what is the maximum standard size overcurrent protective device that may be used to protect a storage-type water heater with a rating of 4,500 watts,

Angular velocity depends upon the radius of the sphere and the height of the incline when a solid sphere rolls without slipping down an incline plane. The correct options are b and c.

A sphere is a three-dimensional shape that is circular and completely round, like a ball or globe. Solid spheres, also known as balls, are objects with a radius and a center point that are fully enclosed by a curved surface in three dimensions.

The angular velocity of a solid sphere rolling down an incline plane without sliding depends on the radius of the sphere and the height of the inclination.

The angular velocity is unaffected by the length of the slope or the mass of the sphere. This is due to the fact that the angular velocity is governed by the sphere's moment of inertia and rotational kinetic energy, both of which are dictated by the sphere's form (radius) and the height of the incline.

Therefore, options are b and c are correct.

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The probable question may be:

Starting from rest, a solid sphere rolls without slipping down an incline plane. at the bottom of the incline, what does the angular velocity of the sphere depend upon? check all that apply.

a. The angular velocity depends upon the length of the incline b. The angular velocity depends upon the radius of the sphere c. The angular velocity depends upon the height of the incline d. The angular velocity depends upon the mass of the sphere

Answer:

Its C

Explanation:

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As the volume of air in the lungs of the diver will reduce when she descends to 10m with air in her lungs without breathing in or out, the approximate new value will be 17.56 L, calculated using Boyle's law.

Boyle's law states that the pressure exerted by a given mass of gas is inversely proportional to its volume at a constant temperature. The mathematical expression for Boyle's law is: P1V1 = P2V2where, P1 and V1 are the initial pressure and volume of the gas, respectively, and P2 and V2 are the final pressure and volume of the gas, respectively.

Let V1 be the initial volume of air in the lungs of the diver, which is 6L. Let P1 be the atmospheric pressure at the surface of the water, which is 1 atm. Let P2 be the pressure at 10 m depth, which can be calculated using the hydrostatic equation: P2 = P1 + ρghwhere, ρ is the density of water, g is the acceleration due to gravity, and h is the depth of the water.

The density of water at standard temperature and pressure is 1000 kg/m3. Therefore, ρgh = 1000 kg/m3 × 9.81 m/s2 × 10 m = 98,100 Pa. Hence, P2 = 1 atm + 98,100 Pa = 2.05 atm. Substituting the values in Boyle's law equation, we get:1 atm × 6 L = 2.05 atm × V2. Therefore, V2 = (1 atm × 6 L) / 2.05 atm = 17.56 L. Approximately, the new value for the volume of air in the lungs of the diver would be 17.56 L.

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Therefore, the momentum of the car is -22555 kg*m/s.

As a result, when the speed of a 1500 kg weighted car increases uniformly from 36 km/h to 72 km/h, the change in momentum is 15000 kgm/s.

In this instance, the car weighs 347 kg and travels at a speed of -65 m/s (negative velocity indicates that the car is moving to the left).

As a result, the car's momentum can be calculated as:

momentum = mass x velocity

momentum = 347 kg x (-65 m/s)

momentum = -22,555 kg m/s

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A shadow zone occurs for P-waves because P-waves refract as they go through the outer core, following a curved path through the mantle, and they do not travel through the outer core.

In more detail, P-waves are generated during earthquakes and propagate through Earth's layers. When they reach the outer core, which is liquid, their speed decreases, causing them to refract or bend.

This refraction creates a curved path through the mantle, leading to an area on Earth's surface where P-waves are not detected, known as the shadow zone. The shadow zone occurs between approximately 103 and 142 degrees from the earthquake's epicenter.

P-waves can still be detected beyond this range because they refract again as they exit the outer core, returning to a more direct path. The fact that P-waves do not travel through the outer core contributes to the formation of the shadow zone, as their energy is not transmitted through this layer.

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An air temperature measuring device used to measure the temperature in a cooler must be accurate to within +/- 1 degree Celsius.

There are many different types of temperature measuring devices available, each with its own level of accuracy and precision.

