Jupiter: largest planet Saturn: has the most conspicuous rings Uranus: has the most highly inclined rotation axis Neptune: has the medium-sized moon Triton in orbit
Jupiter is the largest planet in the Solar System, with a diameter of over 140,000 kilometers and a mass about 318 times that of Earth. It is the fifth planet from the Sun and is known for its strong magnetic field and large number of moons, including the four Galilean moons - Io, Europa, Ganymede, and Callisto - which were discovered by Galileo Galilei in the 17th century.
Saturn is the second-largest planet in the Solar System and is known for its beautiful and prominent ring system, which is composed of ice, rock, and dust particles. The rings are tilted relative to the planet's equator, and the width of the rings varies from about 10 meters to over 20,000 kilometers.
Uranus is the seventh planet from the Sun and is notable for its unusual orientation, with its axis of rotation tilted at an angle of about 98 degrees relative to its orbit around the Sun. This means that Uranus experiences extreme seasons, with each hemisphere experiencing about 42 years of daylight and darkness.
Neptune is the eighth and outermost planet in the Solar System and is known for its bright blue appearance and strong winds. It has a medium-sized moon called Triton, which orbits the planet in a retrograde direction (opposite to the planet's rotation). Triton is thought to be a Kuiper Belt object that was captured by Neptune's gravity and is the only large moon in the Solar System that orbits in this direction.
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Which vector is the sum of the vectors shown below?
The vector that runs from the upper right vector's head to the lower left vector's tail is the vector sum. None of the vectors presented as possible answers in this case appear to fit the direction.
Which vector depicts the addition of the two provided vectors?The outcome is the total of at least two vectors. Either the triangle approach or the parallelogram method can be used to determine the product of two vectors.
Which vector contains the sum of the other two?The sum of two or more vectors is known as the outcome. It comes about as a result of multiplying two or more vectors. The resultant is a term used to describe the addition of two or more vectors.
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The 3.0 cm-diameter water line in the figure splits into two 1.0 cm-diameter pipes. All pipes are circular and at the same elevation. At point A, the water speed is 2.0 m/s and the gauge pressure is 50 kPa.
What is the gauge pressure at point B?
At point B, the gauge pressure is 22 kPa.
Calculation:
Given gauge pressure is 50 kPa.
Diameter is 3.0cm
speed is 2.0m/s
the gauge pressure is 22 kPa.
How can you figure out a point's gauge pressure?Pg denotes gauge pressure, which is related to absolute pressure as follows: Pa is the local atmospheric pressure, and pg is equal to p - pa. Example: 32.0 psi is the tire pressure as measured by an automobile tire gauge. 14.2 psi is the atmospheric pressure in the area.
What is a point's gauge pressure?In order to calculate gauge pressure, atmospheric (ambient) pressure is subtracted from absolute pressure. A scenario where the absolute pressure is higher than the atmospheric pressure is referred to as positive overpressure, and a situation where the absolute pressure is lower than the atmospheric pressure is referred to as negative overpressure.
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Incomplete question:
The 3.0-cm diameter water line shown at right splits into two 1.0-cm diameter pipes. All pipes are circular and at the same elevation. At point A, the water speed is 2.0 m/s and the gauge pressure is 50 kPa. What is the gauge pressure at point B?
A)12 kPa B)22 kPa C)29 kPa D)38 kPa E)42 kPa
A 64 kg male ice skater is facing a 41 kg female ice skater. They are at rest on the ice. They push off each
other and move in opposite directions. The female skater moves backwards with a speed of 3.6 m/s. What is
the velocity of the male skater?
From conservation of linear momentum, the magnitude of the forward velocity of the male skater is 2.31 m/s
What is Momentum ?Momentum can simply be defined as a product of mass and velocity. It is a vector quantity.
Given that a 64 kg male ice skater is facing a 41 kg female ice skater. They are at rest on the ice. They push off each other and move in opposite directions. The female skater moves backwards with a speed of 3.6 m/s.
According to Newton's third law, in any action, there will be equal and opposite reaction.
The velocity of the male skater can be known from the conservation of linear momentum. That is
MV = mu
Where
M = mass of the male = 64 KgV = male speed = ?m = mass of the female = 41 Kgu = female speed = 3.6 m/sSubstitute all the parameters into the formula
64 × V = 41 × 3.6
V = 147.6 / 64
V = 2.31 m/s
Therefore, the velocity of the male skater is 2.31 m/s in the opposite direction.
