determine by direct integration the moment of inertia of the shaded area with respective to the y axis. (20 points)

The critical radius is 0.146×10⁻⁹m   and activation energy of iron is 0.5327×10⁻⁴⁵Joules

We have some data fields, we need to find the critical radius of iron.

We know very well that critical radius is given by the formula

critical radius=(2×Surface energy × Melting point)/Latent heat of fusion

or in other words, r=(2×S×[tex]T_m[/tex])/Δ[tex]H_l_a_t_e_n_t[/tex]

whereas

Also temperature if given in degree celsius, we need  to convert this into kelvin,

Using the formula,

K=C+273°

=>K=1538°+273K=1811K

So, putting the respective values, we get

=>r= -(2×0.0204×1811)/(-1.85×10⁹×273)

=>r= (73.88/505.05)×10⁻⁹m

=>r=0.146×10⁻⁹m

Now, talking about the activation free energy.

Activation free energy is given by the formula

G=[16×3.142×(critical radius)³×(Melting point)²] / [(3×(Super Colling value)²×(Latent heat of fusion)²]

So, putting the respective values of different quantities, we get

=>G = [16×3.142×(0.146×10⁻⁹)³×(1811)²]/(3×(273)²×(-1.85×10⁹)²

=>G=(407686.907×10⁻²⁷)/(765226.508×10¹⁸)

=>G=0.5327×10⁻⁴⁵Joules

Hence, if nucleation is homogeneous the critical radius r* is 0.146×10⁻⁹m  and the activation free energy ΔG* is 0.5327×10⁻⁴⁵Joules.

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(Complete question) is:

(a) For the solidification of iron, calculate the critical radius r* and the activation free energy ΔG* if nucleation is homogeneous. Values for the latent heat of fusion and surface free energy are –1.85 × 109 J/m3 and 0.204 J/m2, respectively. Use the supercooling value ΔT = 273 K, and the melting point of iron is 1538°C.

If a 20 N force is applied to the crate acting to the right, the resulting static friction force acting on the crate if 20 N to the left

f = μ N

N = W

f = Frictional force

μ = Co-efficient of friction

N = Normal force

W = Weight / Force of gravity

W = 50 N

N = 50 N

μ = 0.5

f = 0.5 * 50

f = 25 N

This means that the crate will start to move if applied force is ≥ 25 N. Any force lesser than or equal to 25 N will be opposed by an equal frictional force. For an applied force of 20 N to the right, the frictional force will be 20 N to the left.

Therefore, the resulting static friction force acting on the crate is 20 N to the left

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If you stare a green dot for a relatively long period of time and then shift your gaze to a blank white screen, you would see a red negative after image.

This is based on the theory of colour vision. It states that all the colours we see and perceive in the natural world are made up of three colour complexes that have the opposite effects. The complexes are the red-green complex, the blue- yellow complex and the black-white complex.

This means that when we perceive one colour, for example, let us take green, the other colour won't be visible. This is what happened here. Later we get to see red and green gets vanished.

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The length of shadow decrease at 0.48 m/s.

Let the distance of the man from building = x

Initially, x = 12

It is given that dx/dt = -1.3 m/s

Let the shadow height be Y

Now, let us solve dy/dt when x = 4

From the concept of similar triangles, let us equate the base upon height ratios.

2/(12-x) = Y/12

Y = 24/(12-x)

dy/dt = 24/(12-x)² dx/dt

At x = 4, dy/dt becomes, 24/(12-4)²* (-1.3) = - 0.48 m/s

The negative sign indicates that the length of the shadow decreases at the rate of 0.48 m/s.

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Yes, The batter hit a home run. The horizontal range is 161.18 m and the time of flight of a projectile is 4.95 s  

What is horizontal range and time of flight of a projectile?