In general, however, a high-quality air temperature measuring device should be accurate to within +/- 1 degree Celsius.

This level of accuracy is sufficient for most applications, including measuring the temperature inside a cooler. However, if a higher level of accuracy is required, such as in scientific or industrial settings, more precise devices may be necessary.

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If her center of mass accelerates only horizontally, the magnitude of the minimum static friction needed so she won't slip is 52 lb.

To find the speed increase of the player, we can utilize the equation a = Δv/Δt, where Δv = 15 ft/s (last speed) and Δt = 2 s (time taken to arrive at that speed). In this way, a = 7.5 ft/s².

To work out the base static erosion expected to forestall slipping, we want to consider the powers following up on the player. The player's weight acts descending (W = mg = 5.59 slug x 32.2 ft/s² = 180 lb), and the power of static erosion acts on a level plane the other way to the course of movement. The greatest power of static grinding is equivalent to the coefficient of static contact (μs) increased by the ordinary power (N = W).

Since the player isn't slipping, the power of static erosion should be equivalent to or more noteworthy than the power expected to evenly speed up her. Accordingly, we can set the power of static contact equivalent to ma*ma (mass x speed increase), which gives:

μsN = ma*ma

μs(W) = ma*ma

μs(180 lb) = (5.59 slug)(7.5 ft/s²)

μs = 0.29

In this manner, the extent of the base static grating required so she won't slip is 0.29 times the heaviness of the player, or around 52 lb.

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The energy density of gasoline is 45 MJ/kg. This high energy density makes gasoline a popular fuel source for internal combustion engines, despite its negative impact on the environment.

The energy density (energy per mass) of gasoline is 45 MJ/kg. This means that when one kilogram of gasoline is burned, it releases 45 megajoules of energy. This is why gasoline is a popular fuel for internal combustion engines, as it contains a high amount of energy per unit of mass. Gasoline is composed of a variety of hydrocarbons, which contain a high amount of energy due to the presence of carbon-carbon and carbon-hydrogen bonds.

When gasoline is burned, these bonds are broken, releasing energy in the form of heat and light. This energy is then used to power vehicles, generators, and other equipment. The energy density of gasoline is an important factor to consider when comparing different fuel sources. For example, while batteries can store a large amount of energy per unit of mass, they are not as energy-dense as gasoline. This is one reason why gasoline is still widely used for transportation, despite its negative impact on the environment.

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Answer:

↓↓↓

Explanation:

For calculating the standard deviation you can use the formula:-

[tex]\mathrm{Standard \;deviation=\sqrt{\cfrac{Sum\;of\;(deviations\; from\;the\; mean)^{2} }{Total \; numbers \; of\; data\; values-1} } }[/tex]

_________________________

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The current flowing through larger loop of wire creates a magnetic field. When the current increases, magnetic field also increases, which induces a current in smaller ring of wire through phenomenon of electromagnetic induction.

In this case, if induced current flows in opposite direction to the current in the larger loop, it is counterclockwise, and it is caused by self-inductance. On other hand, if induced current flows in the same direction as current in larger loop, it is clockwise and caused by mutual inductance. Self-inductance occurs when a changing current in a wire induces a voltage in the same wire, while mutual inductance occurs when the changing current in one wire induces a voltage in another wire in close proximity.

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The error in setup may result in inaccurate experimental data, affecting the outcome and Reliability of the experiment.

1. Gas flow: The gas flow may be disrupted, as the longer tube is meant to be submerged in the liquid (usually water) to collect the gas, while the short tube should be connected to the gas source.

2. Inefficient collection: With the long tube connected to the gas source, the gas may not be collected efficiently, causing some of it to escape before reaching the submerged end.

3. Liquid displacement: Since the short tube is not designed to be submerged, it might not displace the liquid effectively, leading to an inaccurate measurement of the gas volume.

4. Safety concerns: This incorrect setup may also pose safety risks, especially if the gas being collected is toxic or flammable.

5. Data accuracy: The error in setup may result in inaccurate experimental data, affecting the outcome and reliability of the experiment.

