It has a planet orbiting at a distance larger than 1 AU when you discover a star that rotates back and forth every 16 months and has the same mass as the sun.
How can a planet's orbit move inward due to a gravitational collision?How can a planet's orbit move inward due to a gravitational collision? Another object receives both energy and angular momentum from it.
Which of the following is true regarding the transit method of finding exoplanets?There are two fundamental obstacles to directly finding exoplanets. One is that as we go farther away from the earth, the angular size of planets decreases and is no longer able to be resolved in a picture.
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the shanghai maglev train takes 8 minutes to travel a distance of 30.5 kilometres.work out the average speed of the train. give your answer in kilometres per hour.
The average speed is 228.75 km/h.
What is speed?Speed is the time rate at which an object is travelling along a route. To put it another way, velocity is a vector, whereas speed is a scalar value.
What is the speed-distance formula?
Speed is equal to distance traveled and time spent.
Distance is determined by multiplying the time and the speed.
Time is determined by speed and distance.
Given:
Distance = 30.5 kilometers
Time= 8 minutes
= 8/60 hour = 2/15 hour
Now, average speed equals distance / time.
= 30.5 x 15/2
= 228.75 Km/ h
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a 0.29 kg harmonic oscillator has a total mechanical energy of 3.6 j. if the oscillation amplitude is 0.22 meters, what is the oscillation frequency f?
If the oscillation amplitude is 0.22m, from a 0.29kg harmonic oscillator which has a total of mechanical energy 3.6j, the oscillation frequency is 4.141Hz.
What is oscillation frequency?It is a number of oscillations in the one-time unit, says per second. For example, a pendulum that takes 0.5s to make one full oscillation has a frequency of 1 oscillation per 0.5s or 2 oscillations / second.
How to calculate the oscillation frequency?
mass (m) = 0.29kg
Total energy (E) = 3.6j
amplitude (x) = 0.22m
E = 1/2 k*x^2
k = 2*E / x^2
= 2 * 3.6 / 0.22^2
= 148.76 N/m
Frequency (v) = 1/2π √k/m
= 1/2*3.14 * √148.76 / 0.22
= 4.141Hz
Therefore, the oscillation frequency is 4.141Hz.
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in each figure, a magnet is located beneath a conducting loop and along its central axis. a velocity vector drawn near the magnet indicates that the magnet is moving, and a velocity vector drawn near the loop indicates that the loop is oving. for each case, indicate the direction of the induced current in the wire loop. the clockwise and counterclockwise directions are defined with respect to an observer viewing the loop from below.
Counterclockwise, Because north pole of magnet is moving towards loop and emf is induced in counterclockwise. b) Clockwise; Because north pole of magnet is moving away from the loop and flux is decreasing through loop so clockwise emf is induced.
Anything that creates a magnetic field is considered to be a magnet. The most noteworthy characteristic of a magnet—a force that pulls on other ferromagnetic elements like iron, steel, nickel, cobalt, etc.—is caused by this invisible magnetic field, which also attracts or repels other magnets.
A piece of equipment built from a substance that has been magnetized and produces a consistent magnetic field is called a permanent magnet. A typical illustration is a fridge magnet used to keep notes on the door of the refrigerator. Ferromagnetic materials are those that are both capable of magnetization and are attracted to magnets strongly (or ferrimagnetic).
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A block of iron has the dimensions of 3. 00 cm x 3. 00 cm x 3. 00 cm. It has a mass of 213 g. What is its density? 0. 0773 g/cm 3 638 g/cm 3 7. 89 g/cm 3 6240 g/cm 3.
Density of iron block is 7. 89 g/cm 3
Define density.
The substance's mass per unit of volume is its density (also known as specific mass or volumetric mass density). The Latin letter D can also be used to represent density, however the most common symbol is ρ (the lower case Greek letter rho). The mathematical definition of density is mass divided by volume.
Density, ρ = Mass (m)/ Volume(V)
Volume = 3 cm × 3cm × 3cm
= 27 cm ³
Mass = 213 g
Density = m/V
= 213/27
= 7.89 g / cm³
The word "specific volume," which is infrequently used in thermodynamics, refers to the reciprocal of a substance's density. A substance's density is an intense attribute in that its mass grows rather than its density when its amount is increased.
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a novelty clock has a 0.014-kg mass object bouncing on a spring that has a force constant of 1.6 n/m. (a) what is the maximum velocity of the object if the object bounces 3.45 cm above and below its equilibrium position?