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cA proton and an electron are held a short distance apart and released from rest. The only nonnegligible forces on the particles are the electrostatic forces they exert on each other. Which of the following statements is true? The magnitude of the electrostatic force exerted on the proton by the electron is greater than that exerted on the electron by the proton. The magnitude of the acceleration of the proton is less than the magnitude of the acceleration of the electron The proton must move a larger distance to have the same magnitude change in potential energy as the electron. The proton must move the same distance to have the same change in speed as the electron.
The magnitude of the electrostatic force exerted on the proton by the electron is greater than that exerted on the electron by the proton.
What kind of force is electrostatic?
The Coulomb's inverse-square law, sometimes known as Coulomb's law, is an observational physical principle that measures the force exerted between two electrically charged particles that are stationary. Common names for the electric created between two charged objects at rest include electrostatic force and Coulomb force.
Electrostatic force, where is it?Between two charges that are separated by a distance, there is an electrostatic force. The size of each charges and the separation between them determine the strength of the electrostatic force. Two charges that are either positive or negative when placed together repel one another.
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the potential difference across the terminals of a battery is 8.20 v when there is a current of 1.55 a in the battery from the negative to the positive terminal. when the current is 3.52 a in the reverse direction, the potential difference becomes 10.40 v.
potential difference across the terminals of a battery is 8.2
V when there is a current of 1.54A in the battery from the negative to the positive terminal. When the current is 3.49A in the reverse direction, the potential difference becomes 9.2V
A-What is the internal resistance of the battery?
B-What is the emf of the battery?
The battery's emf is 8.87V and its internal resistance is 0.43. The internal resistance of the battery is 0.19, and its emf is 8.49 V.
1).
8.2=E−1.55r
10.40=E+3.52r
Solving these two equations we get
r=0.43Ω and E=8.87V
2).
8.2=E−1.54r
9.2=E+3.49r
Solving these two equations we get
r=0.19Ω and E=8.49V
The opposition a substance provides to the flow of electrical current is referred to as resistance. The capital letter R is used to symbolize it. The ohm, frequently written as a word and occasionally represented by the uppercase Greek letter omega, is the commonly used unit of resistance.
A component's resistance is one ohm when a one-volt potential difference (voltage) is present across it and an electric current of one ampere flows through it. (See Ohm's law for further information on how current, resistance, and voltage are related.)
Generally speaking, the current in a direct-current (DC) electrical circuit is inversely proportional to the resistance while the supplied voltage is held constant.
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A riverside warehouse has several small doors facing the river. Two of these doors are open. The walls of the warehouse are lined with sound-absorbing material. Two people stand at a distance L=150 from the wall with the open doors. Person A stand along a line passing through the mid-point between the open doors, and person B stands a distance y=20m to his side. A boat on the river sounds its horn. To person A, the sound is loud and clear. To person B, the sound is barely audible. The principal wavelength of the sound waves is 3.00 m. Assuming person B is at the position of the first minimum, determine the distance d between the doors, center to center.
The distance d between the doors, center to center is 11.3m
Location. of A = central. maximum, location. of B = first. minimum.
ΔY = [Ymin - Ymax] = λL/d (0 + 1/2) - 0 = 1/2 λL/d = 20m
distance d = λL/40m = 3 * 150/40 = 11.3m
The length of a particular path between two points, such as the distance walked through a maze, is what is referred to as an object's "distance traveled" [6]. Even a ball thrown straight up or the Earth after it completes an orbit can be considered as having a closed distance along a closed curve that begins and ends at the same location. As the curve's arc length, this is formalized mathematically.
A distance can also be signed, with a forward distance being positive and a backward distance being negative.
When constructing automobiles or mechanical gears, designers should take into account circular distance, which is the distance covered by a point on a wheel's circle (see also odometry). The wheel's circumference measures.
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On the surface of the moon, gravity is 1.6m/s^2. An astronaut has a mass of 90kg.
(a) Calculate his weight on earth.
(b) State his mass when on the moon.
(c) Calculate his weight on the moon.
Answer:
Hope this helps.
Explanation:
(a) To calculate the astronaut's weight on Earth, you can use the formula for weight, which is W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity. On Earth, the acceleration due to gravity is approximately 9.8 m/s^2. So the astronaut's weight on Earth would be W = 90 kg * 9.8 m/s^2 = <<90*9.8=882>>882 N.
(b) The astronaut's mass when on the moon is the same as it is on Earth, which is 90 kg.