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The required position of motion if the weight is released 1 m below the equilibrium position with an upward velocity of 12 m/s is calculated to be 5/3 e^(-8t) -2/3 e^(-2t).

Mass m is attached to the spring with the spring constant k and β be the positive damping constant. According to Newton's second law,

m d²x/dt² = -kx - β dx/dt

where,

The displacement from the equilibrium position is x(t)

The equation can be re-written as,

d²x/dt² + β/m dx/dt + k/m x = 0

Mass is given as 1 kg

k is given as 16 N/m

β is given as 10

d²x/dt² + 10 dx/dt + 16 x = 0

The auxiliary equation can be written as,

m² + 10 m + 16 = 0

Its solutions are, m = -8, -2

The general solution can be written as,

x(t) = c₁ e^(-8t) + c₂ e^(-2t)

From the given conditions, we can write,

x(0) = 1 m

x'(0) = 12 m/s

We can write the equation of motion as,

x(t) = 5/3 e^(-8t) -2/3 e^(-2t)

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When a pendulum is 4 meters long and it swings so that the mass at the bottom rises above 1 meter above its lowest position, the angle that the pendulum has swung through is approximately  53.13 degrees.

The angle that the pendulum swings through can be calculated using the law of cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.

In this case, the pendulum can be treated as a simple pendulum, which means that its motion can be approximated as a simple harmonic motion. The amplitude of this motion is the maximum angle through which the pendulum swings, and is related to the length of the pendulum and the maximum height that the mass reaches.

The maximum height that the mass reaches is 1 meter above its lowest position, which means that the total height that the mass travels is 4 + 1 = 5 meters. This is also the length of the hypotenuse of a right triangle, with the pendulum length of 4 meters as one of the legs.

The other leg is the distance that the mass moves horizontally, which can be calculated as the square root of the difference between the hypotenuse squared and the length of the other leg squared:

distance = sqrt(5^2 - 4^2) = 3 meters

The angle that the pendulum swings through is then given by the inverse cosine of the ratio of the adjacent leg to the hypotenuse:

angle = cos^-1(3/5) = 53.13 degrees

Therefore, the pendulum swings through an angle of approximately 53.13 degrees.

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The kinetic energy required for the satellite to attain a geosynchronous orbit is approximately 3.00 × 108 J.

When answering questions on Brainly, a question-answering bot should always be factually accurate, professional, and friendly, be concise and not provide extraneous amounts of detail, and use the following terms provided in the student question while also ignoring any typos or irrelevant parts of the question.

In response to the student question, we will calculate the gravitational potential energy and kinetic energy required for a 3120-kg satellite to attain a geosynchronous orbit.

Gravitational potential energyTo calculate the gravitational potential energy required to attain a geosynchronous orbit, we use the formula:U = -G (Mm/r)where U is the gravitational potential energy, G is the universal gravitational constant (6.67 × 10-11 N m2/kg2), M is the mass of the Earth (5.98 × 1024 kg),

m is the mass of the satellite (3120 kg), and r is the radius of the geosynchronous orbit (42,164 km).Substituting these values into the equation:U = -6.67 × 10-11 × 5.98 × 1024 × 3120 / 42,164 × 103U = -9.84 × 1010 JSo the gravitational potential energy required for the satellite to attain a geosynchronous orbit is approximately 9.84 × 1010 J.

Kinetic energyTo calculate the kinetic energy required to attain a geosynchronous orbit, we use the formula:KE = (1/2)mv2where KE is the kinetic energy,

m is the mass of the satellite (3120 kg), and v is the velocity of the satellite just before launch (456 m/s).Substituting these values into the equation:KE = (1/2) × 3120 × (456)2KE = 3.00 × 108 J

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The homogeneous portion of a mixture that is characterized by uniform properties and capable of being separated by mechanical means is called a phase.

A phase can be a solid, liquid, or gas, and it can be identified based on its physical and chemical properties. Separation of phases can be achieved by mechanical means such as filtration, centrifugation, or sedimentation. The ability to separate phases is important in various fields such as chemistry, biology, and engineering, as it allows for the isolation and purification of desired components from a mixture. The term "homogeneous" means that the components are evenly distributed throughout the phase.

