or eating it.Avoid cross-contamination. Keep raw meat away from cooked food to prevent contamination. You should never use the same knife or cutting board to cut both raw meat and fresh vegetables.
If you need to use the same cutting board, make sure to clean it thoroughly before reusing it.
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snow is falling vertically at a constant speed of 7.0 m/s. at what angle from the vertical do the snowflakes appear to be falling as viewed by the driver of a car traveling on a straight, level road with a speed of 32 km/h?
The angle from the vertical at which the snowflakes appear to be falling as viewed by the driver of the car is 53.3 degrees.
When the car is moving, the snowflakes appear to be falling at an angle due to the relative motion between the observer and the snowflakes. To calculate this angle, we first convert the speed of the car from km/h to m/s. Then, we use the tangent function to find the angle between the vertical direction and the apparent direction of snowfall. The tangent of the angle θ is the ratio of the horizontal and vertical components of the velocity of the snowflakes. Since the snow is falling vertically, the velocity in the vertical direction is 7.0 m/s. The horizontal component is equal to the velocity of the car, which is 8.89 m/s after conversion.
Using the tangent function, we find:
tan θ = 8.89 / 7.0
θ = 53.3 degrees
Therefore, the snowflakes appear to be falling at an angle of 53.3 degrees from the vertical as viewed by the driver of the car.
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A phoneme is the largest unit of sound in a word.truefalse
False. A phoneme is actually the smallest unit of sound in a word that can change its meaning. For example, in English, the words "cat" and "bat" differ by only one phoneme which changes the meaning of the word.
Phonemes are distinct sounds that are used to distinguish one word from another in a language. They are not the same as letters, although they are often represented by letters in written language. The number of phonemes varies across languages, with some languages having more or fewer phonemes than others.
Phonemes are important for understanding how sounds are organized in language, and they are studied in fields such as linguistics and speech pathology. By understanding phonemes and their patterns, researchers can better understand how language is processed and produced, and how language disorders may affect communication.
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Which of the curves in the figure represents an isobaric process? (a) horizontal (b) a steep curve (c) a less steeper curve (d) a very steep curve.
The curve that represents an isobaric process is the horizontal curve in the figure.
An isobaric process is a thermodynamic process that occurs at constant pressure. This means that the pressure of the system does not change during the process, and the horizontal curve in the figure represents a constant pressure.In contrast, a steep curve represents a rapid change in pressure, which indicates that the process is not isobaric. A less steep curve also indicates a change in pressure, albeit at a slower rate than a steep curve. Therefore, neither of these curves represents an isobaric process. Similarly, a very steep curve also represents a change in pressure that is not constant, and therefore, it does not represent an isobaric process.
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When a ray of light strikes a surface, it can be _, _ or _
Answer;
it can be incident ray.
long after the switch is closed and the current becomes very small, what is the voltage difference across the capacitor? long after the switch is closed and the current becomes very small, what is the voltage difference across the capacitor? it depends on the capacitance of the capacitor. it depends on the resistance of the resistor. the same as the emf of the battery roughly half the emf of the battery
After the switch is closed and the current becomes very small, the voltage difference across the capacitor depends on the capacitance of the capacitor and the initial voltage across it.
Assuming that the capacitor was initially uncharged, it will start to charge up as the current flows through the circuit. As time passes and the current becomes very small, the capacitor will approach its maximum charge and the voltage difference across it will approach the same value as the EMF of the battery. However, the voltage across the capacitor will never quite reach the full EMF of the battery because of the presence of the resistor, which limits the current and causes the charging process to be gradual.
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Using the definition of the speed of light (299,792,458), if light has a wavelength of 7E-7m, what is it's frequency?
Answer:
Frequency= velocity of radiation÷ wave length
Describe the conservation of mechanical energy of a 5.0 kg stone perched near the edge of cliff 25.0 m high which falls down to the ground below. Determine the velocity of the stone just before it hits the ground. Use the base of the cliff as a reference point, and write down all assumptions made.
NEED ASAP PLS
the fraction of oxygen molecules in air moving at more than 250 m/s is 0.0103%.