(c) To calculate the astronaut's weight on the moon, you can use the same formula as before, but with the acceleration due to gravity on the moon, which is 1.6 m/s^2. The astronaut's weight on the moon would be W = 90 kg * 1.6 m/s^2 = <<90*1.6=144>>144 N.
as the sun rotates, an individual sunspot can be tracked across its face. from eastern to western limb, this takes about as the sun rotates, an individual sunspot can be tracked across its face. from eastern to western limb, this takes about 12 hours. a week. two weeks. a month. 5.5 years.
A specific sunspot can be followed as it moves over the Sun's surface as it revolves. This takes approximately from eastern to western limb.
While moving over the Earth-side of the sun, super sunspot AR2192 generated 10 major solar flares, six of which were X-class and four of which were above M5-class. These photos from NASA's SDO, taken between October 17 and October 29, 2014, show a sunspot that is the largest since November 1990 moving across the front of the sun. Try restarting your device if playback doesn't start right away. These photos from NASA's SDO, taken between October 17 and October 29, 2014, show a sunspot that is the largest since November 1990 moving across the front of the sun. Try restarting your device if playback doesn't start right away. Your watched videos might be added to.
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if a thin film has a thickness that is if a thin film has a thickness that is 14 of a wavelength, destructive interference will always occur. 14 of a wavelength, constructive interference will always occur. 12 of a wavelength, constructive interference will always occur. 12 of a wavelength, destructive interference will always occur. none of the above is always true.
However, at an oblique angle of incidence, the thickness will be equal to the cosine of the angle at the quarter or half-wavelength points. At a normal angle of incidence, the thickness will normally be a quarter or half multiple of the center wavelength.
What is the thin film's wavelength?White light is incident on a thin film of soap solution at an angle of incidence of I = sin-1(4/5). Two black overlapping fringes with wavelengths of 6.1 x 10-7 m and 6.0 x 10-7 m are seen in the reflected light.
How is interference in thin films determined?The index of refraction affects the wavelength of light. Thus, the wavelength of the light incident on the thin film itself must be taken into account in interference concerns.
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9. a solid metal ball of radius 1.3 cm bearing a charge of 6.2 nc is located near to and along the midline of a hollow uniformly charged plastic rod of radius 1.9 cm and length 12.5 m bearing a uniformly distributed charge of 7.1 nc (see the figure) on its outer surface. the distance between the center of the rod and the center of the ball is 25.5 cm.
Since a metal ball is considered a solid sphere So the electric field inside the metal ball is given by E = (p/3∈₀)r
Where r is the distance from the center and rho is charge density. Hence at the center r = 0
Then electric field
E = (p/3∈₀) x 0 = 0 N/C
Hence electric field at the center of the metal ball is due to its own charge only being 0N/C.
An electrical property is associated with any point in space when some form of electric charge is present. The magnitude and direction of the electric field are represented by the value of E and are called field strength or electric field strength or simply electric field.
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Disk A has a weight of 5 lb and Disk B has a weight of 10 lb. If no slipping occurs between them,
determine the couple moment M which must be applied to Disk A to give it an angular acceleration of 4 rad/s
2
. Radius A is 0.5 ft. Radius B is 0.75 ft.
The couple moment M = 0.233 lb.ft
Given,
The weight of disc A = 5 lb
The radius of disc A = 0.5 ft
The weight of disc B = 10 lb
The radius of disc B = 0.75 ft
Angular acceleration of disc A = 4 rad/s²
Let,
The couple moment = M
Disc A:
∑[tex]M_{A} = I_{A} \alpha_{A}[/tex]
M - F(0.5) = (1/2)(5/32.2)(0.5)²(4)
2M - F = 0.078 ..........................(1)
Disc B:
∑[tex]M_{B} =I_{B} \alpha _{B}[/tex]
F = (1/2)(10/32.2)(0.75)²[tex]\alpha _{B}[/tex] .............(2)
[tex]r_{A} \alpha _{A} =r_{B} \alpha _{B}[/tex]
0.5(4) = (0.75)[tex]\alpha_{B}[/tex] .....................................(3)
By solving equations (1), (2), and (3) we get
M = 0.233 lb.ft
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In the engine of a locomotive, a cylindrical piece known as a piston oscillates in SHM in a cylinder head (cylindrical chamber) with an angular frequency of 180rev/min. Its stroke (twice the amplitude) is 0.76m. What is its maximum speed?
A cylindrical component known as a piston oscillates in the cylinder head (cylindrical chamber) of a locomotive's engine. 0.76 meters is the stroke, which is twice the amplitude. Its greatest speed is 7.2m/s.