Answer: The maximum velocity of the object if the object bounces 3.45 cm above and below its equilibrium position is 4.62 m/s.
Reason:
The maximum velocity of the object is 4.62 m/s. This can be calculated by using the equation v = sqrt(2 * g * x), where g is the acceleration due to gravity (9.8 m/s2) and x is the displacement from the equilibrium position (3.45 cm), or 0.0345 m.
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An infinitely long wire carrying a current of 3.10 A is bent at a right angle as shown in the figure. Determine the magnitude and direction of the magnetic field at the point P a distance
a = 23.9 cm
from each leg of the right angle bend.
magnitude ? T
direction ?
The direction of the magnetic field depends on the direction of the current in the wire.
What is magnetic field?
A magnetic field is indeed a vector field which explains the magnetic influence on moving electrical charges, electric currents, as well as magnetic materials. A force perpendicular to the charge's own motion and the magnetic field acts on it when the charge is moving through a magnetic field. The magnetic field of a permanent magnet pulls on magnetic material like iron and attracts as well as repels other magnets. The three other magnetic effects of paramagnetism, diamagnetism, as well as antiferromagnetism also exert minute forces on "nonmagnetic" materials in a nonuniform magnetic field, though these forces are typically so minute that they can only be discovered by laboratory equipment. Electric currents, like those used in electromagnets, as well as electric fields that change over time produce magnetic fields that surround magnetised materials.
The magnitude of the magnetic field at P can be determined using the equation B = μ0I/2πr, where μ0 is the permeability of free space, I is the current, and r is the distance from the wire. Thus, the magnetic field at P is:
B = (4π x 10-7 T•m/A) x (3.10 A) / (2π x 0.239 m) = 0.817 T
The direction of the magnetic field depends on the direction of the current in the wire. If the current is flowing in the clockwise direction, then the magnetic field will be directed out of the plane of the paper at P. If the current is flowing in the counterclockwise direction, then the magnetic field will be directed into the plane of the paper at P.
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a bicycle and ridder together have a momentum of 318 kg*m/s and are moving at 8 m/s l. what is their combined mass?
Answer: 39.75 kg
Explanation:
p = mv where,
p = momentum
m = mass
v = velocity
Given p=318 kg*m/s
v=8 m/s
therefore, 318=8*m
or, m= 318/8= 39.75
according to the special theory of relativity, all laws of nature are the same group of answer choices in all reference frames. in all uniformly moving reference frames. for both linear or circular motion. all of the above none of the above
According to the special theory of relativity, all laws of nature are the same in all uniformly moving reference frames. Option B.
Einstein's Special Theory of Relativity states that the same laws of physics apply to all inertial frames of reference and that the speed of light is the same for all observers. The basic laws of physics are the same for all inertial frames of reference.
Because otherwise, we wouldn't call it a fundamental law. Call them contingency laws and look for deeper fundamental laws that are invariant under a larger set of symmetries. Describes the propagation of matter and light at high speed. It is based on the constancy of the speed of light and the relativity principle in all inertial frames of reference.
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) what are the possible reasons we discussed for the existence of different types of galaxies in the universe?
There are many different sizes and shapes of galaxies. Low-angular-momentum protogalactic clouds may have generated spheroidal star systems, whereas clouds with larger angular
what is angular momentum?The characteristic of just about any rotating object determined by the product of the moment of inertia and the angular velocity is known as angular momentum. It is a characteristic of rotating bodies determined by the sum of their moment of inertia + angular velocity.
Why is angular momentum important? What is it?The rotational equivalent of linear momentum in physics is called angular momentum, also known as moment of momentum , rotational momentum. Because this is a constant number total angular momentum of such a closed environment stays constant—it is a significant physical quantity.
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if the collision is elastic, what are the final velocities v1 and v2 of particles 1 and 2? give the velocity v1 of particle 1 followed by the velocity v2 of particle 2, separated by a comma. express each velocity in terms of v.
Velocities V1 and V2 will exchange in general. Velocity may increase or decrease. If V1 decreases, then V2 increases. The angle between velocities also gets changed.
For a head-on elastic collision for two equal masses, the velocities gets exchanged. For a non-head-on elastic collision for two equal masses, the angle between the velocities is always 90 degrees.
Where the projectile is much heavier than the target, the velocity of the given target particle changes to about twice that of the projectile after the collision. And the projectile velocity will remain unchanged. In this case, the angle between the projectile and the target remains less than 90 degrees.