The horizontal range of the projectile is given by R = (u^2 * Sin(2θ ) )/g
The time of flight of a projectile is given by , T = 2*u*Sinθ  /g
In the given problem
velocity of projectile, u = 41 m/s
angle of projection,θ = 35
The horizontal range of the projectile is given by R = (u^2 * Sin(2θ ) )/g

                                                                    = (41)^2 * Sin (70) / 9.8

                                                                     = 1681 * 0.9396 /9.8

                                                                    =  1579.62/9.8

                                                                   =   161.18 m
Therefore, the batter hit a home run as the range is greater than the distance to the fence(120m)
The time of flight of a projectile is given by ,

T = 2*u*Sinθ  /g

 = 2 * 41 * sin(35) / 9.8

 = 2 * 41 * 0.573 / 9.8

 = 470.33 / 9.8

 = 4.95 s                

Therefore the time of flight of a projectile is 4.95s

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The power required to change a sport utility vehicle's speed is 2725 Watt.

A measure of how quickly an object's location can shift in any direction. Speed is defined as the distance traveled divided by the time required to cover that distance. It is a scalar because speed only has a directions and no magnitude. In common usage and kinematics, the speed of an object is a scalar quantity and is defined as the amount of the change within this object's motion per unit of time or over time.

Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in metres per second (m/s) in this example since the distance is measured in metres (m) and the time is measured in seconds (s).

Speed is a unit of measurement for how quickly something is moving. The most popular speed measurements are miles per hour (mph), kilometers per hour (km/h), and metres per second (m/s).

Mass of the sport utility = 1600kg

Initial velocity (v1) - 15m/s, (152 = 225)

Final velocity (v2) - 40m/s, ( 402 = 1600)

To find the energy required, Kinetic energy (K.E) = 1/2 mv2

K.E = final K.E - initial K.E

= 1/2(v2-v1)

= 1/2×1600×(1600-225)

= 80 × 1375

= 11000 J

Power = Energy (E)/Time (t) = 1100joule/4sec

= 2725Watt.

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The magnitude of the normal force acting on the space vehicle will be 5070 newtons. So option (4) is correct.

Given that,

The mass of the space vehicle is 1300 kilograms

It travels at a speed of 4.8 meters per second along the level surface of mars.

The g' (gravitational field strength) on the surface of mars is 3.9 newtons per kilogram

We need to find the normal force acting on the space vehicle

We know, N = mg' (where N is normal force)

N = (1300 × 3.9) Newton

N = 5070 Newton

So, the magnitude of the normal force acting on the space vehicle that is traveling at 4.8 meters per second along the level surface of mars will be 5070 newtons.

The normal force is the force that surfaces exert to prevent solid objects from passing through each other. The normal force is one type of ground reaction force.

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Fill in blank answers are- electron degeneracy pressure, nova, massive star supernova, white dwarf limit, accretion disk and white dwarf supernova

The radius of a white dwarf is determined by a balance between the inward force of gravity and the outward push of electron degeneracy pressure.

A nova occurs when hydrogen fusion ignites on the surface of a white dwarf in a binary system.

A massive star supernova occurs when fusion creates iron in the core of a star.

A white dwarf in a close binary system will explode as a supernova if it gains enough mass to exceed the white dwarf limit.

An accretion disk consists of hot, swirling gas captured by a white dwarf (or neutron star or black hole) from a binary companion star.

A white dwarf supernova can occur only in a binary system, and all such events are thought to have the same luminosity.

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A horse near the outside rail of a merry-go-round and a horse near the inside rail will have same angular speed.

ω = 2 π / T

ω = Angular speed

T = Time period

ω ∝ 1 / T

Time period is the time taken by an object to complete one full rotation. A horse near the outside rail of a merry-go-round or a horse near the inside rail will both complete one rotation at the same time. So, angular velocity will be the same for both.

Therefore, a horse near the outside rail of a merry-go-round and a horse near the inside rail will have same angular speed.

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The percent error in this measurement with an error margin of 0.5m is 5.8%

The accuracy and proximity of an estimate to the actual value of a specific experiment or quantity are measured in terms of percent error. Using this strategy, you may assess whether or not the data collecting is going in the proper path. Experts in statistics and big businesses are its main users. Students that are interested in studying economics should place a high priority on it.

The difference between a quantity's exact value and its approximate value is used to calculate percent error. This difference is then divided by the exact value and multiplied by 100 to represent it as a percentage of the exact value.

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The cross-section need to be revolved to create a sphere is Y = 1 .

The cross-section is defined as the shape obtained by the intersection of a solid and a plane. A cross section of a spatial figure is a two dimensional geometric figure. In other words, a cross-section is the shape obtained by cutting a solid surface parallel to the substrate.