Steps
The conservation of mechanical energy states that the total amount of mechanical energy in a system remains constant, as long as no external forces act on the system. In the case of the falling stone, the mechanical energy is initially in the form of potential energy due to its position near the top of the cliff. As the stone falls, the potential energy is converted into kinetic energy, which is the energy of motion.
Assumptions:
There is no air resistance acting on the stone.
The stone is a point object with no internal energy.
The gravitational field is uniform near the surface of the Earth.
Using the conservation of mechanical energy, we can write:
Initial energy = Final energy
where the initial energy is the potential energy of the stone at the top of the cliff, and the final energy is the kinetic energy of the stone just before it hits the ground. The potential energy is given by:
PE = mgh
where m is the mass of the stone, g is the acceleration due to gravity, and h is the height of the cliff. Substituting the given values, we have:
PE = (5.0 kg)(9.81 m/s^2)(25.0 m) = 1226.25 J
The final energy is the kinetic energy of the stone just before it hits the ground. The kinetic energy is given by:
KE = (1/2)mv^2
where v is the velocity of the stone. Substituting the given mass and solving for v, we have:
v = sqrt(2KE/m)
We can use the initial potential energy to find the final kinetic energy:
PE = KE
1226.25 J = (1/2)(5.0 kg)v^2
v = sqrt(245.25) = 15.67 m/s
Therefore, the velocity of the stone just before it hits the ground is 15.67 m/s.
To determine the fraction of oxygen molecules in air moving at more than 250 m/s, we need to use the Maxwell speed distribution, which gives the distribution of speeds of particles in a gas at a given temperature. At room temperature (25°C or 298 K), the most probable speed of oxygen molecules is given by:
vmp = sqrt(2kT/m)
where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of the molecule. For oxygen (O2), m = 32 g/mol = 0.032 kg/mol.
Substituting the given values, we have:
vmp = sqrt(2(1.38x10^-23 J/K)(298 K)/(0.032 kg/mol)) = 484.5 m/s
To find the fraction of oxygen molecules moving at more than 250 m/s, we need to integrate the Maxwell distribution from 250 m/s to infinity and divide by the total number of molecules:
Using numerical integration, we find:
f = 0.000103
Therefore, the fraction of oxygen molecules in air moving at more than 250 m/s is 0.0103%.
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a 0.61 m copper rod with a mass of 0.043 kg carries a current of 15 a in the positive x direction. what are the magnitude and direction of the minimum magnetic field needed to levitate the rod?
The magnitude and direction of the minimum magnetic field needed to levitate the rod is 0.244T.
To calculate the magnitude and direction of the minimum magnetic field needed to levitate the rod, we must first calculate the magnetic force,
[tex]F_{mag}[/tex], that the magnetic field exerts on the copper rod.
This force is equal to the product of the current and the magnetic field,
[tex]F_{mag} = I *B,[/tex]
where I is the current, and
B is the magnetic field.
In this case, I = 15A, and
B is the magnitude and direction of the minimum magnetic field needed to levitate the rod.
To calculate 'B' by rearranging the equation to
[tex]B = F_{mag}/I.[/tex]
Since the force, [tex]F_{mag},[/tex] must be equal to the weight of the rod,
[tex]F_{mag} = mg[/tex],
where m is the mass of the rod, and
g is the acceleration due to gravity,
we can further rearrange the equation to B = mg/I.
Substituting the given values,
[tex]B = 0.043kg *9.8m/s^2/15A = 0.244T[/tex] in the positive x direction.
Therefore, the minimum magnetic field needed to levitate the rod is 0.244T in the positive x-direction.
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in what direction are the magnetic field lines surrounding a straight wire carrying a current that is moving directly away from you
The magnetic field lines surrounding a straight wire carrying a current that is moving directly away from you would form concentric circles around the wire, following the right-hand rule.
When a straight wire carrying a current is moving directly away from you, the magnetic field lines surrounding the wire will form concentric circles around it. The direction of these magnetic field lines can be determined by applying the right-hand rule. If you point your right thumb in the direction of the current flow, the direction of the magnetic field lines would be in the direction that your fingers curl around the wire. Specifically, the magnetic field lines will be perpendicular to the plane of the circles formed by the wire, and the direction of the field lines will be clockwise if the current is flowing towards you and counterclockwise if the current is flowing away from you. This is due to the way that the magnetic field lines wrap around the wire as a result of the current flow.