In the case of a head-on elastic collision, when there is a small projectile and a much more heavy target, the projectile will bounce back with the same speed, and the massive target will gain a very small velocity. In this case, the angle of the path of the projectile will be more than 90 degrees.
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A 45. 0 kg woman stands up in a 60. 0 kg canoe 5. 00 m long. She walks from a point 1. 00 m from one end to a point 1. 00 m from the other end (fig. P8. 92). If you ignore resistance to motion of the canoe in the water, how far does the canoe move during this process?.
The distance that the canoe moves in this process is 1.29 meters.
We first have to find the center of mass
X = MsXs + McXc/ Mw+Mc
Where
Ms = Woman's mass = 45
Mc = Canoe's mass = 60kg
Xs = position from left= 1 cm
Xc = position from left end of canoe's mass = 2.5cm
When we put these values into the equation we have:
X= 1.857
The center of gravity lies at the center of this boat. Therefore,
3.14 metres
To get the distance that is moved by this canoe distance = 3.143-1.857
= 1.286
≈ 1.29 meters
Thus, The distance that the canoe moves in this process is 1.29 meters.
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17. Astronomers estimate that the plains of venus are only about 500 to 600 million years old. How do they estimate dates like this?
They estimate dates by counting the number of craters visible on the surface and comparing crater counts to other worlds.
Crater counting is a technique for determining the age of a planet's surface based on the suppositions that impact craters are absent from freshly formed planetary surfaces and that they collect through time at a known pace.
The density of craters on a planet's surface can be used to estimate the relative ages of various regions; the older the surface, the more craters it has accumulated.
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an automobile engine provides 508 joules of work to push the pistons and generates 2277 joules of heat that must be carried away by the cooling system. calculate the change in the internal energy of the engine. e
Answer:
Explanation:
Given:
Q = 2277 J
A = 508 J
__________
ΔU - ?
ΔU = Q - A
ΔU = 2277 - 208 = 2069 J
(c) a cylindrical rod of uniform density is located with its center at the origin, and its axis along the z axis. its radius is 0.06 m, its length is 0.7 m, and its mass is 4 kg. it makes one revolution every 0.05 s. if you stand on the x axis and look toward the origin at the rod, the rod spins clockwise. what is the rotational angular momentum of the rod? what is the rotational kinetic energy of the rod?
Angular momentum is given by L=Iω.becomes part of their thermal energy.
In physics, angular momentum is the rotational analog of linear momentum. Its miles are an essential physical amount due to the fact it's miles a conserved amount the overall angular momentum of a closed machine stays steady. Angular momentum has a route and significance, and each is conserved.
Angular momentum is described as The assets of any rotating object given by using second of inertia instances angular speed. it's miles the property of a rotating body given via the product of the instant of inertia and the angular velocity of the rotating object.
The method for angular momentum is written as L = Iω, where L is angular momentum, I is rotational inertia and ω the Greek letter omega is angular speed. To simplify this, you can say that an item's angular momentum is the product of its mass, speed, and distance from the point of rotation.
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how big does the sun appear to be from plutos surface from the neighborhood of pluto, new horizons took this photo showing the disk of pluto with the sun shining to the upper left
The solar seems to be 1/39th, or zero.026 times as large as visible from Earth. when considered from the floor of Pluto.
Pluto is so far away from the sun (common distance to her is three,670,050,000 miles) that the solar seems much darker and smaller than it does from Earth.
From Pluto, the solar seems as a very brilliant star, illuminating Pluto at some point of the day approximately as a great deal as the whole Moon illuminates the Earth at night.
Nearest (perihelion) 2.seventy six billion miles from our megastar. at the furthest point (Aphelion) it's miles four.58 billion miles away. that is approximately zero.000456308 light years from sun.
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a 185 g185 g object is attached to a spring that has a force constant of 78.5 n/m.78.5 n/m. the object is pulled 8.25 cm8.25 cm to the right of equilibrium and released from rest to slide on a horizontal, frictionless table. calculate the maximum speed ????maxvmax of the object.
The maximum speed of the object is 1.28 m/s.
What is Speed?
Speed is described as the rate at which an object's position changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it only has a direction and no magnitude.
One meter per second is the speed of an object, for instance, if it starts at the origin and moves three meters in three seconds. Simple math can be used to calculate speed. time-distance ratio.
According to the given information:
Force constant K:78.5 n/m
Mass: 0.185 kg
The maximum speed of the object is,
[tex]$$\begin{aligned}v_{\mathbf{n} E} & =A \omega \\& =A \sqrt{\frac{k}{m}}\end{aligned}$$[/tex]
Here A is the amplitude, k is force constant, m is mass.
