when an egg is boiled in a pot of water on the stove, there is more than one kind of heat transfer. heat is transferred from the stove to the pot directly since they are physically touching. heat is also transferred from the pot to the egg, carried through the water. what two kinds of heat transfer are represented? when an egg is boiled in a pot of water on the stove, there is more than one kind of heat transfer. heat is transferred from the stove to the pot directly since they are physically touching. heat is also transferred from the pot to the egg, carried through the water. what two kinds of heat transfer are represented? stove to pot

Answers

Answer 1

The three ways that heat can be transferred from one media to another are radiation, conduct, and heat transport.

Give a definition of radiation.

Radiation is the name for energy that spreads out from a source and travels through the environment at the speed of light. This energy has wave-like properties and is complemented by a magnetic field and an electrostatic potential. Electromagnetic waves can sometimes be referred to as "radiation."

How would we receive radiation?

People are exposed to radiation by cosmic rays, radioactive materials in the environment, water, food, and air, and even within their own bodies. Human-made radiation sources are commonly used in business, science, and medicine. The two types of radiation are radiation and non-ionizing radiation.

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Related Questions

An electromagnetic wave in a vacuum traveling in the +x direction generated by a variable source initially has a wavelength λ of 235 μm and a maximum electric field Emax in the +y direction of 4.40×10−3 V/m . If the period of the wave is then increased by a factor of 2.30, what is the equation of the resulting magnetic field component of the wave?
What are the coefficients in the equation for the magnetic field component of the wave after the period increases by a factor of 2.30?
want: Bmax, k, w
I continue to get "You have used the initial period to calculate the final wavenumber. Keep in mind that the period has been increased."
the solutions I have are:
Bmax= 14.667*10^-12
k= 26737
w= 3.487*10^12

Answers

An electromagnetic wave in a vacuum consists of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of wave propagation. The equations for the electric and magnetic fields of an electromagnetic wave can be written in the form:

E = E0 cos(kx - wt) and B = B0 cos(kx - wt)

Where E0 and B0 are the amplitudes of the electric and magnetic fields, respectively, k is the wave number, x is the position, t is the time, and w is the angular frequency.

The wave number k is related to the wavelength λ and the angular frequency w is related to the period T by the following equations:

k = 2π/λ and w = 2π/T

Given that the wavelength of the wave is 235 μm and the period is T = 2.3 * (1/500 s) = 4.6 x 10^-4 s

The wave number k is:

k = 2π/λ = 2π/235 x 10^-6 m = 8.57 x 10^7 rad/m

The angular frequency w is:

w = 2π/T = 2π/(4.6 x 10^-4 s) = 1369.6 rad/s

The equation for the electric field component of the wave is given as:

E = E0 cos(kx - wt) = 4.40 x 10^-3 V/m cos(8.57 x 10^7 x - 1369.6 t)

The equation for the magnetic field component of the wave is given as:

B = B0 cos(kx - wt) = B0 cos(8.57 x 10^7 x - 1369.6 t)

The coefficient for the magnetic field component of the wave is B0, which is not specified in the question, it can be determined by using the relationship between the Electric field, Magnetic field and the speed of light.

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a 37 g plastic ball is moving to the left at 14 m/s . how much work must be done on the ball to cause it to move to the right at 14 m/s ?

Answers

A 37 g plastic ball is travelling to the left at 14 m/s, hence 3.6j of effort must be done on the ball to make it move to the right. The definition of work done includes both the application of force.

Concerning the body and its movement. Consider a block placed on a horizontal, frictionless surface. A fixed force F exerts its influence on this block. This force acts to move the body through a distance d in a straight line and in the force's direction.

Work done to stop the ball is equal to 1/2m(v1^2 - v2^2) = 1/2(0.037)(0 - 14^2) = -3.6j.

Work performed to accelerate the ball equals 1/2m(v1^2 - v2^2) = 1/2(0.037)(14^2 - 0) = 3.6j.

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all the planets revolve around the sun in a(n) direction a. clockwise b. counterclockwise c. northerly d. southerly e. all the above

Answers

In the solar system the planets are revolving about the sun and rotation about their axes in a counterclockwise direction and revolving from west to east. Hence option 'b' is correct.

Rotation? What do you mean?

The circular movement of an object about its center is referred to as rotation. Things can rotate in a variety of ways. the Earth's rotation. When a round, three-dimensional object rotates around in an invisible line inside of its center, it is a relatively common type of rotation.

