An astronaut weighs 8.00 × 102 newtons on the surface of Earth. What is the weight of the astronaut 6.37 × 106 meters above the surface of Earth?

Answers

Answer 1

The new weight of the object from the description would now be  2  × 10^2 N.

What is the relationship of the force and the distance?

Given that the force between two bodies is inversely proportional to the square of their distance, doubling that distance results in a force that is one-fourth of what it was before.

We would now know that the force that is now acting on the object is;

Weight = 1/4 * 8.00 × 10^2 N

Weight = 2  × 10^2 N

This is true when we consider the universal gravitational law that governs the force on the object.

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Related Questions



A mineral scratches a piece of fluorite but cannot be scratched by a piece of glass. What is this mineral’s hardness?

Answers

Answer:

The mineral's hardness is greater than 4 but less than 5.5 on the Mohs hardness scale.

Carbon plays an important role in living things. The carbon cycle describes the

storage and exchange of carbon between the Earth's biosphere (living matter),

atmosphere

(air), hydrosphere (water), and geosphere (earth).

a. Explain how the carbon, found in the fossil fuel emissions, impacts each sphere.

Answers

Explanation:

The Carbon Cycle and Earth's climate Carbon Dioxide is an atmospheric constituent that plays several vital roles in the environment. It is a greenhouse gas that traps infrared radiation in the atmosphere. it plays a crucial role in the weathering of rocks. it is the carbon source for plants.

Baring pneumothorax, this pressure is always lower than atmospheric pressure (that is, negative pressure) is called

Answers

Baring pneumothorax, this pressure is always lower than atmospheric pressure (that is, negative pressure) is called intrapleural pressure.

Intrapleural pressure refers to the pressure within the pleural cavity, which is the space between the lungs and the chest wall. Under normal conditions, the intrapleural pressure is maintained at a level lower than atmospheric pressure. This negative pressure is crucial for maintaining lung inflation and facilitating the process of breathing.

The negative intrapleural pressure is generated by the opposing forces acting on the lungs and chest wall. The elastic recoil of the lungs tends to collapse them inward, while the elastic recoil of the chest wall tends to expand it outward. These opposing forces create a negative pressure in the pleural cavity, which keeps the lungs expanded and allows for efficient gas exchange during respiration.

The negative intrapleural pressure is essential for maintaining the integrity of the lungs and promoting their optimal function. However, in the case of pneumothorax, air enters the pleural cavity, equalizing the pressure with atmospheric pressure and leading to a loss of the negative pressure. This can result in lung collapse and difficulty in breathing.

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what happens to the molecules when carbon dioxide is heated

Answers

When the molecules of carbon dioxide is heated, it is disintegrated into molecules of carbon monoxide and oxygen atoms.

CO2 → CO + O

This is the basic reaction expected to happen by carbon dioxide molecules are heated. However it may also disintegrate into C2, O2, C, etc.

Since heat is absorbed in this reaction, it is an example of endothermic reaction. In an exothermic reaction heat is released. These are the basic two types of chemical reactions on basis of heat.

Therefore, when the molecules of carbon dioxide is heated, it is disintegrated into molecules of carbon monoxide and oxygen atoms.

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A proton, moving with a velocity of viî, collides elastically with another proton that is initially at rest. Assuming that after the collision the speed of the initially moving proton is 2. 70 times the speed of the proton initially at rest, find the following. (a) the speed of each proton after the collision in terms of vi initially moving proton ✕ vi initially at rest proton ✕ vi (b) the direction of the velocity vectors after the collision (assume that the initially moving proton scatters toward the positive y direction) initially moving proton ° relative to the +x direction initially at rest proton ° relative to the +x direction

Answers

The correct answer is that the final speed of the initially moving proton is \(vi/3.7\), and the final speed of the initially at rest proton is \(4.7vi/3.7\).

