the mass of the block is too large and the block is too close to the left end of the bar (near string b) then the horizontal bar may become unstable (i.e., the bar may no longer remain horizontal).what is the smallest possible value of x such that the bar remains stable (call it xcritical )?express your answer for xcritical in terms of m1 , m2 , d , and l .

Answers

Answer 1

The answer for xcritical is d - [(m₁/m₂) (l/2 - d)].

According to the principle of moments,

The sum of clockwise moments must be equal to the sum of anticlockwise moments.

So,

[m₂g(d - xcritical)] - [m₁g(l/2 - d)] = 0

Therefore,

xcritical = d - [(m₁/m₂) (l/2 - d)]

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Related Questions

An object attached to an ideal spring executes simple harmonic motion. If you want to double its total energy, you could An object attached to an ideal spring executes simple harmonic motion. If you want to double its total energy, you could double the mass. double the force constant (spring constant) of the spring. double both the mass and amplitude of vibration. double the amplitude of vibration. double both the amplitude and force constant (spring con

Answers

Answer:

double the force constant

Explanation:

For this exercise we see that the unit mass to the spring executes a simple harmonic motion, the maximum mechanical energy is

             Em = ½ k A²

where A is the range of motion

To double the energy we must increase the amplitude or the spring constant

Therefore, to double the total energy we must increase the amplitude by an amount √2

or we can increase the spring constant to double

The correct answer is to double the force constant

True or false? All three types of ionising radiation have the potential to make cells become cancerous or even kill them completely.

Answers

Answer:

true

Explanation:

All three types of ionising radiation have the potential to make cells become cancerous or even kill them completely.

How much work is required to move a -4.0 mC charge from the negative plate to the positive plate of this system?A) -1.2 Ã 10-2 JB) +1.2 Ã 10-2 JC) -2.4 Ã 10-2 JD) +2.4 Ã 10-2 JE) -5.4 Ã 10-2 J

Answers

1.2 Ã 10-2 J work is required to move a -4.0 mC charge from the negative plate to the positive plate of this system. Therefore the correct option is option A.

The labour necessary to transfer a charge from one capacitor plate to the other is calculated as follows:

W = qV

where V represents the potential difference between the plates and q represents the charge.

The charge is -4.0 mC in this instance, and the plates' respective potential differences are:

80 V is equal to V = Ed = (2.0 x 104 N/C)(4.0 x 10-3 m).

where d is the distance between the plates and E is the strength of the electric field.

As a result, the necessary task is:

W = (-4.0 x 10^-3 C)(80 V) = -0.32 J

A) -1.2 10-2 J (rounded to two significant numbers) is the response.

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What is the force of friction caused by a block with a weight of 150N being pushed across a floor with a coefficient of friction equal to 0.5?

Answers

Answer:

75 N

Explanation:

F = μF = 0.5(150) = 75N

Your oven has a power rating of 5000 watts.
a. How many kilowatts is this?
b. If the oven is used for 2 hours to bake cookies, how many kilowatt-hours (kWh)
are used?
c. If your town charges $0.15/kWh, what is the cost to use the oven to bake the
cookies?

Answers

a) 5000 watts is equal to 5 kilowatts.

b) If the oven is used for 2 hours to bake cookies, 10 kWh is used.

c) If your town charges $0.15/kWh, the cost to use the oven to bake the cookies is $1.50.

a. To convert watts (W) to kilowatts (kW), we divide by 1000.

Therefore, 5000 watts is equal to 5 kilowatts.

b. To calculate the kilowatt-hours (kWh) used, we need to multiply the power rating (in kW) by the time (in hours). So, for 2 hours, we have:

Energy used = Power x Time

Energy used = 5 kW x 2 hours

Energy used = 10 kWh

c. The cost to use the oven to bake the cookies can be calculated by multiplying the energy used (in kWh) by the cost per kWh. So, for a cost of $0.15/kWh, we have:

Cost = Energy used x Cost per kWh

Cost = 10 kWh x $0.15/kWh

Cost = $1.50

Therefore, the cost to use the oven to bake the cookies is $1.50.

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an unknown additional charge q3 is now placed at point b, located at coordinates (0 m , 15.0 m ). find the magnitude and sign of q3 needed to make the total electric field at point a equal to zero. express your answer in nanocoulombs to three significant figures.

Answers

The magnitude and sign of q3 needed to make the total electric field at point a equal to zero is +0.3nc.