What do the Earth's rotation and revolution mean?

The term "rotation" describes how an object spins around its own axis. When an object is in revolution, it is moving in an orbit around another object. For instance, the 24-hour day is created as the Earth moves on its own axis. The 365-day year results from the Earth's rotation around the Sun.

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an electromagnetic wave has a frequency of 12 mhz. what is its wavelength in vacuum?

Answers

The wavelength of an electromagnetic wave in a vacuum is equal to the speed of light (c) divided by the frequency (f): 2.5 x 10^2 m

What is electromagnetic wave?

An electromagnetic wave is a type of energy wave that consists of oscillating electric and magnetic fields. These waves are generated by the vibration of electric charges and travel at the speed of light. Electromagnetic waves can be used to transmit information over long distances, such as in radio and television transmissions. They can also be used to transfer energy, such as in microwave ovens and solar cells. Electromagnetic waves come in many different forms, such as visible light, X-rays, and gamma rays.

λ = c/f
λ = 3.0 x 10^8 m/s / 12 x 10^6 Hz
λ = 2.5 x 10^2 m

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Echolocation is a form of sensory perception used by
most bats, toothed whales and porpoises, as well as a
few birds. The animal emits a pulse of sound which
is reflected from objects; the reflected pulse is then
detected by the animal to learn about its environ-
ment or interact with other animals. Echolocation • waves emitted by whales have frequencies of about 200,000Hz. (a) What is the wavelength of the whale's echolocation wave? (b) If an obstacle is 100m from the whale, how long after the whale emits a wave will the reflected wave return to him?

Answers

Answer:

(a) What is the wavelength of the whale's echolocation wave?

9. you're standing in a large room when a loud noise is made and you hear a series of echoes. which characteristic of sound best explains what just happened? a. diffraction b. diffusion c. reverberation d. focusing

Answers

Option (c) reverberation is the best choice. Reverberation can be decreased by utilizing materials that absorb sound before it reaches the room's walls and ceiling, preventing the sound from being reflected.

What is reverberation?

Reverberation is the characteristic of sound that best explains what just happened in this scenario. Reverberation occurs when sound waves are reflected off of surfaces in a room, creating multiple echoes that can be heard. When a loud noise is made in a large room, the sound waves will reflect off of the walls, floor, and ceiling, creating a series of echoes that can be heard. This is known as reverberation.

Which is better, reverberation or echo?

Both open and closed places can produce echoes. In tight environments with many reflecting items, reverberation occurs. The distance of the item can be determined using the echos. Reverberation cannot estimate the distance of a reflecting object because the travel time is too brief.

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a lazy physics student is made to walk to the plank. the plank is 8m above the water. if the student is pushed off the plank with a horizontal velocity of 10m/s how long will it take him to hit the water?responses

Answers

If a 10 m/s velocity is used to force the pupil off the board. To reach the water will take 1.28 seconds.

What are some examples of velocity?

The speed when something that moves in a specific direction is known as its velocity. as even the speed of something like a car driving north on something like a highway or the pace at which a rocket takes off.

Why is velocity either 0 or -?

It only contains magnitude since it is a scale parameter. Since a negative sign indicates a direction and rate does not indicate direction, the value can only be positive or zero.

Δy = vi t+1/2 at^2

v_ i = 0

a = 9.8 m/s^2

8 = 0 + 1/2(9.8)t^2

t^2 = 1.63

t = 1.28 s

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A woman wishes to move a basket of grapes 10 m. How many seconds will it take her if she uses 14 N of force and 2 W of power?

Answers

Answer:

Explanation:

Assuming that the woman is moving the basket of grapes at a constant speed, we can calculate the time it will take her by using the equation t = F/P, where t is the time in seconds, F is the force in newtons, and P is the power in watts. Plugging in the given values, we get t = 14/2 = 7 seconds. Therefore, it will take the woman 7 seconds to move the basket of grapes 10 m using 14 N of force and 2 W of power.

Determine the correct sequence of trials.Add HCl to water and measure pH Add HCl to buffers and measure pH Add NaOH to water and measure pH Make assigned buffer(s) Add NaOH to buffers and measure pH

Answers

Dilute the unknown until its absorbance is inside the standard curve. The full strength concentration can be calculated after identifying the diluted quantity if the dilution process is documented.

High concentration is what?

A chemical that is present in large quantities relative to the volume is said to have a high concentration in a solution. For example, the Great Salt Lake contains very few fish due to the high concentration of salt.