In an elastic collision between two particles, both momentum and kinetic energy are conserved. Since one proton is initially at rest, the total momentum before the collision is given by \(p = mv = mviî\), where m is the mass of the initially moving proton. After the collision, the momentum is conserved, and we have \(p = mv = (2.7m)(vf)\), where vf is the final velocity of the initially moving proton. Equating the initial and final momenta, we get\(mvi = (2.7m)vf + mvp\), where vp is the final velocity of the initially at rest proton. Since the collision is elastic, the total kinetic energy before and after the collision is conserved, so we have\(0.5mv^2 = 0.5(2.7m)v^2 + 0.5mvp^2\), where v is the final velocity of the initially moving proton. Solving these equations, we get \(vf = (vi/3.7)î\) and \(vp = (4.7vi/3.7)î\). Therefore, the final speed of the initially moving proton is \(vi/3.7\), and the final speed of the initially at rest proton is \(4.7vi/3.7\). The direction of the velocity vectors after the collision can be found using conservation of momentum, and we find that the angle made by the initially moving proton with the +x direction is \(tan-1(3/4)\), and the angle made by the initially at rest proton with the +x direction is \(tan-1(-4/3)\).

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what kind are ray diagram is this. pls identify it

what kind are ray diagram is this. pls identify it

Answers

Letter A is the plane surface

Letter B is the incident ray

Letter C is the reflected ray.

What are the terms of the ray diagram?

The terms of the ray diagram is illustrated as follows;

(i) This arrow indicates the incident ray, which is known as the incoming ray.

(ii) This arrow indicates the normal, a perpendicular line to the plane of incidence.

(iii) This arrow indicates the reflected ray; the out going arrow.

(iv) This the angle of incident or incident angle.

(v) This is the reflected angle or angle of reflection.

Thus, based on the given letters, we can match them as follows;

Letter A is the plane surface (surface containing the incident, reflected rays)

Letter B is the incident ray

Letter C is the reflected ray.

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HELP ASAP!! WILL TRY TO GIVE BRAINLIEST

How are facilitated diffusion and active transport similar and different?

Answers

Answer:

Facilitated diffusion and active transport both utilize proteins to transport substances across membranes. Differences between active transport and facilitated diffusion 1. Active transport requires an input of energy, usually ATP, while facilitated transport does not.


Is the moment of inertia of a body is unique? Give reason to your answer.

Answers

Answer:

The moment of inertia  about a "fixed"  axis is unique.

The moment of inertia of a square is different for an axis that passes perpendicular to the center of the square as opposed to an axis that lies in the plane of the square.

Torque = I * alpha shows that angular acceleration depends on I but not on the angle thru which I rotates     α = ω / t

Three horizontal forces are applied to a medal ring, as shown. One of the forces is 10N, and the second force is 12N at an angle of 100* from the first. Find the third forces such the ring is in equilibrium (i.e,. the sum of the three forces is zero)

Three horizontal forces are applied to a medal ring, as shown. One of the forces is 10N, and the second

Answers

Explanation:

Horizontal components:

10 N     +    12 cos (-100) =   + 7.916 N  

Vertical components

0   +    12 sin (-100)  = - 11.818 N

To have equilibrium, the third force must be of the same MAGNITUDE and OPPOSITE direction

   so    Horizontal = - 7.916 N

           Vertical  = + 11.818 N  

Magnitude =  sqrt ( -7.916^2 + 11.818^2 ) = 14.22 N

  at angle   arctan (- 11.818/7.916 ) =   123.8  degrees  

 

Three horizontal forces are applied to a medal ring, as shown. One of the forces is 10N, and the second

material speed of light
space 3 x 108 m/s
water 2.25 x 108 m/s
glass 2 x 108 m/s
air 3 x 108 m/s
Light moves from air into a new material. The greatest refraction would occur when light passes through which material?
A. air
B. water
O c. glass
D. It would refract the same amount in each material.

Answers

Answer:

c glass

Explanation:

beacause glass is transparent and it would be easier to for refraction

Eating pizza with friends after a football game is most likey an example of which food choice factors?

A.time and cost
B.family and friends
C.nutritional content
D.advertising
E.Other:

Answers

Answer:

time and cost

Explanation:they have to pay for the pizza and take time to eat it

Answer:

B: Family and Friends

Explanation:

According to the class I had on this a few years ago, I can confirm that this was the answer.

