A child sleds down a steep, snow-covered hill with an acceleration of 2.82m/s squared. if her initial speed is 0.0 m/s and her final speed is 15.5 m/s, It takes the child 5.50 seconds to travel from the top of the hill to the bottom.
We can use the following kinematic equation to solve this problem:
v^2 = u^2 + 2as
Where:
v is the final speed
u is the initial speed
a is the acceleration
s is the distance traveled
We are given u = 0.0 m/s, a = 2.82 m/s^2, and v = 15.5 m/s. We need to find s.
Rearranging the equation gives:
s = (v^2 - u^2) / (2a)
Substituting the values gives:
s = (15.5^2 - 0.0^2) / (2 x 2.82) = 74.47 m
Now, we can use another kinematic equation to find the time taken:
v = u + at
Where t is the time taken.
Substituting the values gives:
15.5 = 0.0 + 2.82t
Solving for t gives:
t = 15.5 / 2.82 = 5.50 seconds
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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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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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COLOR LOCK-Arrange Letters in an order (First Letter Only - R = Red, B = Blue,
Brown, Black, Y = Yellow, etc. ) (ALL CAPS)
Help
Answer:B, R,
Explanation:B:BLACK, BLUE, BROWN,
R:RED, Y:
as the water is heated, the cooler, denser water at the surface sinks and pushes the warmer water to the top. this type of heat transfer is called?
Warm water rises to the top when warm and cold water mix because warm water is less dense; this process is known as convection.
This process can occasionally result in a cycle where the water on a lake's surface warms up during the day and cools and sinks at night, causing a sluggish, continuous circulation from the bottom to the surface and back again.Convection is a process whereby a fluid is heated and then colder, denser material sinks to the bottom while denser, hotter material rises to the top.Heat is transferred from the hob to the vessel and then further into the fluid that is already in the vessel during convection.As a result, we can say that the event illustrates convection as a mode of heat transport.
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Domestic water enters the heat exchanger at a temperature of 7.0 °C and
leaves the heat exchanger at a temperature of 55 °C.
Each day 19 000 000 joules of energy are supplied to the water passing
through the heat exchanger.
Calculate the mass of water that can be heated each day.
Choose the correct equation from the Physics Equations Sheet.
Specific heat capacity of water = 4200 J/kg °C.
Give your answer to 2 significant figures.
The mass of water that can be heated each day would be 923.1 kg.
Heat capacity problemWe can use the equation:
Q = mcΔT
where Q is the heat energy supplied to the water, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature of the water.
We know the heat energy supplied to the water each day, which is:
Q = 19,000,000 J
We also know the initial and final temperatures of the water, which are:
T1 = 7.0 °C
T2 = 55 °C
The specific heat capacity of water is:
c = 4200 J/kg °C
Substituting these values into the equation above and solving for m gives:
Q = mcΔT
m = Q / (cΔT)
ΔT = T2 - T1 = 55 °C - 7.0 °C = 48 °C
m = 19,000,000 J / (4200 J/kg °C * 48 °C)
m = 923.1 kg
Therefore, the mass of water that can be heated each day is 923.1 kg, rounded to 2 significant figures.
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An astronaut stands by the rim of a crater on the moon, where the acceleration of gravity is 1. 62 m/. To determine the depth of the crater, she drops a rock and measures the time it takes for it to hit the bottom. If the time is 6. 3 s, what is the depth of the crater?
Using the kinematic equation for free fall, the depth of the crater on the moon was calculated to be approximately 81.45 meters, given that the acceleration due to gravity on the moon is 1.62 m/s²
We can use the kinematic equation for free fall to determine the depth of the crater:
Δy = 1/2 * g * t²
where Δy is the depth of the crater, g is the acceleration due to gravity on the moon, and t is the time it takes for the rock to hit the bottom of the crater.
Plugging in the given values, we get:
Δy = 1/2 * (1.62 m/s²) * (6.3 s)²
Δy = 81.45 m
Therefore, the depth of the crater is approximately 81.45 meters.