We use v[tex]_{m}[/tex] =ωx[tex]_{m}[/tex]=2πfx[tex]_{m}[/tex], where the frequency is 180/(60s)=3.0Hz and the amplitude is half the stroke, or x[tex]_{m}[/tex]=0.38m. Thus,
v[tex]_{m}[/tex]=2π(3.0Hz)(0.38m)=7.2m/s.
A piston is a disc or short cylinder that fits snugly inside an engine cylinder and imparts motion to a pump or a liquid or gas by moving up and down against it. Pneumatic and hydraulic cylinders, reciprocating engines, reciprocating pumps, gas compressors, and other related devices all have pistons. It is the moving part that has a cylinder around it and piston rings that seal the gas tightness.
To transfer force from the expanding gas in the cylinder to the crankshaft via a piston rod and/or connecting rod is the function of a piston rod and/or connecting rod in an engine.
The processes of intake, compression, combustion, and exhaust are all four-stroke operations in automobile engines.
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Radio waves travel at the speed of light, 300,000 km/s. The wavelength of a radio wave received at 100 megahertz is
A) 0.3 m.
B) 3.0 m.
C) 30 m.
D) 300 m.
E) none of these
B
Option (B)- 300,000 km/s is the speed at which radio waves move through the air. A radio wave with a frequency of 100 megahertz has a wavelength of 3.0 m.
Use the relationship: wavelength = speed/frequency = 300,000,000 m/s / 100,000,000 = 3 m.
The electromagnetic spectrum's longest wavelengths, which are found in a radio wave, are normally found at frequencies of 300 gigahertz (GHz) and lower. The wavelength for 30 Hz is 10,000 kilometers (6,200 miles) while the wavelength for 300 GHz is 1 mm (shorter than a grain of rice) (longer than the radius of the Earth). Like all electromagnetic waves, radio waves move at the speed of light in a vacuum and at a nearly same, slightly slower speed in the Earth's atmosphere. Charged particles, such as time-varying electric currents, that are accelerating produce radio waves. All warm objects emit blackbody radiation, which includes naturally occurring radio waves emitted by lightning and celestial objects.
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jocelyn was researching what makes certain surfaces have mirror-like qualities. she knows that most mirrors are made from aluminum, as are soda cans. she wondered why she can see her face in a mirror but not in a soda can. fill in the correct words to complete the sentences. the mirror is polished smooth, so that reflection occurs. the soda can, however, has a rougher surface, so that reflection occurs.
The Mirror is polished smooth so that specular reflection occurs. The soda can have a rougher surface, so that diffusion reflection occurs.
What is specular reflection?Diffuse reflection reflects light in a variety of directions, as opposed to specular reflection, which reflects all light that comes from a single direction at the same angle.
The incident light is only reflected in one outgoing direction during specular reflection. On a surface known as a specular surface, which resembles a mirror, light reflects at the angle of incidence.
The finest example of specular reflection is found in mirrors, which have a highly reflective substance that reflects the whole visible light spectrum under the glass surface.
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A concave mirror with a focal length of 40 cm. How far should the mirror be
held from his face in order to give an image of two-fold magnification
The mirror should be held at a distance of 60cm
What is Magnification?Magnification is defined as the ratio of the height of image to the height of object. It can also be defined as the ratio of distance of image from mirror or lens to the distance of object from lens.
Magnification is given as v/u . where v is the image distance and u is the object distance.
therefore 2 = v/u
v = 2u
from the mirror formula
1/f = 1/v+ 1/u . where F is the focal length
represent 2u for v
1/f = 1/2u + I/u
1/f = 3/2u
1/40 = 3/2u
2u = 120
divide both sides by 2
u = 120/2
u = 60cm
therefore the object distance is 60cm. This means that to have a double sized image , the distance from the mirror and his face must be 60cm.
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A circular saw is powered by a motor. When the saw is used to cut wood, the wood exerts a torque of 0.80N on the saw blade. If the blade rotates with a constant angular velocity of 20 rad/s the work done on the blade by the motor in 1.0 minis:
A. 0
B. 480 J
C. 960 J
D. 1400 J
J E. 1800 J
If the blade rotates with a constant angular velocity of 20 rad/s the work done on the blade by the motor in 1.0 min IS 960 J.
A torque is a force that causes rotation. Tells how effective force is at twisting or rotating an object.
Conditions for Equilibrium is that when FNet = 0 Translational EQ (Center of Mass) tNet = 0 Rotational EQ (True for any axis). Choose axis of rotation wisely to make problems easier, But as long as you’re consistent everything will be okay.
Gravitational Force Weight = mg, acts as force at center of mass, Torque about pivot due to gravity t = mgd, object not in static equilibrium.