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Explanation: In a double beam spectrometer with a reference cell, interferences due to the light source, the environment, and the sample holder can be subtracted out of an air spectrum.

The reference cell is filled with a gas that is transparent and has no absorption bands in the spectral range of interest. The reference cell and the sample cell are alternatively placed in the path of the light source. The detector records the intensity of the light passing through both cells, which is then compared to the intensity of the light passing through the sample cell only.

By using the reference cell as a baseline, any interferences due to the light source or the environment (e.g., variations in temperature, pressure, or humidity) can be subtracted out, as these will affect the intensity of the light passing through both cells equally. Similarly, any interferences due to the sample holder or any contaminants in the sample can be subtracted out, as these will affect the intensity of the light passing through the sample cell only.

The result is a spectrum that reflects only the absorption or transmission of the sample itself, without interference from other sources.

When using a double beam spectrometer with a reference cell, several interferences can be subtracted out of an IR spectrum which are: Background absorption, Stray light, Sample cell absorption and Instrumental noise.

A spectrometer is an instrument that measures the light intensity and the wavelength of light. The double beam spectrometer works on the principle of the single beam spectrometer but with two beams of light. The use of a double beam spectrometer with a reference cell enables you to measure the absorption of infrared radiation at different wavelengths due to a specific chemical compound.

Interferences that can be subtracted out of an IR spectrum due to the usage of a double beam spectrometer with a reference cell:

1. Background absorption: Background absorption occurs when an IR beam from the source is absorbed by the atmosphere or by the instrument components. This absorption can be reduced by subtracting the IR spectrum of the reference material from the spectrum of the sample.

2. Stray light: Stray light is a problem that occurs when the IR beam from the source is not completely focused on the sample. This leads to a low intensity of the IR beam reaching the detector. It can be reduced by the use of appropriate filters.

3. Sample cell absorption: This is the absorption of the sample cell material that contributes to the IR spectrum. This can be corrected by subtracting the spectrum of the empty reference cell from the spectrum of the sample.

4. Instrumental noise: This is the background noise in the IR spectrum that is due to the instrument. It can be reduced by using appropriate signal processing techniques.

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To determine the work done on the object from 0s to 5s, a student can use the equation ΔK = (1/2)mv², where ΔK is the change in kinetic energy of the object, m is its mass, and v is its velocity.

Since the velocity of the object is changing with time, the student can use the equation ΔK = (1/2)mΔv², where Δv is the change in velocity of the object from 0s to 5s. To find Δv, the student can read the initial velocity, v0, from the y-axis at 0s and the final velocity, vf, from the y-axis at 5s. Then, Δv = vf - v0.

Substituting the values of Δv and m into the equation ΔK = (1/2)mΔv², the student can calculate the change in kinetic energy of the object from 0s to 5s. This change in kinetic energy represents the work done on the object during this time interval.

Using the given values in the problem, the mass of the object is 2 kg. The initial velocity, v0, can be read from the y-axis at 0s, which is approximately 0 m/s. The final velocity, vf, can be read from the y-axis at 5s, which is approximately 4 m/s.

Therefore,

Δv = vf - v0

     = 4 m/s.

Substituting these values into the equation,

we get

ΔK = (1/2)(2 kg)(4 m/s)²

      = 16 J.

Therefore, the work done on the object from 0s to 5s is 16 J.

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By Lenz's law, the induced current in the copper loop will flow in a clockwise direction when viewed from above the magnet.

Lenz's Law, which stipulates that the direction of the induced current is such that it opposes the change in magnetic flux that caused it, may be used to determine this. The magnetic flux through the copper loop grows as the magnet's north pole gets closer, causing a current to be induced and a magnetic field to be created that opposes the magnetic field that is getting closer. This necessitates that, when viewed from above the magnet, the induced current flow in a clockwise direction.

The magnetic flux through the copper loop also reduces as the magnet's north pole moves away from it, causing a current to flow through the loop and create an opposing magnetic field to the one that is leaving. To counteract the shift in magnetic flux, the induced current must continue to flow in a clockwise direction.