[tex]$$\begin{aligned}v_{\mathrm{ne:}} & =\left(6.25 \times 10^{-2} \mathrm{~m}\right) \sqrt{\frac{78.5 \mathrm{~N} / \mathrm{m}}{0.185 \mathrm{~kg}}} \\& =1.28 \mathrm{~m} / \mathrm{s}\end{aligned}$$[/tex]
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What is shepherding? (it involves space)
Answer:
What is a Shepherd planet?
Image result for What is shepherding? (it involves space)
An international team of astronomers exploring the disk of gas and dust around a nearby star have uncovered a compact cloud of poisonous gas formed by ongoing rapid-fire collisions among a swarm of icy, comet-like bodies.
Explanation:
A force of 570 N keeps a certain ideal spring stretched a distance of 0.900 m.
Part A:
What is the potential energy of the spring when it is stretched 0.900 mm?
Express your answer with the appropriate units.
Part B:
What is its potential energy when it is compressed 9.00 cm?
Express your answer with the appropriate units.
The potential energy of the spring when it is stretched 0.900 mm is 228 J. The potential energy when it is compressed is 2.88J.
Hooke's law states that the elongation of a material is proportional to the applied stress within the elastic limits of the material.
Using Hooke's law
F = kx
570 = k * 0.9
k = 712.5 N/m
(a) energy at x = 0.8 m
U = 0.5 k x^2 = 0.5* 712.8* 0.8^2
U = 228 J
(b) U = 0.5 * 712.8* 0.09^2
U = 2.887 J
Elastic potential energy is the potential energy released as a result of the deformation of an elastic body. B. Spring extension is stored. This is equal to the work done to stretch the spring, which depends on the spring constant k and the stretched distance. The force exerted by the spring is the restoring force that helps return the spring to its equilibrium length.
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the aorta carries blood away from the heart and eventually branches into a large number of capillaries that distribute the blood to various body organs. if for an average person, the aorta has a radius of 1.2 cm and blood travels through it at a speed of 36 cm/s and the capillaries have an average radius of 5.0 10-4 cm and blood travels through them at a speed of 0.008 cm/s, determine the approximate number of capillaries in the human body.
13.7 × [tex]10^{8}[/tex], the approximate number of capillaries in the human body, that are carrying blood from the aorta.
What is Aorta?
A huge, cane-shaped blood channel called the aorta carries oxygen-rich blood to your body. It travels across the chest and belly after beginning in the lower left corner of the heart. Blood arteries leave the aorta along the way and extend to the organs and supporting tissue.
What are the Calculations?
The speed of the blood in the aorta is v = 35cm/s
the radius of the aorta is r = 1.1 cm
the area of the cross-section of the aorta is A =π[tex](1.1cm^{2} )[/tex]
the speed of the blood in the capillary v ' = 0.078 cm/s
radius of the capillary is r = 6.3 × [tex]10^{-4}[/tex]cm
Now area of cross-section of capillary is A' = Π[tex](6.3 * 10^{-4}) ^{2}[/tex]
Let there be N number of capillaries
The volume rate of flow in the aorta is the total sum of the volume rate of flows in the capillaries.
Then Av = N*A' *v'
Π(1.1cm)² (35 cm/s) = N * (Π[tex](6.3 * 10^{-4}) ^{2}[/tex])* 0.078 cm/s
N = 13.7 × [tex]10^{8}[/tex]
Hence, 13.7 × [tex]10^{8}[/tex], the approximate number of capillaries in the human body, that are carrying blood from the aorta.
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a large metal ball is at rest, and a small rubber ball is moving at a high velocity. when they collide, the large metal ball begins to roll slowly. what must have happened to the momentum of the small rubber ball?(1 point)
The small rubber ball was moving quickly as well as a huge metal ball is now at rest. The massive metal ball starts to roll more slowly once they meet, slowing the small rubber ball's speed.
What is a momentum in physics?Momentum is characterized as the intensity of a body's motion. As momentum depends on both velocity as well as the direction of a body's motion, it is quantified by "mass velocity". Because velocity is just a vector and mass is a scalar, momentum is a vector.
What is momentum and example?Momentum can be viewed as a body's "power" while it is moving, or the amount of force it can exert on another body.