As we know,
work = torque x angular displacement
θ = ωt
θ = 20 x 60
θ = 1200rad
hence,
work = 0.80 x 1200
W = 960J
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an archer shoots an arrow. consider the action force to be exerted by the bowstring against the arrow. the reaction to this force is the question 39 options: friction of the ground against the archer's feet. grip of the archer'shand on the bow. air resistance against the bow. arrow's push against the bowstring.
This means that if object 1 hits object 2, object 2 will also hit object 1 with the same amount of force.
It is given that the string exerts a force on the arrow during the shooting of an arrow.
From Newton's third law, the arrow should also apply a force on the string. Thus, the reaction force is, arrow's push against the bowstring. Option (a) is correct.
The third law states that the two equal and opposite forces act on the two bodies in the system.
This means that if object 1 hits object 2, object 2 will also hit object 1 with the same amount of force.
The third law also satisfies the gravitational force between the two objects. The attractive force between the two objects is the same for both. Depending on their masses, their accelerations may vary, but the pull force between them remains the same.
Complete question:An archer shoots an arrow. Consider the action force to be the bowstring against the arrow. The reaction to this force is the:
A. arrow's push against the bowstring
B. weight of the arrow
C. air resistance against the bow
D. grip of the archers hand on the bow
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what's the effect of gravity on the balance?
Answer:
Explanation:
The lower your center of gravity, the easier it is to keep your balance. If you're sitting on a chair, you can lean over more than if you're standing up. With your center of gravity low, you can lean further to one side or the other without creating enough turning force to tip you over.
did theoretical and experimental values agree? if they did not agree, explain why. in newton second law atwoood lab
Conclusion/Discussion In conclusion, we tested the theory of Newton's Second Law of Motion using the Atwood Machine. In order to test the proportionalities the second law suggests, I was able to plot two graphs and successfully calculate the acceleration of each of my trials.
The second law of Newton will be thoroughly investigated in this experiment. According to Newton's second law, force is defined as mass times acceleration (F=mxa). Simply said, his law outlines the connection between an object's mass, acceleration, and required force to move it.
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wo identical blocks are pushed up frictionless inclines as shown. consider the portion of the motion of block 1 during which it moves a distance l1 , and the portion of the motion of block 2 during which it moves a distance l2, which is greater than l1. each block is displaced the same vertical distance z.
In terms of work produced, the gravitational force acting on block 2 is equal to that acting on block 1.
The quantity of labor is equal to zero when an object moves a fixed distance. The movement of the item as well as the applied load define the quantity of work. It rises in tandem with displacement and vice versa.
Blocks 2 and 1 are the same and are frictionlessly raised to the identical height, h = Z.
As a result, both blocks will have the same mass and gravitational pull.
m1 = m2
FG = m1g = m2g
Gravitational acceleration (g) is indicated here.
the labor put in while block 2 is subject to the gravitational pull.
W2 = m2gh
When gravity pulls on block 1, what labor is done on block 1?
W1 = m1gh
W1 = m1gZ
W1 = m2gZ , [m1=m2]
W1 = W2
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The question is -
Two identical blocks are pushed up frictionless inclines as shown. Consider the portion of the motion of block 1 during which it moves a distance of L 1 and the portion of the motion of block 2 during which it moves a distance of L 2. Each block is displaced the same vertical distance Z. The hand pushes parallel to the incline with the same magnitude of force F B H in both cases. Block 2 moves at a decreasing speed. Is the absolute value of the work done by the gravitational force on block 2 greater than, less than, or equal to the work done by the gravitational force on block 1? Explain.
a pulley on a friction- less axle has the shape of a uniform solid disk of mass 2.50 kg and ra- dius 20.0 cm. a 1.50 kg stone is attached to a very light wire that is wrapped around the rim of the pul- ley (fig. e9.47), and the system is released from rest. (a) how far must the stone fall so that the pulley has 4.50 j of kinetic energy? (b) what percent of the total kinetic energy does the pulley have?
The system's potential energy will be lost because it is no longer at rest, while its kinetic energy will increase.
Therefore,
Loss in potential energy = gain in (kinetic energy of the pulley + kinetic energy of the stone) ...........…..(1)
Let, the stone falls by a distance of h.