Hence, when viewed from above the magnet, the induced current in the copper loop will move in a clockwise direction.

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Your question is incomplete. The complete question is:

The north pole of a magnet is at a set distance from a copper loop which is rotating as shown below. if you are looking at the loop from above the magnet, will you say the induced current is circulating clockwise, counterclockwise, or is equal to 0? Refer to the image attached to solve the question.

If the pulley were not frictionless, the total kinetic energy would be smaller than the magnitude of the potential energy change.

1. In a frictionless pulley system, the total mechanical energy (potential energy + kinetic energy) is conserved. This means that any decrease in potential energy will result in an equal increase in kinetic energy.
2. However, when there is friction in the pulley, some of the mechanical energy is lost as heat due to the friction between the pulley and the rope.

This energy loss results in a decrease in the total mechanical energy of the system.
3. As a result, when the potential energy of the system decreases (e.g., when a weight is lifted), the total kinetic energy gained by the system will be less than the potential energy lost, as some of the energy has been dissipated as heat due to friction.
4. Therefore, when there is friction in the pulley, the total kinetic energy will be smaller than the magnitude of the potential energy change.

This is because some of the energy that would have been converted to kinetic energy is instead lost to the environment as heat.
In summary, a non-frictionless pulley system would have a smaller total kinetic energy compared to the magnitude of the potential energy change due to energy loss as heat from friction.

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The energy density of butter and similar foods is 4.5 MJ/kg. This value represents the amount of energy stored in a given mass of food and is related to the food's calorie content.

The energy density (energy per mass) of butter and similar foods can be measured in megajoules per kilogram (MJ/kg). Energy density is important for understanding the amount of energy stored in a given mass of food, which is related to its calorie content.


1. Determine the macronutrient content of the food (i.e., grams of fat, carbohydrates, and protein per serving).
2. Multiply the grams of fat by 9 kcal/g, as fat provides 9 kcal of energy per gram.
3. Multiply the grams of carbohydrates and protein by 4 kcal/g, as both carbohydrates and proteins provide 4 kcal of energy per gram.
4. Add the energy content from each macronutrient to get the total energy content of the food.
5. Divide the total energy content by the mass of the food (in kg) to obtain the energy density (in MJ/kg).

Among the given answer choices, the correct energy density for butter and similar foods is 4.5 MJ/kg. This value is equivalent to 1,000 kcal/kg, as there are approximately 0.004184 MJ in 1 kcal. Butter and similar high-fat foods have high energy densities due to their high fat content, which provides more energy per gram compared to carbohydrates and proteins.

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The true statement about mass movement is: some mass movements occur with no discernible trigger.

Mass movements can be caused by various factors, such as changes in slope, water saturation, or even sudden events like earthquakes, not all events have a discernible trigger. Some events occur due to natural processes such as erosion or weathering, while others may be influenced by human activity.

However, water does play a significant role in mass movement events, as saturation with water can increase friction among particles and trigger movement. Sometimes they can happen without a clear, identifiable cause.

Therefore some mass movements occur with no discernible trigger.

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Light is observed to converge to a point after being reflected from a plane mirror. The incident rays were diverging before striking the mirror.

Light is observed to converge to a point after being reflected from a plane mirror. This can only happen when the incident rays are diverging before hitting the mirror. When diverging rays strike the plane mirror, they reflect off the surface and follow the law of reflection.

The angles of incidence and reflection are equal, causing the rays to appear as if they are converging towards a point behind the mirror. This point is called the virtual focus or the virtual image, and it is not an actual physical point where light converges. Instead, it is the point where the reflected rays seem to be coming from when extended backward.

This phenomenon occurs because plane mirrors form virtual images of objects, and the images are the same distance behind the mirror as the object is in front of it.

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Answer:

3. descriptive

Explanation:

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When an aperture is placed in front of a converging lens, the image will remain real, but its brightness will decrease, and its sharpness may improve due to reduced spherical aberration.