My answer would be this because you are socializing with friends (according to the question) and you would just select it automatically due to background knowledge.

Hope I helped! ☺

The vector labeled "X" in the figure below could potentially be__.

centrifugal force

centripetal force

angular velocity

tangential velocity

Answers

The vector labeled "X" in the figure below could potentially be tangential velocity. Tangential velocity represents the linear speed of an object moving along the circumference of a circular path.

The phrase "circular motion" refers to the movement of an item that follows a circular route. Typical circular motions include;

the rotation of a wheel's tyrethe rotary motion of fan bladesthe use of a rope to spin a stone

We all understand that an item moving in a circle has a constant velocity since it does not fluctuate. However, because the direction of the velocity is constantly shifting, we may consider an item that is moving in a circle to be accelerating.

As a result, we can observe that a circular motion has both velocity and acceleration. Tangential velocity is always tangent to the circle at that point.

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How do the overload and progression principles work together for strength training?

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If you are exercising with a specific goal in mind, such as improved strength or cardio fitness. Exercise training's guiding principles include overload, recuperation, progression, reversibility, and specificity.

Your muscles will remain challenged and you'll get stronger if you change or advance your workouts.

To get the most out of any training programme, you must follow certain rules. You won't benefit much from your workouts if you don't adhere to these rules. Exercise training's guiding principles include overload, recuperation, progression, reversibility, and specificity. The concept of specificity is especially important if your exercise programme is designed to help you achieve a particular goal, like increased strength or improved aerobic fitness.

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During a demonstration of Newton’s laws of motion, a student used the setup shown in Figure 1. The student flicked the index card with a fingertip, and the coin fell straight down into a plastic cup as shown in Figure 2.

A: A falling body accelerates at a constant speed.


B: The motion of an object is constantly changing due to magnetic forces.
C: The force friction causes an object in motion to move faster.
D: An object remains at rest, or at a constant speed, an unbalanced force acts on it.

Answers

Answer:

D. An object remains at rest, or at a constant speed, an unbalanced force acts on it.

The coin was at rest until the card was removed, so it tended to remain in the same location. Once the card was gone, the unbalanced force of gravity caused the coin to fall.

I hope this helped!+*♡

An ion rocket engine produces 1 newton of thrust. What acceleration can it give to a space probe with a mass of 1000kg?.

Answers

By using the thrust force, the acceleration is  0.001 m/s².

We need to know about force to solve this problem. According to second Newton's Law, the force applied to an object will be proportional to mass and acceleration. Hence, it can be written as

F = m . a

where F is force, m is mass and a is acceleration

From the question above, we know that

F = 1 N

m = 1000 kg

By substituting the given parameters, we can calculate the acceleration

F = m . a

1 = 1000 . a

a = 1/1000

a = 0.001 m/s²

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define the construction of electric current ?

Answers

Answer:

Please refer the the definition of an electric current below

Explanation:

Electric current is the flow of electric charge in a circuit. It is defined as the rate at which electric charge flows through a given area of a conductor. The flow of electric charge is caused by the motion of electrons, which are negatively charged particles that exist in most materials.

Electric current is generated by applying a potential difference, or voltage, across a conductor. The voltage causes a difference in electric potential energy between the ends of the conductor, and this difference drives the flow of electrons through the conductor. The electrons move from the negative terminal of the voltage source towards the positive terminal, and as they move, they transfer energy to the conductor in the form of heat or light.

The amount of current that flows through the conductor is determined by the voltage applied and the resistance of the conductor. Resistance is a property of the conductor that resists the flow of current, and it is measured in ohms. According to Ohm's law, the current in a circuit is directly proportional to the voltage and inversely proportional to the resistance.

This relationship can be expressed as

\(\sf I=\dfrac{V}{R}\)

where
\(\sf I\) is the current in amperes

\(\sf V\) is the voltage in volts

\(\sf R\) is the resistance in ohms

Ocean divers:
must breathe a mixture of oxygen and helium
cannot withstand the pressure of the ocean without special equipment
may one day breathe with artificial gills
all of the above

Answers

Answer:

all of the above.Explanation:

Answer:

im not sure but i think b. cannot withstand the pressure...

if not all the above.