What is an example of concentration?

You can determine how much solute has been dissolved in the solvent by looking at the concentration of the solution. For instance, the concentration may be stated as 1 teaspoon of salt per 2 cups of water if you add 1 teaspoon to 2 cups of water.

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A 5.0 kilogram block accerlerating at 6.p meters per second along a rough horizontal force,f, of 50. newtons. What js the magnitude in newtons if the force of friction

Answers

The magnitude of the force of friction in this scenario would be 300 Newtons. This is calculated by multiplying the mass (5 kg) by the acceleration (6 m/s^2), and then multiplying that total by the coefficient of friction (50 N).

n and k are positive integers. When n is divided by 23, the quotient is 2k and the remainder is j. What is the value of j + k?(1) When n is divided by 15, the quotient is 3k and the remainder is 5j(2) When n is divided by 9, the quotient is 5k and the remainder is 5j

Answers

The value of j + k where n and k are positive integers and j is the remainder is 46/225.

Statement 1: When n is divided by 15, the quotient is 3k and the remainder is 5j

From this statement we know that n = 15(3k) + 5j,

Statement 2: When n is divided by 9, the quotient is 5k and the remainder is 5j.

From this statement we know that n = 9(5k) + 5j,

We know that 23 and 15 have a common factor of 1, so we can use statement 1 to find the value of j+k:

n = 15(3k) + 5j

n = 23(2k) + j

From these two equations, we know that -

15(3k) = 23(2k) + j

solving we get,

225k = 46k + j

j+k = 46k/225k = 46/225

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a student drops a rock off of a bridge. the final velocity of the rock just before it hits the water below is -8.0 m/s. what is the height of the bridge? assume negligible air resistance

Answers

A pupil throws a rock down a bridge. The rock's final speed shortly before it lands in the sea following is a brief -8.0 m/s. How tall is the bridge? vf=24.2487113m/s

What metaphorical significance does a bridge have?

Whether it connects both worlds or two different realms, the bridge is fundamentally a symbol of communication and togetherness. It can be viewed as the link between God because of this. It can be the gateway to reality or just a metaphor for movement and crossing.

Calculation

vi=0, x=30, a=9.8, t=?, vf=?

x=vi*t+.5*a*t^2

30=.5*9.8*t^2

30=4.9*t^2

t=2.4743583s

vf=vi+a*t

vf=0+9.8*2.4743583

vf=24.2487113m/s

Then change it to negative because you are going down.

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a spring has a spring constant k of 10.0 n/m. determine the work needed to stretch the spring from 4.0cm to 6.5cm

Answers

A spring has a spring constant;Work = 1/2 * k * (Δx)^2,

Work = 1/2 * 10.0N/m * (0.065m - 0.04m)^2,Work = 0.009825 J

What is the constant ?

The constant in mathematics is a number that has a fixed value. A constant can be a single number, such as pi or e, or it can represent a set of numbers, such as the set of prime numbers. Constants are often used in equations and formulas to represent values that do not change. For example, the equation for the area of a circle is A = πr2, where π is a constant with a value of 3.14159.

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t what speed does a 2000 kg compact car have the same kinetic energy as a 16000 kg truck going 24 km/hr

Answers

At speed v = 18.86 m/s = 67.8 km/h  a compact car have the same kinetic energy as a truck.

What are some instances of kinetic energy?

The energy of motion, or kinetic energy, can be observed in the motion of an object or a subatomic particle. There is kinetic energy in every particle every moving thing. A human walking, a baseball soaring through the air, food falling from a table, and a charged particle in an electric field are all instances of kinetic energy in motion.

Given in the question,

mass of car = 2000kg

mass of truck = 16000kg

speed of truck, vt = 24 km/h = 6.67 m/s

by using Kinetic energy equation for truck,

K = 1/2 mvt²

K = 1/2 ×16000×(6.67)²

K = 355911.2 J

since the kinetic energy is same for car and the truck

Kcar = Ktruck

1/2 mv² = 355911.2

v² = 355911.2/ 1000

v = √355.9112

v = 18.86 m/s = 67.8 km/h

At speed v = 18.86 m/s = 67.8 km/h  a compact car have the same kinetic energy as a truck.

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a 2.0 kg block is forced against a horizontal spring of negligible mass, compressing the spring by 15 cm. when the block is released from the compressed spring, it moves 60 cm across a horizontal tabletop before coming to rest. the force constant of the spring is 200 n/m. calculate the coefficient of sliding friction between the block and the table

Answers

The block and table have a sliding friction coefficient of 0.083.