Given, the mass of the pulley disk mₚ = 2.50 kg
Its radius r = 20.0 cm = 0.2 m
Its moment of inertia I = (1/2)mₚr²
I = (1/2)(2.50 kg)(0.2 m)²
I = 0.05 kgm²
Given, the kinetic energy of the pulley disk = 4.50 J
If w the angular velocity of the pulley,
(1/2)Iw² = 4.50 J
(1/2)(0.05 kgm²)w²= 4.50 J
w² = 9/0.05 rad²/s²
w² =180 rad²/s²
v² = 180(0.2)^2 m²/s²
v² = 7.2 m²/s²
Given, the mass of the stone mₛ = 1.50 kg
Its kinetic energy = (1/2)(1.50 kg)(7.2 m²/s²) = 5.4 J
Potential energy loss of the stone = (1.50 kg)(9.80 m/s²)h
(a) Therefore, from equation (1), w get
(1.50 kg)(9.80 m/s²)h = 4.5 J + 5.4 J
h = (9.9 J)/(1.50 kg)(9.80 m/s²)
h = 0.673 m
So, the stone must fall by a distance of 0.673 m.
(b) Total kinetic energy of the system = 9.9 J
The kinetic energy of the pulley = 4.50 J
The pulley’s fraction of kinetic energy = 4.50 J/9.9 J
= 0.455 = 45.5%
Therefore, the pulley has 45.5% of the total kinetic energy.
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Vinegar is a solution of acetic acid in water. Which term best describes water in this solution?
Answer:
Solvent
Explanation:
In a solution of vinegar, water is the solvent. A solvent is a substance that dissolves another substance (in this case, acetic acid) to form a solution. The substance that is dissolved is called the solute. In the case of vinegar, the solute is acetic acid and the solvent is water.
star a is 5l ight years away an identiccal star of the absolute luminosity star b is 10 light years away compare tehir relative apparent brightness
In terms of the amount of light years energy received, star A should appear 100 times brighter than star B. This is due to the fact that received energy diminishes according to squared distance.
How far apart are two stars from one another?Contact binaries are binary star systems with members whose distance from one another is so great that their outer envelopes actually touch. This structure can actually be rather stable, with typical lifetimes measured in millions or even billions of years, which may surprise you.
How do we figure out how far away the stars are from Earth?When the Earth is at the other end of the star's orbit, six months later, astronomers take another measurement of the star's position. This results in a base line that is equal to the sum of the two angles used to measure the star and the double distance from Earth to the Sun's center (about 300,000,000 km). The distance to a nearby star can be calculated using these three variables in a very straightforward trigonometric manner.
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observe the above block diagram. consider 43.8440 rad/s/v to be the steady state value (also known as dc gain), and 0.0310 sec to be the ol time constant. the tach sensitivity is given by 0.0250 v/(rad/s). for a gain of 1.0000, the closed loop time constant , in seconds, is
The closed loop time constant , in seconds, is Vo(t) = (410/9 – 205/4 e-t + 205/36 e-9t) u(t).
What is steady state ?
The term "steady-state" refers to the condition in which a conductor can no longer absorb heat. During this stage, the temperature stabilizes. The heat, however, is constantly lost to the environment.
What is time constant ?
A first-order, linear time-invariant (LTI) system's reaction to a step input is characterized by a parameter known as the time constant, which is typically represented by the Greek letter tau. A first-order LTI system's primary defining attribute is its time constant.
Vin(s) 2/s+1 205/s+9 vo(s)
W(s) /Vin(s) = 2x205/(s+1) (s+9)
For step response
Vin(s) = 1/s
Vo (s) = 410/s (s) (s+9)
Using partial fraction method
Vo(s) = A/s + B/s+1 + C/s+9 - (1)
A= 410/(s+1) (s+9)|s=0 = 410/(0+1) (0+9) = 410/9
A= 410/9
B= 410/s(s+9) |s=-1 = 410/(-1) (=1+9) = -205/4
B = -205/4
C= 410/(s) (s+1)|s = -9 = 410/(-9) (-9+1) = 205/36
C=205/36
Substitute value of A,B and C in eq (1)
Vo(s) = 410/9s – 205/4(s+1) + 2052/36(s+9)
Apply inverse la place transform both side
L-1 (Vo(s) ) = L-1(410/9s) – L-1(205/4(s+1) ) + L-1 (205/36(s+9)
Vo(t) = 410/9 L-1 (1/s) -205/4 L-1 (1/s+1) + 205/36 L-1(1/(s+9))
Vo(t) = 410/9u(t) -205/4 e-t u(t) + 205/36 e-9t u (t)
Vo(t) = (410/9 – 205/4 e-t + 205/36 e-9t) u(t)
Therefore, the closed loop time constant , in seconds, is Vo(t) = (410/9 – 205/4 e-t + 205/36 e-9t) u(t).