Explanation:

A 2.0   kg 2.0kg2, point, 0, start text, k, g, end text cart moving right at 5.0   m s 5.0 s m ​ 5, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction on a frictionless track collides with a 3.0   kg 3.0kg3, point, 0, start text, k, g, end text cart initially at rest. The 2.0   kg 2.0kg2, point, 0, start text, k, g, end text cart has a final speed of 1.0   m s 1.0 s m ​ 1, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction to the left. What is the final speed of the 3.0   kg 3.0kg3, point, 0, start text, k, g, end text cart?

Answers

The final speed of the 3.0  kg cart is  4 m/s.

What is conservation of momentum principle?

When two bodies of different masses move together each other and have head on collision, they travel to same or different direction after collision.

The external force is not acting here, so the initial momentum is equal to the final momentum. For elastic collision, final velocities is different for both the bodies.

m₁u₁ +m₂u₂ = m₁v₁ +m₂v₂

A 2.0  kg cart moving right at 5.0  m/s on a frictionless track collides with a 3.0 kg  cart initially at rest. The 2.0   kg cart has a final speed of 1.0 m/s  to the left.

Substitute the values for m₁ = 2kg, m₂ =3kg, u₁ =5 m/s and u₂ =0 m/s, then the final velocity will be

3x0 +2x5 = -2x1 + 3v₂

v₂ = 4 m/s

Thus, the the final velocity 3.0  kg cart is  4 m/s.

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A group of stars connected by lines is circled and labeled Saturn.

The night sky is filled with images of wild animals. Which animal is the circled constellation named after?


scorpion

serpent

snake

salamander

A group of stars connected by lines is circled and labeled Saturn.The night sky is filled with images

Answers

Answer: scorpion I think

Two helium isotopes fuse to form beryllium, as shown below. The mass of beryllium is 2.73 x 107 kg less than the combined mass of the two helium atoms. How much energy was produced during this reaction? The speed of light is 3 x 108 m/s. Show your work. Use E = mc².

3/2He+ 4/2He → 7/4Be​

Answers

A chemical element with the symbol Be and atomic number 4 is known as beryllium. Beryllium is a solid at room temperature and is categorized as an alkaline earth metal. The molar mass of beryllium (atomic number 4) is 9.012 g/mol. Accordingly, if all 6.22x1023 Beryllium atoms were put together in a mole, they would weigh 9.012g on a triple beam balance.

Explain about the mass of beryllium?

The atomic mass unit serves as the unit of measurement for mass (amu). A mass unit of an atom is 1.66 x 10-24 gram. The mass of one nucleon, which can be either a single proton or neutron, is roughly equal to one unified atomic mass unit, which is numerically equivalent to 1 g/mol.

In the aircraft industry in particular, beryllium is employed in gears and cogs. A silvery-white metal is beryllium. It has a low density and is relatively soft. Gyroscopes, springs, electrical contacts, spot-welding electrodes, and non-sparking tools all use beryllium in alloys with copper or nickel.

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colors seen on some tv screens result from color

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Colors seen on some TV screens result from color additive mixing, which involves combining the primary colors of red, green, and blue (RGB) in varying intensities to produce a full range of colors.

By adjusting the amount of each primary color that is displayed, different hues and shades can be created. This process is also known as the RGB color model.

Each pixel on the TV screen is made up of three subpixels, one for each primary color, which are illuminated to create the desired color.

This allows for the creation of millions of colors using only three primary colors.

Other color models, such as the CMYK model used in printing, use subtractive mixing to achieve the desired color.

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How much work is done to move a 1,000 N car 20 meters?

Answers

Answer:

The answer is 20,000 J

Explanation:

The work done by an object can be found by using the formula

workdone = force × distance

From the question

force = 1,000 N

distance = 20 m

We have

workdone = 1000 × 20

We have the final answer as

20,000 J

Hope this helps you

If you free the cork in a highly pressurized champagne bottle, the resulting launch of the cork will, in principle, cause the bottle to recoil. A filled champagne bottle has a mass of 1. 8 kg. The cork has a mass of 7. 5 g and is launched at 22 m/s.