A converging lens focuses incoming parallel rays towards its focal point. If an aperture, like an iris, is placed in front of the lens, only the central rays will pass through. This will reduce the amount of light entering the lens, which in turn decreases the brightness of the image.

However, since the rays passing through the central part of the lens are less affected by spherical aberration, the image's sharpness may improve. The image remains real as the nature of the lens and the object's position outside the focal point do not change.

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With the river bed. Assuming the contact area is proportional to the square of the particle's diameter:
F = τc × A
A ≈ D²

To calculate the critical tractive force necessary to dislodge a particle with an average Diameter of 70mm in a river bed, you can follow these steps:

1. Determine the particle's size (D) and convert it to meters: D = 70mm = 0.07m.

2. Calculate the submerged weight (Ws) of the particle. You'll need to know the specific gravity (G) of the particle material and the density of water (ρw). Assuming a typical specific gravity of 2.65 for sediment particles and water density of 1000 kg/m³:
Ws = (G - 1) × ρw × V × g
where V = (4/3)π(D/2)³ is the particle volume and g = 9.81 m/s² is the gravitational acceleration.

3. Calculate the critical shear stress (τc) using the Shields equation:
τc = ρw × g × R × (D/2)
where R is the submerged specific gravity, R = G - 1.

4. Determine the critical tractive force (F) by multiplying the critical shear stress by the particle's contact area (A) with the river bed. Assuming the contact area is proportional to the square of the particle's diameter:
F = τc × A
A ≈ D²

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The  change in gravitational potential energy of the ball is 83.3 J.

When a ball of mass 5.0 kg is lifted off the floor a distance of 1.7m, what is the change in gravitational potential energy of the ball?The change in gravitational potential energy of the ball is determined by the formula given below;

ΔPEg=mgh

Where;ΔPEg = Change in gravitational potential energy.m = Mass of the object.

g = Acceleration due to gravity.

h = Height of the object.The mass of the ball is given as 5.0 kg,

and the height it was lifted is 1.7 m.

Acceleration due to gravity, g, is 9.8 m/s2.

Substituting these values in the above formula gives the change in gravitational potential energy of the ball.

ΔPEg= mgh

= 5.0 kg × 9.8 m/s2 × 1.7

m= 83.3 J

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To make a proton undergo cyclotron motion, the magnetic field must be perpendicular to the direction of motion of the proton.

This is because the force on a charged particle moving in a magnetic field is given by the Lorentz force: F = q(v x B) where F is the force on the charged particle, q is the charge of the particle, v is the velocity of the particle, and B is the magnetic field. The direction of the force is perpendicular to both v and B, and is given by the right-hand rule. If the magnetic field is perpendicular to the direction of motion, the force will always be perpendicular to the velocity, which causes the proton to undergo circular motion in a plane perpendicular to the magnetic field. This is called cyclotron motion.

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Answer:

The earth rotates once each day.

We know that because the earth rotates daily and the sun rises in the east and sets in the west the moon must also rise in the east and set in  the west.

It takes the moon about 28 days to go around the earth so it will travel 1/28 the way around the earth in a single day so it will appear much like the sun,

Note that if we choose the earth to rotate counter clockwise about the sun the moon will also be rotating counter clockwise about the earth.

The moon rises in the east and sets in the west because earth rotates once each day.

Rotation refers to the act of rotating or spinning around an axis or center. The earth rotates, which means that it spins around its axis. The earth rotates once every 24 hours, which results in day and night.

Around the same time that Earth spins, the Moon orbits Earth. The moon's orbit is about 27.3 days long. That's why it takes roughly 27 days for the Moon to return to the same position relative to the sun and Earth each month. Because of the earth's rotation, the moon appears to rise in the east and set in the west.

The moon rises in the east and sets in the west because Earth rotates once each day. This rotation causes the appearance of celestial objects, like the moon, to move across the sky from east to west.

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Paula is investigating the electrical conductivity of various materials, which falls under the category of electromagnetism in the field of physics.