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consider a rocket that has a specific heat ratio of 1.25 and a nozzle area ratio of 10:1. the stagnation pressure is 400 psi. using the plots below, estimate the design altitude for the rocket.
The points of the design altitude for the rocket, when the stagnation pressure is of 400 psi, using given plots will be :-
The Exit velocity and Pressure in the case of a rocket motor are 1290m/s and 8.1 atm respectively. The C* and thrust propellant calculations are based on certain formulas.
Exit velocity is v_e = sqrt((2 * C_p * 3000 K) / (1.25 - 1)) * sqrt((1.25 + 1) / 2) * (1 - (p_e / 60 atm) ^ ((1.25 - 1) / 1.25)) = 1290 m/s.Exit pressure is p_e = 60 atm * ((2 / (1.25 + 1)) * (1 - (1290 m/s / sqrt((1.25 + 1) / 2 * C_p * 3000 K)) / (1 - (p_e / 60 atm) ^ ((1.25 - 1) / 1.25)))) ^ (1.25 / (1.25 - 1)) = 8.1 atm. This is the pressure at the nozzle exit.To calculate c* for the propellant, we can use the equation c* = sqrt(1.25 * 8.314 J/mol-K * 3000 K / 18) = 654.3 m/s.To calculate the mass flow rate for the rocket, we find that m_dot = 60 atm * (pi * (5 cm / 2)^2 / 4) * 654.3 m/s / sqrt(3000 K) = 4.1 kg/s.To calculate the thrust of the rocket, we can use the equation that F= 4.1 kg/s * 1290 m/s + (8.1 atm * (pi * (30 cm / 2)^2 / 4) - 60 atm * (pi * (5 cm / 2)^2 / 4)) = 45600 N. This is the thrust produced by the rocket at sea level.To calculate the thrust coefficient of the rocket motor, we can use the equation C_F = (2 / (1.25 + 1)) * (1 - (1290 m/s / sqrt((1.25 + 1) / 2 * C_p * 3000 K)) / (1 - (8.1 atm / 60 atm) ^ ((1.25 - 1) / 1.25))) = 0.8. This is the thrust coefficient of the rocket motor.To calculate the effective exhaust velocity of the rocket motor, we can use the equation v_e, eff = v_e + g * Isp, where v_e, eff is the effective exhaust velocity, v_e is the exit velocity, g is the acceleration due to gravity, and Isp is the specific impulse. At sea level, g = 9.8 m/s^2.The specific impulse of the rocket motor is given by the equation Isp = (1.25 * 8.314 J/mol * K * 3000 K) / (9.8 m/s^2 * 18 g/mol) = 279 s.The effective exhaust velocity of the rocket motor is v_e, eff = 1290 m/s + 9.8 m/s^2 * 279 s = 36660 m/s. This is the effective exhaust velocity of the rocket motor when fired at sea level.To calculate the thrust of the rocket motor, we can use the equation F = 8.1 atm * 28.3 cm^2 * 1290 m/s = 3.1 * 10^6 N.To calculate the thrust coefficient, we can use the equation C_F = 3.1 * 10^6 N / (8.1 atm * 0.2 cm^2) = 0.16.To calculate the effective exhaust velocity of the rocket motor when fired in space, we can use the equation v_e = sqrt((2 * C_p * 3000 K) / (1.25 - 1)) * sqrt((1.25 + 1) / 2) * (1 - (0 / 60 atm) ^ ((1.25 - 1) / 1.25)) * sqrt(1 - ((18 / 18) ^ 2)) = 1290 m/s.To calculate the specific impulse of the rocket motor, we can use the equation I_sp = 1290 m/s / 9.8 m/s^2 = 131 s. This is the specific impulse of the rocket motor when fired in space.Therefore, these are the points of the design altitude for the rocket, when the stagnation pressure is of 400 psi, using given plots.