Answers

The speed of the bottle when recoiling if it could move freely is 0.092 m/s.

The problem isn't complete. A similar problem is in the attachment. When we free the cork from the bottle, the cork and the bottle have a collision. According to the law of conservation of momentum, the momentum before and after the collision is the same.

p = p'

m₁ v₁ + m₂ v₂ = m₁ v₁' + m₂ v₂'

m₁ = the mass of the cork = 7.5 grams = 0.0075 kgm₂ = the mass of the bottle = 1.8 kgv₁ = the speed of the cork before collision = 22 m/sv₁' = the speed of the cork after collision = 0
Because the cork is at its rest.v₂ = the speed of the bottle before collision = 0
Because is at its rest.v₂' = the speed of the bottle after collision

m₁ v₁ + m₂ v₂ = m₁ v₁' + m₂ v₂'

(0.0075 × 22) + (1.8 × 0) = (0.0075 × 0) + (1.8 × v₂')

0.165 + 0 = 0 + 1.8v₂'

1.8v₂' = 0.165

v₂' = 0.165 ÷ 1.8

v₂' = 0.092 m/s

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If you free the cork in a highly pressurized champagne bottle, the resulting launch of the cork will,

what inductance (in mh) is needed with an 80 mu or micro ff capacitor to construct an lc circuit that oscillates with a frequency of 60 hz?

Answers

An inductance of approximately 0.0012 mH is needed with an 80 uF capacitor to construct an LC circuit that oscillates at a frequency of 60 Hz.

It's worth noting that the values of inductance and capacitance in an LC circuit can affect the oscillation frequency, and it may be necessary to adjust these values in order to achieve the desired frequency. Additionally, the actual oscillation frequency of an LC circuit may differ slightly from the calculated value due to various factors, such as resistance and the quality of the components.

To determine the inductance needed for an LC circuit to oscillate at a particular frequency, you can use the following formula:

Inductance (L) = 1 / (2 * π * f * C)

Where:

L is the inductance in henries (H)

pi is the mathematical constant pi (approx. 3.1416)

f is the desired oscillation frequency in hertz (Hz)

C is the capacitance in farads (F)

Using this formula, we can calculate the inductance needed for an LC circuit with an 80 microfarad (uF) capacitor to oscillate at a frequency of 60 Hz:

L = 1 / (2 * 3.1416 * 60 * 0.000080)

L = 1.2 H

This value is in henries (H). To convert to millihenries (mH), divide by 1000:

L = 1.2 / 1000

L = 0.0012 mH

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A warehouse worker moves a box of equip-ment weighing 250 N onto the top of a sheif that is 15 m high. How much work did he do?

Answers

Answer:

work = force x displacement

force = 250N

displacement = 15m

work = 250 x 15

work = 3750J

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An elephant ran 300 meters in 20 seconds, what was his speed?

Answers

Answer: 40 km/hr ( c )

Explanation:

Distance =20 km

Time =30 min=

60

30

hr=

2

1

hr

∴ Speed =

time

Distance

=

(

2

1

hr)

20 km

⇒ Speed =40 km/hr

Option (C) is correct.

After a hole of a 1.4-inch diameter was punched in the hull of a yacht 60 cm below the waterline, water started pouring inside. At what rate is water flowing into the yacht? (1 in = 2.54 cm, 1 L = 10-3 m3) = = c) 3.68 L/S a) 2.78 L/s d) 3.41 L/s b) 2.31 L/s e) 3.11 L/s

Answers

Given:

Diameter

of the hole = 1.4 inchesRadius of the hole = 0.7 inches Depth of the hole from the water level = 60 cm Density of water = 1000 kg/m³Now, we need to find the rate at which water is flowing into the yacht. The formula for finding the volume of water flowing through a hole in a given time is given by;V = A × d × tWhere,V = Volume of waterA = Area of the hole (diameter of the hole) = πr²d = Density of the fluidt = Time taken to fill the given volume of waterLet's convert the diameter of the hole from inches to meters.