What leads to conflict?

Although friction is assumed to be created by the interaction between the microscopic bumps on surfaces when they brush against each other, scientists are not entirely sure what causes it. It is challenging for the surface to slide over one another because the spikes on each surface flex and exert stress on one another.

What can lessen abrasion?

The friction between both the edges can be decreased by using lubricants like oil or grease. Friction can be decreased by cleaning the surface, which makes it smooth.

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Which of the following cannot overcome an objects inertia?
O
O
friction
A balanced force (net zero force)
Gravity
An unbalanced force

Answers

An unbalanced force cannot overcome an objects inertia.

Define inertia?

A property of matter by which it remains at rest or in uniform motion in the same straight line unless acted upon by some external force. : an analogous property of other physical quantities (such as electricity) : indisposition to motion, exertion, or change : inertness.The resistance of a body to changes in its momentum. Because of inertia, a body at rest remains at rest, and a body in motion continues moving in a straight line and at a constant speed, unless a force is applied to it.

Inertia is property of object, inability to change its position or confugaration of given body.. Mass is measurement of Inertia.. so Unit of Inertia is Kilo Gram. in SI method. If you need, unit of moment of Inertia then it is Kg m^2.

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A proton moves along the x-axis with vx=1.0×107m/s. a. As it passes the origin, what are the strength and direction of the magnetic field at the (1 cm, 0 cm, 0 cm) position? Give your answer using unit vectors. Express your answer in terms of the unit vectors i^, j^, and k^. b. As it passes the origin, what are the strength and direction of the magnetic field at the (0 cm, 1 cm, 0 cm) position? Give your answer using unit vectors. Express your answer in terms of the unit vectors i^, j^, and k^. c. As it passes the origin, what are the strength and direction of the magnetic field at the (0 cm, -2 cm, 0 cm) position? Give your answer using unit vectors. Express your answer in terms of the unit vectors i^, j^, and k^.

Answers

Projectile motion occurs when an item moves both vertically and horizontally through the air while solely being affected by gravity (r = 2 cm).

what is Various proton examples ?

A proton is, for instance, the core of a hydrogen ion or the H+ ion. No of the composition, each hydrogen atom has one proton; each particle has two; each lithium atom has three; and so on. Protons are really the positively charged electrons which are evident in the the nucleus of an atom. Atoms, electrons, and neutrons make up an atom. The nucleus, which is in the middle, contains all of an atom's mass. Protons and neutrons, collectively referred to as nucleons, are found in the nucleus.

What is the name of a neutron?

Given that it is a compound particle consisting of quarks, the neutron is categorized as a hadron. Due to the fact that the neutron is made up of three valence quarks, it is also categorized as a baryon. The neutron's magnetic moment and finite size both point to it being a composite particle as opposed to an elementary one.

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a bulldozer pushes a boulder with a force of 18,000 n over a distance of 53 m, in a time of 60 s. how much work is done by the bulldozer?

Answers

The bulldozer's work done is measured in joules is 954000J, since it is capable of moving a boulder 53 metres with 18,000 newtons of force in just 60 seconds. Force and motion must coexist.

Applied to the body as well as to how the body moves. Consider a block that has been placed on a flat, frictionless surface. This block is affected by a constant force F. The body is moved by this force across a distance of d in a straight line and in the force's direction. In physics, a force is an effect that has the ability to change how an object moves. Due to a force, a massed object may change.

Work done = Force*cos(theta)*d = Force*d = 18,000*53 = 954000J

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what will happen if you plug in a 220v appliance into a 120v outlet? 0 / 1 point nothing will happen the appliance could get damaged the appliance will charge at a slower rate the outlet could get damaged

Answers

If you plug in a 220v appliance into a 120v outlet then whatever that would happen would depend upon the kind of load.

If one is have a passive load that is without power electronics. For example- a basic heater, then the  current in the device would be reduced to the half of the actual and its power will reduce to a quarter according to the Ohm´s law. But if one is having an active load where its power is kept constant, it will consume double the amount of current in order to compensate for the reduction of voltage that has occurred. This could eventually lead to the device getting damaged.

Voltage is defined as the pressure from an electrical circuit's power source which eventually pushes charged electrons (current) through a conducting loop, and enables them to do work such as illuminating a light.

Voltage = pressure, and it is measured in volts (V).