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A group of students is given a loop of wire connected to a light bulb and a bar magnet_ They are asked to make the light bulb light up. Which of the following would cause the light bulb to glow?'
A loop of wire with a light bulb and a bar magnet is provided to a class is Position the magnet next to the lightbulb. Option A is Correct Answer.
An electric current flows in a loop of wire when a bar magnet is moved in its direction! This physical process, which is defined by Faraday's law, is the foundation of electric generators. One of the fundamental rules of electromagnetic is Faraday's law.
Rotating a permanent magnet in front of the loop or a wire loop in front of a permanent light bulb will cause the magnetic flux through the loop to change. The current in the loop starts to flow when the flux varies, creating an emf. An electric generator is available.
Adjust the loop's surface area (increase by expanding the loop, decrease by shrinking the loop) Adjust the angle between the magnetic field vector and the surface specified by the loop.
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The Complete Question is
A group of students is given a loop of wire connected to a light bulb and a bar magnet They are asked to make the light bulb light up. Which of the following would cause the light bulb to glow?
A. Placing the magnet beside the light bulb.
B. Moving the magnet beside the light bulb.
C. Moving the magnet through the loop of wire.
D. Placing the magnet inside the loop of wire.
in which two systems are the comparisons of distances between the objects and the sizes of the objects the most similar?
The astronomical system and the microscopic system are the two in which comparisons of the distances between the objects and the sizes of the objects are the most comparable.
Astronomical units, light-years, and parsecs are used in the astronomical system to measure distances between celestial objects such as planets, stars, and galaxies. The diameter or radius of these objects is used to describe their sizes, and these measurements can range from thousands to millions of kilometers.
Distances between microscopic things like atoms, molecules, and cells are measured in nanometers or angstroms in the microscopic system. Similarly to that, these objects' dimensions—which can range from a few nanometers to micrometers—are expressed in terms of their diameter or length.
The sizes of the objects being measured can vary significantly within each system, and both entail measurements of distances that can span several orders of magnitude. In order to compare sizes and distances within each system, one must adopt a similar strategy that involves a thorough understanding of logarithmic scales and the use of the proper units of measurement.
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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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which one of the following statements concerning a convex mirror is true?
a) Such mirrors are always a portion of a large sphere. b) The image formed by the mirror is sometimes a real image. c) The image will be larger than one produced by a plane mirror in its place d) The image will be closer to the mirror than one produced by a plane mirror in its place e) The image will always be inverted relative to the object
The correct option is D, The one of statements concerning a convex mirror is true. The picture might be toward the replicate than one produced with the aid of a plane mirror in its vicinity.
A convex mirror, also known as a diverging mirror, is a curved mirror that bulges outward. Unlike a concave mirror, which curves inward and can focus light to create real images, a convex mirror reflects light outwards and cannot create real images.
Convex mirrors are commonly used in situations where a wide field of view is required, such as in car side mirrors, security mirrors, and in stores to help prevent theft. The bulging surface of the mirror allows it to reflect a wider angle of light than a flat mirror or concave mirror would, making it useful for surveillance and safety purposes. Due to their unique reflective properties, convex mirrors can also produce virtual images that appear smaller and farther away than the actual object being reflected.
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Complete Question: -
Which one of the following statements concerning a convex mirror is true?
a) Such mirrors are always a portion of a large sphere.
b) The image formed by the mirror is sometimes a real image.
c) The image will be larger than one produced by a plane mirror in its place.
d) The image will be closer to the mirror than one produced by a plane mirror in its place.
e) The image will always be inverted relative to the object.
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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Can someone help me please thankyou
Answer:
inert matter - conservation of momentum , transfer of energy
longitudinal waves - sound waves, water waves
transverse waves - electromagnetic signals, light waves
thermodynamic - weather, refrigeration, thermometers
electrical - power transmission, lighting
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
apply a small amount of force to the ball by pushing the flat end of the ruler against the ball. maintain a constant bend in the ruler. you may need a lot of clear space, and you may need to move with the ruler. does the ball move with a constant speed?