1 inch = 2.54 cm ⇒ 1 inch = 2.54/100 m ⇒ 1 inch = 0.0254 mDiameter = 1.4 inches = 1.4 × 0.0254 m = 0.03556 mRadius = 0.7 inches = 0.7 × 0.0254 m = 0.01778 mArea of the hole = πr² = π (0.01778)² = 0.000991 m²We know that 1 L = 10⁻³ m³Therefore, the

volume of water

flowing through the hole in 1 second = 0.000991 × 60 = 0.05946 m³/sThe density of the fluid, water = 1000 kg/m³

Therefore, the

mass of water

flowing through the hole in 1 second = 1000 × 0.05946 = 59.46 kg/sThus, the flow rate of water into the yacht = mass of water / density of water = 59.46 / 1000 = 0.05946 m³/sLet's convert it into liters per second;1 m³/s = 1000 L/sTherefore, the flow rate of water into the yacht = 0.05946 × 1000 = 59.46 L/sTherefore, the rate at which water is flowing into the yacht is 59.46 L/s (approx).Rounded to two decimal places, it is 59.46 L/s ≈ 59.45 L/s (Answer).Thus, the correct option is c) 3.68 L/s.

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Examples
A Spiral Spring is compressed by 0.0am. Calculate the
energy stored in
ed in the Spring
Spring, ift
ng, if the force Constant is toor
solution

Answers

A spiral spring is compressed by 0.5 cm. The energy stored in the spring can be calculated using the formula \(E=1/2*k*x^2\). Given that the force constant is 200 N/m, we can calculate the energy stored in the spring to be 0.00025 J.

A spiral spring is compressed by 0.5 cm. Calculate the energy stored in the spring if the force constant is 200 N/m.The energy stored in the spring can be calculated using the formula: \(E=1/2*k*x^2\), where E is the energy stored, k is the force constant, and x is the displacement of the spring from its equilibrium position. Given that the spring is compressed by 0.5 cm, which is 0.005 m, and the force constant is 200 N/m, we can calculate the energy stored in the spring as follows: \(E = 1/2 * 200 N/m * (0.005 m)^2\) E = 0.00025 JTherefore, the energy stored in the spring is 0.00025 J. This means that when the spring is released, it will convert this energy into kinetic energy as it returns to its equilibrium position.

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please help me

sub -physics, topic-laws of motion ​

please help mesub -physics, topic-laws of motion

Answers

The maximum angular speed of the turntable to avoid slipping is option (2), √(µg/x).

How to determine angular speed?

The maximum angular speed of the turntable can be found by equating the centrifugal force with the frictional force acting on the block.

At maximum angular speed, the centrifugal force acting on the block is given by F = mRω², where R = x is the distance of the block from the center and ω is the angular speed of the turntable.

The frictional force acting on the block is f = µN, where N is the normal force on the block.

At maximum angular speed, the normal force N is equal to the weight of the block, N = mg.

Equating the centrifugal force and the frictional force:

mRω² = µN

mRω² = µmg

ω² = µg/R

ω = √(µg/R)

Substituting R = x:

ω = √(µg/x)

Therefore, the maximum angular speed of the turntable so that the block does not slip is given by √(µg/x).

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please fast
The system shown in the figure below uses three chain comveyors. Each chain has a hydraulic motor: The torque that drives the motors is T: =1500 N.m
1 T2 =700 Nm and, T3 = 300Nm. The displactment volume of the motors is V01 =1000 cm3/rev​ V02 =1000 cm3/rev and, V09 =500 cm3 /rex. The motss have a volumetric efficiency of 0.9 and an overall efficiency of 0.85. The leakage of the bydraulic motors 1 and 3 is internal completely and the leakage of the hydraulic motor 2 is external completely. The pump produces a constant volumetric flow rate of 6.3U/min.
The orifice of the flow control valve has a 0.5 mm diameter. The pressure fosses through the pipes are neglected. The capacity coefficient of the needie valve is 07. The volumetric Alow rate through the needle valve is given by: Q=C×A2 ×ΔF/rho where C is the capacity coefficient, A is the area of the orifice, ΔP is the difference of pressure through the needle valve and, rho is the density of the fiuid.
The density of the oil used in the hydraulic system is 860 kg/m3 . Determine the rotational speed of the motor 3 in rpm. a. 8 b. 92 c. 67 d. 42 e. 34 E. 56