What is the charge?

Electric charge is a physical property of matter that causes matter to experience a force when placed in an electromagnetic field.Electric charge can be positive or negative (commonly carried by protons and electrons, by convention). Like charges, they repel each other, and unlike charges, they attract. An object with no net charge is referred to as neutral. The early knowledge of how charged substances interact is now called classical electrodynamics and is still accurate for problems that do not require consideration of quantum effects.

Two point charges are placed on the x axis. The first charge, q1 = 8.00 nC , is placed a distance 16.0 m from the origin along the positive x axis; the second charge, q2 = 6.00 nC , is placed a distance 9.00 m from the origin along the negative x axis.

q3 = +0.3nc

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An object of height 5cm is placed at 20cm from a concave mirror of focal length 10cm. The image height is​

Answers

Since the magnification is equal to 1, the image height is​ the same as the object height which is 5 cm

What is Optical Magnification ?

Magnification is when the ratio of the size of the image to the size of the object is greater than 1

Given that an object of height 5cm is placed at 20cm from a concave mirror of focal length 10cm.

The object distance u = 20 cmThe object height h = 5 cmFocal length f = 10 cmThe image distance v = ?The image height H = ?

To find the image height, let us first find the image distance by using the formula below

1/f = 1/u + 1/v

Substitute all the parameters

1/10 = 1/20 + 1/v

1/v = 1/10 - 1/20

1/v = (2 - 1)/20

1/v = 1/20

v = 20 cm

Magnification = v/u = H/h

20/20 = H/5

H = 5 cm

Therefore, the image height is​ the same as the object height which is 5 cm

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An emt asks you how he can decrease the chances of being involved in a collision when driving with lights and siren at night. Your advice would be:__________

Answers

An EMT asks you how he can decrease the chances of being involved in a collision when driving with lights and sirens in progress. Your advice would be as if the lights of the oncoming car are blinding you, glance to the right side of the road rather than at it.

Drivers up to 3,000 feet away can be rendered blind by headlights approaching from behind. If you feel you won't be able to see after a car passes you, slow down and try not to look directly into its headlights.

If approaching headlights are blinding you while you are driving at night, look to the right side of the road. You'll be able to see other automobiles thanks to your peripheral vision. On your car, apply some reflective tape.

Items are visible at night because of their rich color and striking contrast. Reflective tape is a fantastic option to wear as a result of this especially in dark colours.

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A person travels 350 km at an average speed of 60 km/hr. How long did it take?

Answers

Answer:  5.8 hours

Explanation:

Time= distance divided by speed, so:

350 divided by 60= 5.8 hours

.The process of making a solution by mixing a solute with a chemically compatible solvent is called?

Answers

The process of making a solution by mixing a solute with a chemically compatible solvent is called "dissolution" or "solubilization."

Dissolution refers to the process of combining a solute, which is the substance being dissolved, with a solvent, which is the substance doing the dissolving, to create a homogeneous mixture called a solution. The solute particles become dispersed and evenly distributed throughout the solvent, resulting in a uniform mixture.

During dissolution, the solute particles interact with the solvent molecules, which surround and separate the solute particles. The solvent molecules have an affinity for the solute particles, allowing them to break the intermolecular forces within the solute and facilitate their dispersal.

It is important to use a chemically compatible solvent, meaning a solvent that can effectively dissolve the specific solute without causing chemical reactions or undesirable side effects. The compatibility between the solute and solvent is determined by their chemical properties, such as polarity, solubility, and interaction forces.

The process of dissolution is a fundamental concept in chemistry and is used in various applications, including preparing solutions for experiments, manufacturing pharmaceuticals, creating mixtures in the food industry, and many other chemical processes.

Therefore, the process of making a solution by mixing a solute with a chemically compatible solvent is called dissolution or solubilization.

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Which types of rocks (igneou, sedimentary, metamorphic) tend to have crystalline textures? How does this texture form?