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the attraction or repulsion between electric charges
The attraction or repulsion between electric charges or the force between two charge bodies is called the coulomb force.
Coulomb's law or coulombs force (or Coulomb's inverse-square law) defines the force wielded by an electric field on an electric charge. This is the force acting between electrically charged objects and is determined by the value of the commerce between two stationary point electric charges in a vacuum. Coulomb's law states" The electrical force of magnet or aversion between two charges is equally commensurable to the forecourt of the distance that separates them." Coulomb's force is a consequence of Newton's third law that states that when two bodies interact, equal and contrary forces appear in each of them.
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Complete question: What is the attraction or repulsion between electric charges or the force between two charge bodies is called?
a circular steel wire 2.00 m long must stretch no more than 0.25 cm when a tensile force of 700 n is applied to each end of the wire. what minimum diameter is required for the wire?
A circular steel wire 2.00 m long must stretch no more than 0.25 cm when a tensile force of 700 n is applied to each end of the wire. The minimum diameter that is required for the wire is 1.50 × 10⁴ m.
The formula that would help solve the problem is:
ΔL = FL/ (πd²E × 4)
Where;ΔL = 0.25 cm=0.0025 m, F = 700N, l = 2.00 m, d = ?, E = 2.0 × 10¹¹Pa
For wire, E = Young’s modulus, and d = diameter.
Substituting values into the formula;
0.0025m = 700N × 2.00m/(πd² × 2.0 × 10¹¹Pa × 4)
0.0025m = 1400/(πd² × 8 × 10¹¹)
0.0025m = 0.00001745/d²
2.25 × 10⁸ = d²
d = √(2.25 × 10⁸) = 1.50 × 10⁴ m
The minimum diameter that is required for the wire is 1.50 × 10⁴ m.
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are the net force on an object and the acceleration of the object directly proportional?explain, using experimental data to support your answer.
Yes, the net force on an object and the acceleration of the object are directly proportional, as shown by experimental data and supported by Newton's second law of motion.
According to Newton's Second Law of Motion, the net force on an object and its acceleration are exactly related. According to this rule, an object's acceleration is inversely related to its mass and directly proportionate to the net force acting on it. The validity of the law has been shown by data from several tests that have repeatedly proven this link. One illustration of such an experiment is measuring the force necessary to accelerate an item using a spring scale. The link between force and acceleration may be determined by applying various forces and observing the resulting acceleration.
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Need help ASAP due 3:00 PM today 3/29/23
Acceleration can be determined from the slope of the velocity-time graph. The slope of the graph indicates how quickly the velocity is changing over time.
How does acceleration vary in a velocity time graph?If the slope of the graph is positive and increasing, then the acceleration is also positive and increasing. This means that the object is accelerating in the positive direction (e.g. speeding up in a positive direction).
If the slope of the graph is positive and decreasing, then the acceleration is positive but decreasing. This means that the object is still accelerating in the positive direction, but at a decreasing rate (e.g. slowing down in a positive direction).
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radiation
Electromag
8. Calculate the momentum and velocity of:
a) An electron having a de Broglie wavelength of 2.0 × 10-⁹ m.
b) A proton of mass 1.67 x 10-27 kg and a de Broglie wavelength of 5.0 nm.
19. Calculate the associated de Broglie wavelength of the electrons in an electron beam which has
been accelerated through a pd of 4000V.
20. An alpha particle emitted from a radon-220 nucleus is found to have a de Broglie wavelength of
5.7 x 10-15 m. Calculate the energy of the alpha particle in MeV.
Electron diffraction
a) The momentum of an electron having a de Broglie wavelength of 2.0 × 10⁻⁹ m is 3.31 × 10⁻²⁴ kg m/s and its velocity is 1.09 × 10⁶ m/s1.
b) The momentum of a proton of mass 1.67 x 10-27 kg and a de Broglie wavelength of 5.0 nm is 1.32 × 10⁻²² kg m/s and its velocity is 2.21 × 10⁶ m/s1.