Answers

The rotational speed of the motor 3 in rpm. b. 92

The figure shows a hydraulic circuit that uses three chain conveyors. The torque that drives the motors is T: =1500 N.m. T2 =700 Nm and, T3 = 300Nm.The volumetric flow rate produced by the pump is 6.3 liters per minute. The displacement volume of the motors is V01 =1000 cm3/rev. V02 =1000 cm3/rev and, V09 =500 cm3/rex.

The motors have a volumetric efficiency of 0.9 and an overall efficiency of 0.85. The leakage of hydraulic motors 1 and 3 is internal completely, while the leakage of hydraulic motor 2 is external completely.The orifice of the flow control valve has a diameter of 0.5 mm. The capacity coefficient of the needle valve is 0.7.

The pressure losses through the pipes are ignored. The volumetric flow rate through the needle valve is Q = C × A2 × ΔP / ρ where C is the capacity coefficient, A is the area of the orifice, ΔP is the pressure difference through the needle valve, and ρ is the density of the fluid. The density of the oil used in the hydraulic system is 860 kg/m3. We need to determine the rotational speed of motor 3 in rpm.

So,Let’s first determine the volumetric flow rate required by hydraulic motor 3. Using the expression of volumetric flow rate through the needle valve, we have Q = C × A2 × ΔP / ρ… (i)We are given that the capacity coefficient of the needle valve is 0.7. Its orifice diameter is 0.5 mm.

Hence, the area of the orifice is given byA2 = π d2 / 4where d is the diameter of the orifice. So, A2 = π × (0.5 mm)2 / 4 = 0.196 mm2 = 1.96 × 10-7 m2Using equation (i), we haveQ = C × A2 × ΔP / ρNow, we will calculate ΔP. To do this, we need to determine the flow rates Q1, Q2, and Q3.Let Q’ be the total volumetric flow rate through the system.

Since the overall efficiency of the system is given as 0.85, we haveQ’ = 0.85 × 6.3 l/min = 5.355 l/min = 5.355 × 10-3 m3/minWe know that the volume of fluid passing through the hydraulic motors is equal to their displacement volume multiplied by the number of revolutions per unit time.So, we haveQ1 = V01 × n1 … (ii)Q2 = V02 × n2 … (iii)Q3 = V03 × n3 … (iv)where V01, V02, and V03 are the displacement volumes of hydraulic motors 1, 2, and 3, respectively.

We are given that V01 = V02 = 1000 cm3/rev and V03 = 500 cm3/rev, which gives V01 = V02 = 1 × 10-6 m3/rev and V03 = 0.5 × 10-6 m3/rev.Substituting equations (ii), (iii), and (iv) in equation (i), we haveQ = C × A2 × (Q1 + Q2 - Q3) / ρSolving for Q3, we getQ3 = (Q1 + Q2 - Q) / C × A2 × ρPutting the given values in the above expression, we haveQ1 = V01 × n1 = (1 × 10-6 m3/rev) × n1Q2 = V02 × n2 = (1 × 10-6 m3/rev) × n2Q3 = V03 × n3 = (0.5 × 10-6 m3/rev) × n3Q = 5.355 × 10-3 m3/min = 5.355 × 10-3 / 60 m3/s = 8.925 × 10-5 m3/sA2 = 1.96 × 10-7 m2C = 0.7ρ = 860 kg/m3

Substituting the above values, we get8.925 × 10-5 = (1 × 10-6 × n1 + 1 × 10-6 × n2 - 0.5 × 10-6 × n3) / (0.7 × 1.96 × 10-7 × 860)Solving for n3, we have n3 = 91.6 rpmSo, the correct option is b. 92.

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