Answers

Answer:

metamorpic rock

Explanation:

it has a crystallin textures

If an object straight down falls 30m in 2 sec , how far will falls in 4 sec , what is the tail wind and headwind​

Answers

Answer:

60 sec

Explanation:

60m because in every 30min in 2sec so 30 × 2= 60 min

A 2 kg trolley is connected by a rope to a 3 kg load passes over a smooth pulley. The load is then released.
a) In the diagram, draw and label the free body diagram.

b) i)if the surface of the table is smooth, what is the acceleration of the trolley?

ii) What is the tension in the rope?

c) i)if the frictional force between the trolley and the surface of the table is 10 N, what is the acceleration of the trolley?

ii)Is the tension in the rope the same as the value in b(ii)? (use g-9.81 N kg-¹)​

Answers

c) i) New acceleration =\((3kg*9.81m/s ^210N) / (2kg+3kg)\)

= 4.69 m/s².

ii) No, the tension is now different: T = \(2kg * 4.69 m/^2\)

= 9.38 N.

How to solve

For the trolley, the forces are gravity (downward), normal force (upward), and tension from the rope (horizontal). For the load, the forces are gravity (downward) and tension from the rope (upward).

b) i) Acceleration (a) = Net force / Total mass

= \((3kg*9.81m/s²) / (2kg+3kg) = 5.89 m/s^2\)

.

ii) Tension (T) = mass of trolley * acceleration

= \(2kg * 5.89 m/s^2 = 11.78 N.\)

c) i) New acceleration =\((3kg*9.81m/s ^210N) / (2kg+3kg)\)

= 4.69 m/s².

ii) No, the tension is now different: T = \(2kg * 4.69 m/^2\)

= 9.38 N.

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A 2 kg trolley is connected by a rope to a 3 kg load passes over a smooth pulley. The load is then released.

Which list correctly names the three types of galaxies? binary, open, globular elliptical, open, binary irregular, spiral, elliptical open, irregular, spiral

Answers

The names the three types of galaxies are: spiral, elliptical, irregular.

What are galaxies?

A galaxy is a vast collection of stars, solar systems, gas, and dust. Gravity holds a galaxy together. A supermassive black hole also resides in the center of our galaxy, the Milky Way.

You see other stars in the Milky Way as you look up at the stars in the night sky. If it's truly dark and you're distant from any cities or residences with lights, you can even make out the Milky Way's dusty bands tracing a path across the sky.

A few galaxies resemble our own in spiral shape. They have curved arms that give it a pinwheel-like appearance. Others have smooth surfaces and oval shapes. We refer to them as elliptical galaxies. There are galaxies that are neither spirals nor ovals, though. They resemble blobs and have irregular forms. Each of these galaxies emits light that we can see from its stars.

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Galaxies are classified based on their shape. The three types of galaxies are spiral, elliptical, and irregular galaxies.

What is a galaxy?

Galaxies are the biggest group of stars and contain a few million stars to many billions of stars. It is also considered the vast cosmic island made up of stars, dust, and dark matter held together by gravity.

Every star in the night sky is the part of Milky Way galaxy and the solar system is present in this galaxy. The closest galaxy to the Milky Way is the Andromeda galaxy.

Galaxies are classified based on their shape and hence they are elliptical, spiral, and irregular galaxies. Spiral galaxies are galaxies that are spiral in shape and appear as a rotating disk of stars and dust. This galaxy contains lots of dust, gas, and young stars.

Elliptical galaxies are the galaxies that are elliptical in shape. The smallest elliptical galaxies are small as globular clusters and the large elliptical galaxies contain trillions of stars. This galaxy contains old stars and hence the galaxy is yellowish in colour.

The galaxies that have not come under the elliptical and spiral galaxies are called irregular galaxies. The spiral galaxies and elliptical galaxies get deformed by gravity and form irregular galaxies.

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Sound travels at approximately 1,500 m/s in sea water. How far will a sonar pulse travel in 90 s?

Answers

Answer:

135,000 m

Explanation:

(1500 m/s) (90 s) = 135,000 m

The distance travelled by sonar pulse will be 135,000 m. Distance is a numerical representation of the distance between two objects or locations.

What is wavelength ?

The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.

The wavelength is also defined as the distance between two locations in a wave that have the same oscillation phase.

The length of a wave is measured in its propagation direction. The wavelength is measured in meters, centimeters, nanometers, and other units since it is a distance measurement.

The distance travelled by sonar pulse is found as;

\(\rm d = v \times t \\\\ \rm d = 1500\times 90 \\\\ \rm d = 135,000 \ m\)

Hence, the distance travelled by sonar pulse will be 135,000 m.