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The gravitational force between two objects is proportional to?

Answers

Answer:

it is proportional to masses of two objects

Determine v₁ and v₂ in the circuit102 Ω 3 A V1 10 Ω 10 V 20 Ω 51%

Answers

The value of v₁ and v₂ is 10V and -10V respectively. This is because of Kirchoff's law. The potential is distributed in the gap and node and the potential is distributed.

The potential difference (which is the same as voltage) is equal to the amount of current multiplied by the resistance. A potential difference of one Volt is equal to one Joule of energy being used by one Coulomb of charge when it flows between two points in a circuit. **Ammeters: **An ammeter measures the flow of current that passes through it. the potential of any cell or battery is the difference between the positive and negative terminal through the terminal difference. by this primary information, we can firmly conclude that the value of v₁ and v₂ is 10V and -10V respectively. This is because of Kirchoff's law. The potential is distributed in the gap and node and the potential is distributed.

Determine v₁ and v₂ in the circuit

A. 3 ohm

B. 10 ohm

C. -10 ohm

D. 20 ohm

E. 2 ohm

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Infrared spectroscopy is a useful tool for scientists who want to investigate the structure of certain molecules. Which of the following best explains what can occur as the result of a molecule absorbing a photon of infrared radiation?

Answers

Energies of infrared photons are the same as the energies of chemical bonds. Molecules absorb infrared photons of characteristic wavelengths, revealing the types & strengths of different bonds in the molecules.

What is the purpose of infrared?

There are several uses for infrared technology. Heat sensors, thermal imaging, and night vision gear are some of the most well-known types. Infrared light is employed in wired and wireless activities in communications and networking.

Animals can perceive infrared, but how?

The human eye cannot sense infrared light because it has different range and less energy than visible light. However, several snake and scorpion species, bed bugs, vampire bats, and mosquito species can see by using parts of the infrared spectrum. Infrared energy can occasionally be "seen" by people as heat.

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What is the reaction energy Q of this reaction? Use c2=931.5MeV/u.

Answers

The reaction energy Q of the reaction is 195 MeV.

₉₂U²³⁵ + ₀n¹ → ₅₄Xe¹⁴⁰ + ₃₈Sr⁹⁴ + 2 ₀n¹

Mass of reactants = 235.04393 + 1.008665 = 236.052595 amu

Mass of products = 139.92144 + 93.91523 + 2* (1.008665) = 235.854000 amu

Mass defect Δ m = 236.052595 - 235.854000 = 0.198 amu

Reaction energy released Q = Δ m * 931.5

                                             = 0.198 * 931.5 = 185 MeV

What is the reaction energy?

The overall reaction energy also referred to as enthalpy, is expressed as the change in energy between the products and the reactants via subtraction. If the reactant energy is higher than the products, then the overall energy will be negative, resulting in an exothermic reaction.

What is the reaction formula?

A chemical reaction equation gives the reactants and products, and a balanced chemical reaction equation shows the mole relationships of reactants and products. Often, the amount of energy involved in the reaction is given.

Thus, reaction energy Q is 185 MeV.

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a gun with a muzzle velocity of is fired at an angle of above the horizontal. find the horizontal and vertical components of the velocity.

Answers

The horizontal and vertical is 1188.321ft/sec and  the velocity is g =32.174 = 32.174t.

What direction is horizontal?

Horizontal pertains to everything that is perpendicular to the horizon. Anything that forms a 90-degree angle (right triangle) with the straight or the horizon is referred to as vertical because it is the opposite of the horizontal. The line that spans from left to right is therefore considered to be horizontal.

horizontal velocity = Vcos the

                               = 1200*cos 8

after time t, horizontal velocity = 1200cos8 ft/sec (it is constant) = 1188.321ft/sec

vertical velocity = V sin theta

                          = 1200*sin8

vertical velocity v= 1200sin8-gt = 167-32.174t ft/sec (till t = 5.19sec)

g =32.174 = 32.174t ft/sec (after t = 5.19sec)

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A 1.80-m-long barbell has a 22.0 kg weight on its left end and a 32.0 kg weight on its right end. where is the center of gravity if the 9.00 kg mass of the barbell itself is taken into account?

Answers

The center of gravity for the barbell is located 1.46 m to the right of the left end weight.

How is the center of gravity calculated for an object with multiple weights on it?