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A Private jet flies the same distance in 10 hours That it commercial jet Flies in 6 hours. If the speed of the commercial jet was 200 mph less than 3 times the speed of a private jet. Find the speed of each jet.answer:Speed of private jet:Speed of commercial jet:
The speed of the private jet and the commercial jet were 200mph and 400mph respectively.
The private jet flies the same distance in 10 hour that the commercial jet cover in 6 hours.
The speed of the commercial jet is 200mph less than 3 time of the speed of private jet.
Now, if we assume the speed of Private jet to be X mph then the speed of the commercial jet will be (3X - 200) mph.
If the distance cover is D, then, for the private jet,
D = 10X
For commercial jet,
D = (3X-200)6
Now, we can write,
10X = 18X - 1200
6X = 1200
X = 200 mph.
So, the speed of the private jet was 200mph and the speed of the commercial jet was 400mph.
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Hand warmers and instant cold packs use _____________________ that release or absorb thermal energy.
Answer: Endothermic and Exothermic reactions
Determine the magnitude and direction of the force between two parallel wires 35 m long and 7.0 cm apart, each carrying 35 A in the same direction. O The force on each wire will be attractive. O The force on each wire will be repulsive. O The wires will not interact.
3.5*10^-5 N/m is the magnitude of the force between two parallel wires 35 m long and 7.0 cm apart, each carrying 35 A current and the force on each wire will be repulsive.
What is Magnitude of force means?The number which shows or represents the strength of the force is termed as the magnitude of that force.
Data given :
Two parallel wires
35 m long and 7.0 cm apart,
each carrying 35 A current .
To find the magnitude and direction of current.
f=μ/4π*2[tex]I_{1}[/tex][tex]I_{2}[/tex]/d
f=[tex]10^{-7}[/tex]*2*35*35/7
f=3.5*10^-5
Hence, 3.5*10^-5 N is the magnitude of the force between two parallel wires 35 m long and 7.0 cm apart, each carrying 35 A current.
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what do we mean by dimension in the context of relativity? what do we mean by dimension in the context of relativity? the number of sides that we can see when we look at an object the size of an object the letter used to represent length mathematically the number of independent directions in which movement is possible
The number of independent directions in which movement is possible dimension in the context of relative motion.
To discuss relative motion in one or more dimensions, the idea of reference frames was initially developed. When we refer to an object's velocity, we are referring to it in relation to the so-called reference frame. When measuring an object's velocity in daily life, the ground or the earth is assumed to be the reference frame.
As an illustration, if you are travelling in a train that is moving at 100 km/h, then from the perspective of another passenger in the train, you are moving at a speed of zero. He says you're standing still. However, if a bystander sees you standing on the ground outside the train, he claims that you are going with the train.
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in comparing two unequal forces on a rigid body, is it possible to have the larger force produce less torque than the smaller force?
Different torques can be generated by the same force. When the force and lever arm are both large, greater torques are generated.
Explain about the torques?A torque is a linear force's reciprocating rotating counterpart. Distance travelled over a predetermined period of time is referred to as speed. Torque and speed are related to one another inversely in proportion. Numerically describing the torque of a rotating object is done by dividing power by angular velocity.
Torque is the unit of measurement for the force that may rotate an item around an axis. The acceleration of an item in linear kinematics is caused by force. An angular acceleration is caused by torque in a manner similar to this. It follows that torque might be viewed as the rotational counterpart to force.
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(a) find the work done by f in moving an object from a point p1 along a path to a point p2 in terms of the distances d1 and d2 from these points to the origin. (b) an example of an inverse square field is the gravitational field f
The strength of gravitational or electrostatic fields is frequently determined using the inverse square law as an illustration, the Earth's surface has a gravitational field strength of about 9.8 N/kg.
Take note that the field F(r) is a vector along the ray passing through each point in space with the coordinates r=(x, y, z) and coming from the coordinate center. So you can visualize the entire field as a blast from a single central point. Picture two points A and B on a sphere with radius |A| that are both located at the same distance from 0 and a path that connects them. You would expend no energy to move a particle along this path because you are always orthogonal to the force's direction. Work accounted for is the work along the path from distance |P2| to distance |P1| along this ray. For all intents and purposes, the points P1 and P2 can be located on the same ray emanating from the origin (while preserving only their distances from it). This is conservative as per physics forums.To understand about gravitational field strength-
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on a keyboard, you strike middle c, whose frequency is 256 hz. a) what is the period of one vibration of this tone? (in ms)
The period of the vibration is 3.9ms
What is Period of a vibration?The period (T) of a vibration is the time to complete one oscillation or revolution and is measured in seconds. The period of vibration is given as
T= 1/F
For example, if the period of a vibration is 0.1 second (one vibration takes 0.1 second), then the frequency of the vibration is 1/0.1=10 vibrations per second or 10 hertz.