The associated de Broglie wavelength of the electrons in an electron beam which has been accelerated through a pd of 4000V is 0.012 nm2.
The energy of the alpha particle in MeV emitted from a radon-220 nucleus is 5.5 MeV3.
de Broglie wavelengthThe de Broglie wavelength is the wavelength, λ, associated with an object and is related to its momentum and mass. According to wave-particle duality, the de Broglie wavelength is a wavelength manifested in all the objects in quantum mechanics which determines the probability density of finding the object at a given point of the configuration space1.
The de Broglie wavelength of a particle is inversely proportional to its momentum.
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if the wire used to make the filament is 0.040 mm in diameter (a typical value), how long must the filament be?
If we have the volume, mass, or material, we can use the diameter of the wire to calculate the length.
To determine the length of the filament, we need more information, such as the volume or mass of the filament, or the specific material it is made from.
Here's a general explanation assuming we have the necessary information:
1. Obtain the volume, mass, or material of the filament.
2. If you have the mass and material, find the density of the material.
Density can be found using reference sources or online databases.
3. If you have the mass and density, calculate the volume of the filament using the formula:
Volume = Mass / Density.
4. Calculate the cross-sectional area of the wire using the diameter.
The cross-sectional area (A) can be found using the formula: A = π[tex](D/2)^2[/tex],
where D is the diameter of the wire.
5. Determine the length (L) of the filament by dividing the volume (V) by the cross-sectional area (A): L = V / A.
Please provide more information about the filament, such as the volume, mass, or material, so we can help you calculate the length.
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g assuming the pressure remains constant, if the radius of a bronchial tube through which gas flows at a rate of 40 l/min is reduced by 16%, find the new flow rate through the bronchial tube.
Given that the rate of gas flow through a bronchial tube is 40 L/min and the radius of the tube is reduced by 16%, we have to find the new flow rate through the bronchial tube is: 16.4 L/min.
As per Poiseuille’s formula, the rate of gas flow through a tube is directly proportional to the fourth power of the radius, i.e., Q = k*r⁴ where Q is the rate of gas flow, r is the radius, and k is a constant.
The new flow rate of the bronchial tube after the reduction of radius can be found as follows:
Let the new radius be r’. Then, r’ = r − 0.16r = 0.84r
Therefore, Q’ = k * r’⁴= k * (0.84r)⁴= k * 0.41r⁴ (rounded to two decimal places)
Now, the rate of gas flow through the bronchial tube is 40 L/min.
Therefore, k*r⁴ = 40=> k = 40/r⁴ Substituting this value of k in the above equation, we get Q’ = 40/r⁴ * 0.41r⁴= 16.4 L/min (rounded to one decimal place)
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the magnetic field inside a 27-cm -diameter solenoid is increasing at 2.4 t/s . how many turns should a coil wrapped around the outside of the solenoid have so that the emf induced in the coil is 15 v ?
The coil wrapped around the outside of the solenoid should have 6 turns so that the emf induced in the coil is 15 v.
Given,
Diameter of solenoid, d = 27 cm; Radius, r = 13.5 cm = 0.135 m; Magnetic field, B = 2.4 T; Number of turns of coil outside the solenoid, N; Emf induced, V = 15 V.
The formula for calculating emf is given by;
e = −N dB/dt
Where, e = induced emf, N = number of turns, dB/dt = rate of change of magnetic field
Rearranging the equation;
N = − e / ( dB/dt )
Solving for N;
N = − e / ( dB/dt )
N = − ( 15 V ) / ( 2.4 T/s )
N = - 6.25 turns
The number of turns of the coil outside the solenoid should be 6.25. Since this is not possible, we round off to the nearest integer, which is 6.
Therefore, the coil wrapped around the outside of the solenoid should have 6 turns so that the emf induced in the coil is 15 V.
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according to the big bang theory, why do we live in a universe that is made of almost entirely of matter rather than antimatter?
According to the big bang theory, we live in a universe that is made of almost entirely of matter rather than antimatter because of a slight excess of matter over antimatter that occurred during the early universe.