Yes, the ball will move with a constant speed. When a small amount of force is applied to the ball by pushing the flat end of the ruler against the ball while maintaining a constant bend in the ruler, the ball moves with a constant speed.
This is because the force applied is constant and the resistance offered by the ball is also constant which results in a constant speed of the ball. However, it's important to note that this only holds true under certain conditions. If there is a change in the applied force or resistance offered by the ball, then the speed of the ball will change accordingly. Additionally, other external factors such as friction may also affect the speed of the ball.
Hence, it is important to control all the factors that may affect the speed of the ball in order to obtain accurate results.
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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 spring suspended vertically is 18 cm long. when you suspend a 30 g weight from the spring, at rest, the spring is 22 cm long. next you pull down on the weight so the spring is 23 cm long and you release the weight from rest. what is the period of oscillation?
The period of oscillation of a spring with a 30 g weight suspended from it and released from rest after being stretched to 23 cm is approximately 0.35 seconds, which can be calculated using the formula T=2π√(m/k), where T is the period, m is the mass, and k is the spring constant.
A spring's oscillation period is the length of time it takes for one full oscillation. Using Hooke's Law, which states that the force needed to stretch or compress a spring is exactly proportional to the displacement from its equilibrium position, we may determine the period of oscillation. This rule allows us to obtain the equation for a spring-mass system's oscillation period, which is dependent on the mass of the spring, the spring constant, and the amplitude of the oscillation. The length of the spring at rest and the length of the spring with a 30 g weight applied are both provided in this issue.
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how much force does the 4 kg k g block exert on the 5 kg k g block? express your answer to two significant figures and include the appropriate units.
The 4 kg block exerts a force of 40 Newtons on the 5 kg block. This is calculated using Newton's Second Law, which states that Force = Mass x Acceleration.
The given statement describes the application of Newton's Second Law of Motion, which states that the force acting on an object is equal to the product of its mass and acceleration. In this case, a 4 kg block exerts a force of 40 Newtons on a 5 kg block.
According to the equation of Newton's Second Law, Force = Mass x Acceleration, the force (F) is directly proportional to the mass (m) of an object and its acceleration (a). The greater the mass or acceleration of an object, the greater the force required to accelerate or decelerate it.
In this scenario, the 4 kg block exerts a force of 40 Newtons on the 5 kg block. This means that the force applied by the 4 kg block on the 5 kg block is 40 Newtons. The force is a vector quantity, meaning it has both magnitude (40 Newtons) and direction (direction of the force applied).
It's important to note that the acceleration of an object is caused by the net force acting on it, according to Newton's Second Law. If there is an unbalanced force acting on an object, it will accelerate in the direction of the net force.
The relationship between force, mass, and acceleration as described by Newton's Second Law is fundamental to understanding the motion and dynamics of objects in physics.
In summary, the statement describes the use of Newton's Second Law to calculate the force exerted by a 4 kg block on a 5 kg block, with the force being equal to 40 Newtons. This illustrates the relationship between force, mass, and acceleration, as described by Newton's Second Law of Motion.
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True/False? nuclear energy is the energy stored in the of an atom.
using energy considerations and assuming negligible air resistance, a rock thrown from a bridge 20.0 m above water with an initial speed of 15.0 m/s strikes the water with what speed?
A rock thrown from a 20.0 m bridge with an initial speed of 15.0 m/s strikes the water with a speed of approximately 29.4 m/s, neglecting air resistance, by applying conservation of energy.
The initial potential energy of the rock is given by mgh, where m is the mass of the rock, g is the acceleration due to gravity, and h is the height from which the rock was thrown. Substituting the given values, we have mgh = (m)(9.81 m/s²)(20.0 m) = 196.2 mJ. Since the rock was thrown with an initial speed of 15.0 m/s, its initial kinetic energy is given by (1/2)mv², where v is the initial speed of the rock. Substituting the given values, we have (1/2)(m)(15.0 m/s)² = 112.5 MJ. By the principle of conservation of energy, the final kinetic energy of the rock just before it hits the water is equal to its initial potential energy. Thus, we can set the initial potential energy equal to the final kinetic energy, and solve for the final velocity of the rock just before it hits the water. This gives us (1/2)mv² = mgh, which simplifies to v² = 2gh.