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a 3.5kg child is swinging on a rope. the length of the rope attached to a tree branch is 7.00m. ths child passes through the lowest point of the curved path with a speed of 3.00m/s. what is the tension on the rope at this moment

Answers

The child's radial/centripetal acceleration at the lowest point of the swing is

a = (3.00 m/s)² / (7.00 m) = 1.29 m/s²

By Newton's second law, the tension in the rope is

T = (3.5 kg) (1.29 m/s²) = 4.5 N

(Does the question really say the child's mass is 3.5 kg? That's little more than the average mass of a newborn, about 3.3 kg. Not exactly a good idea to put a newborn on a swinging rope...)

Los Angeles and San Francisco are approximately 615 km apart and moving together at a rate of about 0.000057 or 5.7x10-5 km/yr. How many years (in the millions - 10^7) will it take for the cities to be neighboring

Answers

It will take approximately 10.7895 million years for Los Angeles and San Francisco to become neighboring cities, assuming they continue moving towards each other at a rate of 5.7x10-5 km/yr.

The distance between the two cities is 615 km, and they are moving towards each other at a rate of 5.7x10-5 km/yr.

To determine the time it takes for them to become neighboring, we divide the initial distance by the relative velocity: 615 km / (5.7x10-5 km/yr) ≈ 10,789,474 years.

Converting this to millions (10^7), we find that it will take approximately 10.7895 million years for Los Angeles and San Francisco to become neighboring cities at their current relative velocity.

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If the vehiche has a speed of 24.0 m/s at point a what is the force of the track on the vehicle at this point?

Answers

Question:

A roller-coaster vehicle has a mass of 500 kg when fully loaded with passengers.  If the vehicle has a speed of 20.0 m/s at point A, what is the force exerted by the track on the vehicle at this point?

See attachment

Answer:

33700 Newton

Explanation:

Given

\(m = 500kg\\v = 24.0m/s\\r=10m\)

First, we determine the forces acting on mass m.

They are: the force exerted by the track (Fn) and the weight of the vehicle (W)

So, the net force is:

\(F_{net} = F_n - W\)

\(W=mg\)

So:

\(F_{net} = F_n - mg\)

Make Fn the subject

\(F_n = F_{net} + mg\)

Fnet is calculated as:

\(F_{net} = F_c = \frac{mv^2}{r}\) --- i.e. the centripetal force

So:

\(F_n = F_{net} + mg\)

\(F_n = \frac{mv^2}{r} + mg\)

\(F_n = \frac{500 * 24^2}{10} + 500 * 9.8\)

\(F_n = 28800 + 4900\)

\(F_n = 33700N\)

If the vehiche has a speed of 24.0 m/s at point a what is the force of the track on the vehicle at this

boxcar at a rail yard is set into motion at the top of a hump. The car rolls down quietly and without friction onto a straight, level track where it couples with a flatcar of smaller mass, originally at rest, so that the two cars then roll together without friction. Consider the two cards as a system from the moment of release of the boxcar until both are rolling together. Answer the following questions yes or no. (a) Is mechanical energy of the system conserved? (b) Is momentum of the system conserved? Next consider only the process of the boxcar gaining speed as it rolls down the hump. For the boxcar and the Earth as a system, (c) is mechanical energy conserved? (d) Is momentum conserved? Finally, consider the two cars as a system as the boxcar is slowing down in the coupling process. (e) Is mechanical energy of this system conserved? (f) Is momentum of this system conserved?

Answers

A) The given statement "Is mechanical energy of the system conserved" is Yes

B) The given statement "Is momentum of the system conserved" is Yes

C) The given statement "Is mechanical energy conserved" is No

D) The given statement "Is momentum conserved" is Yes

E) The given statement "Is mechanical energy of this system conserved" is No

F) The given statement "Is momentum of this system conserved" is Yes

When the boxcar rolls down the hump, the only forces acting on it are gravitational forces, which are conservative forces. As a result, the mechanical energy of the boxcar-earth system is conserved as it rolls down the hump.

The two cars will both be traveling at the same speed and direction once they are coupled together. As a result, the momentum of the system will be conserved when the boxcar and flatcar couple together.

For the boxcar and the Earth as a system, the mechanical energy is not conserved since energy is converted to kinetic energy in the process of the boxcar gaining speed. However, momentum is conserved as the boxcar accelerates down the hump.

When the boxcar is slowing down in the coupling process, energy is converted to thermal energy and sound energy. As a result, the mechanical energy of this system is not conserved. However, the momentum of this system is conserved.