Similarly if the frequency of a vibration is 256hz, the period T= 1/F= 1/256=0.0039s
1second= 1×10³ms
therefore 0.0039s = 0.0039×10³= 3.9ms
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According to the principle of continuity, the velocity of a fluid multiplied by the cross section through which it flows at one point will equal the product ofA) velocity and cross section at another point.B) velocity and pressure at another point.C) a constraint factor.D) none of the above
According to the principle of continuity, the velocity of a fluid multiplied by the cross-section through which it flows at one point will equal the product of velocity and cross-section at another point.
The principle of continuity, also known as the continuity equation, is the fluid mechanic's principle. Simply put, what flows into a defined volume over a specified period of time minus what flows out of that volume over that specified period of time must accumulate in that volume. The substance in that volume is depleted if the accumulation's sign is negative.
This is so that our eyes, once they start to follow anything, will keep moving in that direction until they come across another thing or object. A line with an arrow at the end of it, for instance, is a great illustration of the continuity concept.
Note that three conditions must be met for a function to be continuous at a point: At that time, the limit must exist.
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you discover a new cluster of galaxies, and the brightest galaxy in this new cluster has an infrared color ratio of 0.65. based on the data in the graph, what is the approximate distance to this new cluster?
The approximate distance to this new cluster is 1 billion light-years.
What is a Galaxy Cluster?
A galaxy cluster, also known as a cluster of galaxies, is a formation made up of a large number of gravitationally connected galaxies, typically with masses between 1014 and 1015 solar masses. Before superclusters were found in the 1980s, they were thought to be the largest known structures in the universe and are now the second-largest known gravitationally bound structures in the cosmos after galaxy filaments.
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The approximate distance to this new cluster is 1 billion light-years.
What is a Galaxy Cluster?
A galaxy cluster, also known as a cluster of galaxies, is a formation made up of a large number of gravitationally connected galaxies, typically with masses between 1014 and 1015 solar masses. Before superclusters were found in the 1980s, they were thought to be the largest known structures in the universe and are now the second-largest known gravitationally bound structures in the cosmos after galaxy filaments.
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At a construction site, a 22.0 kg bucket of concrete is connected over a very light frictionless pulley to a 375 N box on the roof of a building. There is no appreciable friction on the box, since it is on roller bearings. The box starts from rest.
A. Find the acceleration of the bucket.
B. How fast is the bucket moving after it has fallen 1.50 m (assuming that the box has not yet reached the edge of the roof)?
A. The acceleration of the bucket is 3.58 m/[tex]s^{2}[/tex].
B. bucket is moving with a velocity of 3.28 m/s.
What is acceleration?
If an object's velocity changes, it is said to have been accelerated. An object's velocity can alter depending on whether it moves faster or slower or in a different direction. A falling apple, the moon orbiting the earth, and a car stopped at a stop sign are a few instances of acceleration. Through these illustrations, we can see that acceleration happens whenever a moving object changes its direction or speed, or both.
What is Velocity?
The direction in which a body or an object is moving.
What are the calculations?
Given that the mass of bucket m = 22.0 kg
Weight of the box W = 375 N
Then the mass of box M = W / g
= 375 / 9.8 m/[tex]s^{2}[/tex]
= 38.27 N
Let T be the tension in the string
Let a be the acceleration of the bucket
Apply Newton's second law to the bucket
mg - T = ma
T = m (g - a) ....... (1)
Apply Newton's second law to the box
T = Ma ....... (2)
From equations (1) and (2) we get
Ma = m (g-a)
( m+ M )a = m g
a = m g / (M + m)
= (22.0 kg) (9.8 m/[tex]s^{2}[/tex]) / (22.0 kg + 38.27 kg )
= 3.58 m/[tex]s^{2}[/tex]
Initial velocity of the bucket u = 0
Let v be the final velocity of the bucket after displacement s = 1.5 m
From equation of motion
v2 - u2 = 2as
v2 - 0 = 2as
v = √2as
v = √2(3.58 m/[tex]s^{2}[/tex])(1.5 m)
v = 3.28 m/s
Hence, the acceleration of the bucket is 3.58 m/[tex]s^{2}[/tex] and the bucket is moving with a velocity of 3.28 m/s.
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