This excess is thought to be due to a process called baryogenesis, which involves the production of baryons (such as protons and neutrons) from an initial state of pure energy during the first fractions of a second after the big bang.
The exact mechanism by which baryogenesis occurred is not well understood, but several possible theories have been proposed, including the idea that it is related to the violation of CP symmetry (which refers to the combination of charge conjugation and parity) in the early universe.
In any case, the slight excess of matter over antimatter meant that when matter and antimatter particles collided and annihilated each other during the early universe, there were more matter particles left over, which eventually led to the formation of the structures we see in the universe today.
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a person shouted at the surface of a well abd heard his echo clearly after 0.3seconds calculate the distance between the person and surface of water in the well
Answer:
Assuming that the sound wave reflected only once off the surface of the water and traveled straight back up to the person, we can calculate the distance between the person and the surface of the water in the well as follows:
Distance = (Speed of sound in air x Time)/2
Where the speed of sound in air is approximately 343 meters per second at standard temperature and pressure, and the time is 0.3 seconds.
Distance = (343 m/s x 0.3 s)/2
Where the speed of sound in air is approximately 343 meters per second at standard temperature and pressure, and the time is 0.3 seconds.
Distance = (343 m/s x 0.3 s)/2
Distance = 51.45 meters
Therefore, the distance between the person and the surface of the water in the well is approximately 51.45 meters.
If a car at rest accelerates uniformly to a speed of 144kmh-1 in 20s, then it covers a distance of:
Explanation:
144 km/hr = 40 km / s
Acceleration = change in velocity / change in time
Acceleration = 40 m/s / 20 s = 2 m/s^2
d = 1/2 a t^2 = 1/2 (2)(20^2) = 400 meters
in a worst-case design scenario, a 2000 kg elevator with broken cables is falling at 4.00 m/s when it first contacts a cushioning spring at the bottom of the shaft. the spring is supposed to stop the elevator, compressing 2.00 m as it does so. spring coefficient is 10.6 kn/m . during the motion a safety clamp applies a constant 17000-n frictional force to the elevator.
The maximum compression of the spring is approximately 0.844 m.
The potential energy of the elevator when it is at the top of the shaft is,
PE = mgh
where m is the mass of the elevator, g is the acceleration due to gravity, and h is the height of the shaft. Since the elevator is falling, its initial potential energy is converted into kinetic energy,
KE = (1/2)mv^2
where v is the velocity of the elevator just before it contacts the spring. When the elevator compresses the spring, some of its kinetic energy is converted into potential energy stored in the compressed spring,
PE = (1/2)kx^2
where k is the spring constant and x is the compression of the spring.
At the point of maximum compression, the elevator's velocity is zero, so its kinetic energy is zero. Thus, the total initial potential energy of the elevator is equal to the potential energy stored in the compressed spring,
mgh = (1/2)kx^2
Solving for x,
x = sqrt(2mgh/k)
Now we can plug in the given values,
m = 2000 kg
v = 4.00 m/s
h = 2.00 m
k = 10.6 kN/m = 10,600 N/m
F_f = 17000 N
g = 9.81 m/s^2
PE_i = mgh = 2000 kg × 9.81 m/s^2 × 2.00 m = 39,240 J
KE_i = (1/2)mv^2 = (1/2) × 2000 kg × (4.00 m/s)^2 = 16,000 J
E_i = PE_i + KE_i = 55,240 J
At the point of maximum compression, the elevator's velocity is zero, so its kinetic energy is zero. Thus, the total energy of the elevator-spring system is equal to the potential energy stored in the compressed spring,
E_f = (1/2)kx^2
Solving for x,
x = sqrt(2E_f/k)
We know that the frictional force F_f acts over a distance of 2.00 m (the distance the spring compresses), so the work done by the frictional force is,
W_f = F_f d = 17000 N × 2.00 m = 34,000 J
Since energy is conserved,
E_i = E_f + W_f
Substituting the expressions for E_i, E_f, and x,
(1/2)mv^2 + mgh = (1/2)kx^2 + F_f d
x = sqrt((mv^2 + 2mgh - 2F_f d)/k)
Plugging in the given values,
x = sqrt((2000 kg × (4.00 m/s)^2 + 2 × 2000 kg × 9.81 m/s^2 × 2.00 m - 2 × 17000 N × 2.00 m)/(10,600 N/m))
= 0.844 m
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an athlete hurts their wrist. they put an ice directly on the wrist. in which direction is the thermal energy moving?