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1.5V battery is connected to a bulb whose resistance is 1.20hm how, much elections have the battery per minute?

Answers

The battery would have approximately 4.68 x 10^20 electrons flow through it per minute when connected to a 1.20 ohm bulb.

To calculate the number of electrons that flow through the circuit per minute, we need to use the formula:
I = V/R
where I is the current, V is the voltage of the battery, and R is the resistance of the bulb.

In this case, the voltage of the battery is 1.5V, and the resistance of the bulb is 1.20 ohms. Plugging these values into the formula, we get:
I = 1.5V / 1.20 ohms
I = 1.25 amps

Now, we need to convert this current to the amount of electrons that flow through the circuit per minute. To do this, we need to use the formula:
n = I*t/q

where n is the number of electrons, I is the current, t is the time in seconds, and q is the charge of an electron (which is 1.602 x 10^-19 coulombs).

We can convert the time from minutes to seconds by multiplying by 60. So, if we assume that the battery is connected to the circuit for one minute, we can calculate the number of electrons as:
n = 1.25 amps * (60 seconds) / (1.602 x 10^-19 coulombs)
n = 4.68 x 10^20 electrons

Therefore, the battery would have approximately 4.68 x 10^20 electrons flow through it per minute when connected to a 1.20 ohm bulb.

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Particles q₁ = -1.21 µC,
q2 = -55.0 µC, and
93 = +148 μC are in a line.

Particles q₁ and q2 are
separated by 0.447 m and particles q2 and q3 are
separated by 0.447 m. What is the net force on
particle q3?

Remember:
Negative forces (-F) will point left
Positive forces (+F) will point right

Answers

The net force on q3 is -1.686 N, with the arrow pointing to the left.

We may compute the force exerted by q1 and q2 on q3 using Coulomb's law:

where k is Coulomb's constant, q1, q2, and q3 are particle charges, and r1 and r2 are the distances between q1 and q3, respectively.

When we substitute the provided values, we get:

The forces' negative sign implies that they point in the opposite direction as the axis's positive direction. As a result, F1 points to the left, whereas F2 points to the right.

The vector sum of F1 and F2 is the net force on q3:

Fnet = F1 + F2 = -0.056 N + (-1.686 N)

As a result, the net force on q3 is -1.686 N and the force is negative will point left.

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which of the following is a subsurface event takes place during the rock cycle
deposition
erosion
weathering
plate tectonics​

Answers

Answer:

The answer is A. Cementing...

Explanation:

hope this helps

Answer:

plate tectonics

Explanation:

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what is the angular speed of the second hand the minute hand and hour ofa smoothly running anolag watch

Answers

Answer:

ω = 2 π f = 2 π / P

The second hand makes 1 revolution every 60 sec (P  = 60 sec)

ω (second hand) = 2 π / 60 sec = .1047 / sec

The second hand makes 60 revolutions for 1 revolution of the minute hand since the minute hand revolves once every hour

ω (minute hand) = 1/60 * .1047 = .001745 / sec

The minute hand makes 60 revolutions in 1 hour or 12 * 60 = 720 revolutions for 1 revolution of the hour hand

.001745 / 720 = 2.424 * 10E-6 / sec

Which one of the following equations is dimensionally homogeneous? show your proof. a.f=ma

Answers

The equation "f = ma" is dimensionally homogeneous. In this equation, "f" represents force, "m" represents mass, and "a" represents acceleration. The proof lies in checking the dimensions of each term and ensuring that they are consistent.

In the equation "f = ma," the terms "f," "m," and "a" represent force, mass, and acceleration, respectively. To determine if the equation is dimensionally homogeneous, we need to verify if the dimensions on both sides of the equation match.

The dimension of force can be represented as [M][L][T]^-2, where [M] represents mass, [L] represents length, and [T] represents time. The dimension of mass is represented as [M], and the dimension of acceleration is represented as [L][T]^-2.

Multiplying the dimension of mass ([M]) with the dimension of acceleration ([L][T]^-2), we obtain [M][L][T]^-2, which matches the dimension of force.

Therefore, the equation "f = ma" is dimensionally homogeneous because the dimensions on both sides of the equation are consistent. The dimensions of force, mass, and acceleration match, satisfying the condition of dimensional homogeneity.