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[NOTE: THIS IS AN INCOMPLETE QUESTION. THE COMPLETE QUESTION IS: Consider a rocket motor equipped with a nozzle in which the stagnation conditions are 3000 K and 60 atm. The specific heat ratio is 1.25 and the molecular weight of the propellant is 18. The nozzle throat diameter is 5 cm and the nozzle exit diameter is 30 cm. a. Calculate the exit velocity b. Calculate the exit pressure c. Calculate c* for this propellant d. Calculate the mass flow rate for the rocket e. If the rocket is fired at sea level, calculate the thrust. f. If the rocket is fired at sea level, calculate the thrust coefficient g. If the rocket is fired at sea level, calculate the effective exhaust velocity h. If the rocket is fired at sea level, calculate the specific impulse. i. If the rocket is fired in space, calculate the thrust. j. If the rocket is fired in space, calculate the thrust coefficient k. If the rocket is fired in space, calculate the effective exhaust velocity I. If the rocket is fired in space, calculate the specific impulse]
Suppose you make a new kind of compact disk that is the same thickness as a current disk but twice the diameter. By what factor will the rotational inertia increase? Idisk= 1/2MR^2 8 2 16
If you make a new kind of compact disk that is twice the diameter of a current disk but has the same thickness, the rotational inertia of the new disk will increase by a factor of 8.
Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It is given by the formula:
I = 1/2 * m * r^2where I is the rotational inertia, m is the mass of the object, and r is the distance from the axis of rotation to the mass of the object.
If you double the diameter of a compact disk but keep the thickness the same, you are effectively doubling the distance from the axis of rotation to the mass of the disk (since the disk is the same thickness). This means that the rotational inertia of the disk will increase by a factor of 8 (2^2), since it is proportional to r^2.
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A driver notices that her 1380-kg car, when in neutral, slows down from 95 km/h to 65 km/h in about 7.0 s on a flat horizontal road. Approximately what power (watts) is needed to keep the car traveling at a constant 80 km/h? Approximately what power (hp) is needed to keep the car traveling at a constant 80 km/h?
.The power of the car is 12.8 watt or 0.017 hp.
Work done per unit time is power of a machine. It is a scalar quantity. Its S.I. unit is watt(w). Energy change is equal to power.
1 hp is equal to 746 w.
The given is,
mass of car = 1380 kg
Initial velocity V1 = 65km/s
Final velocity V2 = 80 km/s
Time t = 7 s
change in kinetic energy = 1/2m ( -v12 = 1/2 ×(80-65) J
= 1/2×180
= 90 J
This is equal to work done.
Now. power = W/t
90/7 = 12.8 w
So the power is 12.8 w = 12.8/ 746 w
0.017 hp.
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A block of mass 2kg starts from rest sliding down a rough inclined plane making an angle of 60⁰ with the horizontal length of plane in 8m it takes 4 second to return the bottom find the cofficent of kinetic friction
The force applied on the body that is on the inclined plane is given as, F=mgsinθ, F=2×9.8×sin30 =9.8N and f=μmgcosθ f=0.7×2×9.8cos30 =11.88N.
What is limiting friction?Any increase in the moving force will result in slippage; limiting friction only exists when the moving force and the force opposing motion are equal.
The limiting frictional force is independent of the area of contact and proportional to the normal reaction between the contacting surfaces.
The amount of friction that can be produced when two static surfaces come into touch. A motion will start as soon as the force applied to the two surfaces surpasses the limiting friction. The normal response force and the coefficient of limiting friction are combined to get the limiting friction for two dry surfaces.
Therefore, The force applied on the body that is on the inclined plane is given as, F=mgsinθ, F=2×9.8×sin30 =9.8N and f=μmgcosθ f=0.7×2×9.8cos30 =11.88N.
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The speed of a sound wave in air depends on
A) its wavelength.
B) All of the above choices are correct.
C) None of the above choices are correct.
D) the air temperature.
E) its frequency.
Option C. None of the above choices are correct, A sound wave in air moves at a certain speed depending on its frequency. None of the wavelengths above it. all the aforementioned air temperatures. ambient temperature.
Under the same physical conditions, the speed of sound is constant for all frequencies in a particular medium. Since the distance covered by the sound wave in a given amount of time is what determines the speed of sound, it can be calculated using the following formula: where v is the velocity, is the sound wave's wavelength, and f is the frequency. Since the distance covered by the sound wave in a given amount of time determines the speed of sound, the following formula can be used to calculate it: Where v is the speed, is the sound wave's wavelength, and f is the frequency.
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The ___________ was used to find a Jupiter-sized planet through careful measurements of the changing position of a star in the sky.
A planet the size of Jupiter was discovered using the astrometric approach by taking meticulous measurements of how a star's location changed over time.
A planet the size of Jupiter was discovered through astrology. use exact measurements of a star's shifting sky position. Its goal is to track the motion of such bodies against the background of other stars, making this technique the best for discovering very big planets that are orbiting stars other than their own. Big astral bodies, stars that are nearby, and astral bodies that are close to Earth are the greatest targets for this technique. Measurement is the quantifying of characteristics of an event or thing so that they can be compared to those of other events or objects.
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