The thermal energy is moving from the athlete's wrist to the ice.
Explanation:
Heat always flows from hotter objects to colder objects. When the athlete puts ice on their injured wrist, the thermal energy (heat) flows from the wrist, which is warmer, to the ice, which is colder. This transfer of thermal energy causes the injured wrist to cool down, reducing inflammation and pain. The ice absorbs the thermal energy from the wrist, causing it to melt and become warmer. Therefore, the thermal energy is moving from the wrist to the ice.
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what diameter must a copper wire have if its resistance is to be the same as that of an equal length of aluminum wire with diameter 3.32 mm
The diameter of the copper wire required to match the resistance of the aluminum wire is about 4.02 mm.
In order for the resistance of a copper wire to be the same as that of an equal length of aluminum wire with a diameter of 3.32 mm. A wire's resistance is influenced by its length, diameter, and resistivity. Since copper has a higher resistivity than aluminum, a copper wire of similar diameter and length to an aluminum wire will have more resistance. Here is a formula that can be used to determine the diameter of a copper wire: Where dCopper is the diameter of copper wire, dAluminum is the diameter of aluminum wire, and k is the ratio of the resistivity of copper to that of aluminum.
Since the diameter of the aluminum wire is given to be 3.32 mm, let's figure out the value of k:From the table, we can see that the resistivity of copper is 1.7 times that of aluminum, so k is 1.7:Thus, dCopper = (3.32 mm) × √(1.7) ≈ 4.02 mm.
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During reading:
1. Name two types of situations in which stars create elements and fling them out into space.
Answer: Reasons are below <3
Explanation:
Reason 1. Some of the heavier elements in the periodic table are created when pairs of neutron stars collide cataclysmically and explode, researchers have shown for the first time.
Reason 2. Light elements like hydrogen and helium formed during the big bang, and those up to iron are made by fusion in the cores of stars.
Brainliest? <33
g a car moving at constant speed around a circular track at a speed of v. the force of friction provides the necessary centripetal force to keep the car on the track. if the speed of the car is doubled, what will be the frictional force that is needed to hold the car on the road?
When the speed of the car is doubled, the centripetal force required to keep it moving in a circular path also doubles, because the centripetal force is proportional to the square of the velocity. Therefore, the force of friction required to provide the centripetal force is 4 times the original frictional force.
To see this, consider the equation for centripetal force:
Fc = mv²/r
where Fc is the centripetal force,
m is the mass of the car,
v is its velocity, and
r is the radius of the circular track.
If the speed of the car is doubled to 2v, the centripetal force required to keep it on the track becomes:
Fc' = m(2v)²/r = 4mv²/r
This means that the new centripetal force required is four times the original centripetal force. Therefore, the force of friction required to provide this centripetal force must also be four times the original force of friction:
Ff' = 4Ff
where Ff is the original force of friction and
Ff' is the new force of friction required.
So, the answer is indeed that the new frictional force required to hold the car on the road when its speed is doubled is 4 times the original frictional force.
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a string 3 m long is fixed on both ends and vibrates in its fundamental mode. what is the wavelength of the vibration?
The wavelength of the vibration of a string 3 m long fixed on both ends in its fundamental mode is 6 m.
The lowest part of a harmonic vibration, or the lowest frequency at which an oscillation occurs is called fundamental mode of vibration.
The basic mode, or first harmonic, is the simplest normal mode, in which the string vibrates in a single loop and is denoted n = 1.
Given, Length of string, l = 3 m
The wavelength of the vibration can be calculated by the following formula:
Wavelength (λ) = 2l/n
where n is the harmonic or mode of vibration.
As it is vibrating in its fundamental mode, n = 1.
Therefore, Wavelength (λ) = 2l/n= 2 × 3 m / 1= 6 m
The wavelength of the vibration is 6 m.
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