The center of gravity for an object with multiple weights on it is calculated by taking the sum of the weights multiplied by their respective distances from a reference point, and dividing by the total weight of the object. The reference point is typically the center of the object, or a point where the object is supported. In the case of the barbell, the reference point would be the center of the barbell, and the distance would be measured from the center of the barbell to the center of the weights. The center of gravity is the point where the weight of the object is balanced and where the object would rotate if suspended from that point.

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A 7,500-W engine is used to lift an I-beam with a mass of 1,000 kg to a height of 150 m. How much work must be done to lift this mass at a constant speed? How long will it take?
Use these formulas: W = F x d F = m x 9.8 m/s² t = W/P

Answers

Answer:

Explanation:

The work that must be done to lift the mass is W = F x d = 1000 kg x 9.8 m/s2 x 150 m = 1,470,000 Joules (1.47 x 106 J).

The time it will take to lift the mass at a constant speed is t = W/P = 1.47 x 106 J/7500 W = 196 seconds (3 minutes 16 seconds).

Explanation:

Power = 7500 watts

mass = 1000kg

height/distance= 150m

work= ?

time = ?

second equation for motion

2nd law of newton

F = ma

for free fall motion a = g= 9.8

force = 9800Newton

now for work done

w = force into displacement

workdone = 1470000 Joules

now finally by power formula

p = workdone upon time

time = workdone upon power

time = 196 second

I hope this would help you!

A man draws a cart of mass 100 kg at a steady rate of 10 m/s on a level road. The tension in the coupling is 100 N. Calculate the power spent on the cart. kw​

Answers

The power spent on the cart is 1000kw  

What is power?

The quantity of energy moved or converted per unit of time is known as power in physics. The watt, or one joule per second, is the unit of power in the International System of Units. Power is also referred to as activity in ancient writings. A scalar quantity is power.

Power is related to other factors; for instance, the power required to move a ground vehicle is equal to the product of the vehicle's velocity, traction force on its wheels, and aerodynamic drag. A motor's output power is calculated by multiplying its torque output by the angular velocity of its output shaft.

How to calculate the power spent on the cart?

A man draws a cart of mass 100 kg

steady rate of 10 m/s

tension in the coupling is 100 N

Calculate power spent on the cart=P*V

P = FV , Where P = power, F = Force, V = velocity.

power spent on the cart=  P*V

                                       =100*10=1000kw    

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which of the following best respresents R= A - B?​
PLEASE I NEED HELP ON THIS!!

Answers

Answer:

the right side one

Explanation:

a+b will go left

13 when dew forms on outdoor objects, can it be assumed that the atmosphere is saturated? if so, why is there often no fog accompanying the dew?

Answers

Dweep point. An significant factor in drying is the dew point. The dew temperature is the point at which a continuous volume of air contains water vapor.

What connection should the dew point go through atmospheric saturation?

In order for air to become soaked without affecting its pressure, it must be chilled to below the dew point. The vapor pressure is affected by changes in pressure, and thus, so is the temperature during which saturation takes place.

Does dew require saturated air to form?

Dew, fog, and clouds—the prelude to rain, snow, sleet, and hail—are the byproducts of condensation, the process by which water vapor is changed into a liquid. Two prerequisites must be satisfied before condensation may take place. 35.

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this year 500 pounds of plutonium 239 (nuclear waste) was dumped in the nevada desert. the half-life of pu-239 is 24,360 years. how long will it take until there is only 1 pound left?

Answers

Time to take until there is only 1 pound left is half life,t  =  218,407 years.

The amount of time needed for the reactant concentration to drop to half its initial value is known as the half-life of a reaction. A constant that is connected to the reaction's rate constant is the half-life of a first-order reaction. First-order reactions include those in radioactive decay. The reduction in radioactive nuclei per unit of time is the rate of decay, or activity, of a sample of a radioactive substance.

Since y' = ky, we can infer that

y = C[tex]e^{kt}[/tex]

Since 500 pounds are initially present

C = 500

Because the half life is 24,360 years, y equals 250 when t equals 24,360. Connecting provides

250 = 500C[tex]e^{24,360k}[/tex]

1/2 = [tex]e^{24,360k}[/tex]

ln(0.5) = 24,360k

k=[tex]\frac{ln(0.5)}{24,360\\}[/tex]=[tex]-2.95 \times 10^{-5}[/tex]

 y = C[tex]500e^{2.95\times 10^{-5t} }[/tex]

 1 = C[tex]500e^{2.95\times 10^{-5t} }[/tex]

t  =  218,407 years.

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