The division of physics known as the  electromagnetism studies  aelectromagnetic force that exists between electrically charged particles. One of the four fundamental forces, the electromagnetic force, produces electromagnetic fields such as magnetic, electric, and optical fields.

An electromechanical generator's internal field serves as an illustration. Electric and magnetic fields that are quickly varying travel as waves and make up electromagnetic waves. When an electrically charged object or magnet accelerates, electromagnetic waves are released. Light is the common name for these waves.

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This means that no heat is required to maintain the temperature inside the enclosure at 55°F, since the outside temperature is also 55°F and there is no temperature difference.

Q = UAΔT

U = 1/r

So, U = 1/20 = 0.05 (units: Btu/hft^2°F)

ΔT = Ti - To

Consequently, the quantity of warmth required to heat the enclosure is:

Q = UAΔT = 0

Temperature is a physical quantity that reflects the degree of hotness or coldness of an object or a system. It is a measure of the average kinetic energy of the particles that make up the object or system. The SI unit of temperature is Kelvin (K), although other units such as Celsius (°C) and Fahrenheit (°F) are also commonly used.

In physics, the temperature is closely related to other physical quantities such as heat, energy, and entropy. Heat is the transfer of thermal energy between two systems at different temperatures, and the direction of heat flow is always from the hotter system to the colder system. The amount of heat transferred depends on the temperature difference between the two systems and their thermal conductivities.

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(a) The new angular velocity of the merry-go-round is 0.048 rad/s.

(b) The new angular velocity of the merry-go-round is 198.03 rad/s.

As per Given data : The diameter of the merry-go-round = 4.2 m

Angular velocity of the merry-go-round = 0.80 rad/s

Number of people standing on the ground = 4 each of mass 65 kg

Total moment of inertia = I

Taking the moment of inertia of 4 people standing on the edge of the merry-go-round to be I',

the new moment of inertia is given by:

I" = I + I'

Given that each person on the edge of the merry-go-round has a mass of 65 kg

Hence, the moment of inertia of 4 people standing on the edge of the merry-go-round is I' = 4 × mr²

where m is the mass of each person = 65 kg and r is the radius of the merry-go-round = 2.1 m

Therefore,

I' = 4 × (65 kg) × (2.1 m)²= 10962 kg·m²

Now, the total moment of inertia

I" = I + I'= 700 kg·m² + 10962 kg·m²= 11662 kg·m²

(a) When the 4 people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round, the moment of inertia increases from I to I".

To find the new angular velocity ω', we can use the conservation of angular momentum:

[tex]L_{initial}[/tex] = [tex]L_{final}[/tex]

where L is the angular momentum

[tex]L_{initial}[/tex]= Iω

[tex]L_{initial}[/tex] = (700 kg·m²) × (0.80 rad/s)

[tex]L_{initial}[/tex] = 560 kg·m²/s

[tex]L_{final}[/tex] = I" ω'ω'

[tex]L_{final}[/tex] = [tex]L_{final}[/tex] / I"

[tex]L_{final}[/tex] = [tex]L_{initial}[/tex] / I"

[tex]L_{final}[/tex] = (700 kg·m² × 0.80 rad/s) / (11662 kg·m²)

[tex]L_{final}[/tex] = 0.048 rad/s

(b) If the 4 people were initially on the merry-go-round and then jumped off radially, the moment of inertia decreases from I" to I.

To find the new angular velocity ω'', we can again use the conservation of angular momentum:

[tex]L_{initial}[/tex] = [tex]L_{final}[/tex]

[tex]L_{initial}[/tex] = I" ω'

[tex]L_{initial}[/tex] = (700 kg·m² + 10962 kg·m²) × ω'

[tex]L_{initial}[/tex] = 11662 kg·m² × ω'ω''

[tex]L_{initial}[/tex] = [tex]L_{final}[/tex] / I

[tex]L_{initial}[/tex] = [tex]L_{initial}[/tex]  / I

[tex]L_{initial}[/tex] = (11662 kg·m² × ω') / 700 kg·m²

[tex]L_{initial}[/tex] = 198.03 rad/s

For similar question on angular velocity

https://brainly.com/question/24158647

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