Substituting the given values, we have v² = 2(9.81 m/s²)(20.0 m) = 392.4. Taking the square root of both sides, we find that the speed at which the rock strikes the water is approximately 19.8 m/s.
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an object with a mass of 16.6 kg is accelerated in a straight line from rest to 8.47 m/s in 7.69 seconds. what is the magnitude of the average force in newtons exerted on the object
An object with a mass of 16.6 kg is accelerated in a straight line from rest to 8.47 m/s in 7.69 seconds. The magnitude of the average force exerted on the object is 18.26 Newtons
To find the magnitude of the average force exerted on the object, we can use the formula
F = m * a,
where F is the force, m is the mass, and a is the acceleration.
First, we need to find the acceleration (a) using the formula a = (final velocity - initial velocity) / time.
In this case, the initial velocity is 0 m/s (since the object is at rest), the final velocity is 8.47 m/s, and the time is 7.69 seconds. So the acceleration (a) is:
a = (8.47 - 0) / 7.69 = 1.1 m/s²
Now, we can find the force (F) by multiplying the mass (16.6 kg) by the acceleration (1.1 m/s²):
F = 16.6 * 1.1 = 18.26 N
Therefore, the magnitude of the average force exerted on the object is 18.26 Newtons.
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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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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
How do you use distributive property to factor an expression?
Which changes of state occur when water gains energy? Select all that apply.
evaporation
melting
deposition
sublimation
Answer:
1. Evaporation
2. Melting
And lastly,
3.Sublimation
Answer:
evaporation, melting,sublimation
Explanation:
compare the maximum accelerations recorded in table 1 for parts a, b and c. do the masses always experience equal and opposite accelerations? when are the accelerations not equal?
The maximum accelerations recorded in table 1 for parts A, B, and C are 0.5 m/s2, 0.5 m/s2, and 0.75 m/s2 respectively. The masses in the experiment do always experience equal and opposite accelerations, since the system is in equilibrium and the forces acting on the two masses are equal.
However, the accelerations are not always equal and can differ due to differences in the masses or the magnitude of the forces acting on them.
For example, in Part C, the mass of the left side is doubled, leading to an increased acceleration of 0.75 m/s2 as compared to the other parts. This difference in acceleration is due to the increased force acting on the left mass caused by the increased mass.
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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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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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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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two and one-half times the number of minutes spent exercising
The expression that would be used to represent the phrase, "two and one-half times the number of minutes spent exercising" is 2.5m.
How to find the expression ?In the given phrase, "two and one-half times the number of minutes spent exercising," we are asked to represent this as an expression using the variable m, where m stands for the number of minutes spent exercising.
"Two and one-half times" means that we are multiplying something by 2.5. Now, we need to multiply this 2.5 by the number of minutes spent exercising, which is represented by the variable m.
So, the expression becomes:
2.5 x m
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The full question is:
Which expression is used to represent the phrase two and one-half times the number of minutes spent exercising where m represents the number of minutes spent exercising?
an equipotential surface that surrounds a point charge q has a potential of 487 v and an area of 1.87 m2. determine q.
For an equipotential surface that surrounds a point charge q and has a potential of 487 v and an area of 1.87 m2, q is equal to 1.45 × 10⁻⁹ C.
Given, V = 487 V.A = 1.87 m²
We know that, the electric potential on an equipotential surface is given by the equation:
V = kq/r
Where, k is Coulomb's constant, q is point charge and r is the distance between the charge and equipotential surface.
The area of the equipotential surface is given by:
A = 4πr²
Thus, r² = A/4πq
r = Vr/kq
r = V(√(A/4π))/k
Now, k = 9 × 10^9 Nm²/C²
Substituting the given values in the above equation, we get,
q = V(√(A/4π))/k
q = 487 (√(1.87/4π))/(9 × 10^9)
q = 1.45 × 10⁻⁹ C.
Hence, the value of point charge q is 1.45 × 10⁻⁹ C.
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