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you double your distance from a sound source that is radiating equally in all directions. what happens to the intensity of the sound? it reduces to

Answers

You double your distance from a sound source that is radiating equally in all directions. The intensity of the sound reduces to one-sixteenth its original value.

What does light intensity mean?

The pace at which light disperses over a surface of a specific region some distance from a source is referred to as intensity. The intensity changes depending on the source's power and distance from it.

The degree, volume, or magnitude of something is its intensity. Examples include fire, emotion, weather, work, or passion. The word "intensity" is occasionally linked to fervour, fire, and violence. It is employed when describing the intensity of something like a flame or possibly a love affair.

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NOTE: The given question is incomplete on the portal. Here is the complete question

QUESTION: You double your distance from a sound source that is radiating equally in all directions. What happens to the intensity of the sound? It reduces to

(A) one-fourth its original value.

(B) one-eighth its original value.

(C) one-sixteenth its original value.

(D) none of the above

you double your distance from a sound source that is radiating equally in all directions. what happens

a honeybee leaves the hive and travels a total distance of 2 km before returning to the hive. what is the magnitude of the displacement vector of the bee? why?

Answers

The magnitude of the displacement vector of the bee will be 2 km. Because the distance between the endpoints is 2km.

What is displacement?

A displacement is a vector in engineering and mechanics that has a length equal to the smallest distance between a point P's initial and final positions. It is a vector quantity. The SI unit of the displacement is the meter.

A honeybee leaves the hive and travels a total distance of 2 km before returning to the hive.

The bee's displacement vector will be 2 kilometers in length. Mostly due to the 2 kilometers between the terminals.

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The specific heat capacity of oxygen is 918j/kg c. That means that it takes 918 J of energy to raise ____ kg of oxygen by 1 degree Celsius. What number completes the sentence

Answers

Answer:

1kg of oxygen(918joules of energy per 1kg of oxygen by 1 degree Celsius)

Can two spheres of different diameters and different
masses have the same moment of inertia?

Answers

Answer:

NO

Explanation:

I=mr^2 this means moment inertia depends upon mass and square of radius or distance.

What is remote sensing

Answers

The process of acquiring information, monitoring, and detecting the characteristics of any phenomenon or an object is called Remote Sensing. This is done by measuring the radiation emitted or reflected by the said object or phenomenon from some distance. Remote Sensing is typically done via a satellite or an airplane to collect data on Earth and other planets in space.

There are some special cameras that are used to collect images through the process of remote sensing. The researchers then "sense" some inferences from these images to get the required data.These cameras capture images of large areas of the Earth's surface. This helps in screening and observing a lot more information than what would have been possible by simply standing on the ground.

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( a ) A Carnot engine operates between a hot reservoir at 320K and a cold one at 260K. If the engine absorbs 500J as heat per cycle at the hot reservoir, how much work per cycle does it deliver? (b) If the engine working in reverse functions as a refrigerator between the same two reservoirs, how much work per cycle must be supplied to remove 1000J as heat from the cold reservoir?

Answers

The Carnot engine delivers 93.75J of work per cycle and the work supplied per cycle to remove 1000J as heat from the cold reservoir is 230.94 J

(a) A Carnot engine operates between two reservoirs and follows a reversible cycle. In this case, the engine operates between a hot reservoir at 320K and a cold one at 260K and absorbs 500J as heat per cycle at the hot reservoir. We can use the Carnot efficiency formula to find the work delivered per cycle:

Efficiency = (Th - Tc) / Th
Efficiency = (320K - 260K) / 320K
Efficiency = 0.1875 or 18.75%

Therefore, the work delivered per cycle can be found by multiplying the efficiency by the heat absorbed:

Work delivered = Efficiency x Heat absorbed
Work delivered = 0.1875 x 500J
Work delivered = 93.75J

(b) If the Carnot engine operates in reverse and functions as a refrigerator between the same two reservoirs, we need to calculate the work that must be supplied per cycle to remove 1000J as heat from the cold reservoir. The coefficient of performance (COP) of a refrigerator is defined as the ratio of heat removed from the cold reservoir to the work supplied to the refrigerator. The COP can be calculated as follows:

COP = Tc / (Th - Tc)
COP = 260K / (320K - 260K)
COP = 4.33  

Therefore, the work supplied per cycle can be found by multiplying the COP by the heat removed from the cold reservoir:

Work supplied = Heat removed / COP
Work supplied = 1000J / 4.33
Work supplied = 230.94 J

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