There are two types of cross sections namely

a. Horizontal or parallel cross section : In a parallel cross section a plane intersects a solid horizontally ( parallel to the base) so that it forms a parallel cross section .

b. Vertical or Perpendicular Cross Section : In  a vertical cross section, the plane intersects the solid shape vertically ( viewed perpendicular to the base) so that it forms a perpendicular cross section.

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Answer:

Around line y=1, therefore, correct answer: D.

(a) The mass of the block is 9.45 grams and

(b) the tension is 53.4 N

Given : mass = 4.00 kg and block mass = 12 kg

the coefficient of friction or μ = 0.25

the force can be calculated by ;

(b) F₋ = μmg

F₋ = (0.25)( 12 ) (9.8)

F₋ = 29.4 N

the total force on the block

Fₐ = ma

Fₐ = (12 )(2)

Fₐ = 24 N

F is the applied force

thus Fₐ= F - F₋

F = Fₐ + F₋

F = 24 + 29.4

F = 53.4 N

And now we can calculate the (a) part by ;

(a) F₋ - Fₐ = m₋g - 39.2

m₋g = 53.4 + 39.2

m- = 92.6/9.8

m - = 9.45 g

Thus the mass of the block is 9.45 gram

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The torque about the origin on the plum if that torque is due to a force F is 12j.

Torque is a measure of the force that can cause an object to rotate approximately an axis. just as a force is what reasons an object to accelerate in linear kinematics, torque is what reasons an object to gather angular acceleration. Torque is a vector quantity.

calculation -

The torque about origin = v x f

= (-2i + 4k) x (6k)

= -12 (i x k) + 0

= 12j

Torque is the rotational equation of linear force. it's also called the instant, second of force, rotational pressure, or turning impact, depending on the field of observation. It represents the capability of pressure to supply an alternate within the rotational movement of the body.

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The Biot-Savart law is used to represent the magnetic intensity because of the availability of magnetic current.

In physics, explicitly electromagnetism, the Biot–Savart law is a condition representing the attractive field produced by a constant electric flow. It states that “ magnetic field due to a current carrying conductor at a distance point is inversely proportional to the square of the distance between the conductor and point, and the magnetic field is directly proportional to the length of the conductor, current flowing in the conductor”.

The Biot Savart Law signifies that it is a scientific articulation which shows the attractive field delivered by a steady electric flow in the specific electromagnetism of material science. It tells the attractive field toward the greatness, length, heading, just as closeness of the electric flow.

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An amplitude is the maximum displacement from the equilibrium position that an object in the periodic motion displays. It is represented as A.

Amplitude refers to the maximum displacement from equilibrium position that an object in the periodic motion shows. An example of amplitude is a pendulum which swings through its equilibrium point in a straight down manner, and then swing to a maximum distance away from the center position.

The symbol used for the representation of amplitude is A. The SI unit of amplitude is the meter (m) as it is a measure of length, however other units of length may also be used.

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The gene contains the instructions to make a protein that has information about the genetic characters of an organism.

Inside our cells there is presence of DNA.

It is a double stranded deoxyribonucleic acid.

This DNA is the place where the genetic characters resides.

But this DNA is made up of different things like the sugar.

So the genetic material is found in a part of DNA called a gene.

A gene is a short section of DNA.

The genes contain instructions that tell your cells to make molecules called proteins. Proteins perform various functions in your body to keep you healthy. Each gene carries instructions that determine your features, such as eye colour, hair colour and height.

Therefore, the gene contains the genetic information and the instructions to make a protein which determines the characteristics of an individual.

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The angular velocities of each object are based on the assumption B > C > A=F> D=E.

Velocity can be defined as the rate that an object moves in a specific direction. as the quickness of a car driving north on a motorway or the pace at which a rocket takes off. Because the velocity vector is scalar, its absolute value magnitude will always equal the motion's speed.

The increase in position (displacement) of an object over a period of time is referred to as its velocity. Speed can only be positive, whereas velocity can be either favourable or unfavourable because it combines both speed and direction.

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Every action has an equal and opposite response, according to Newton's Third Law.

Newton's Third Law of Motion is essential for rocket launch. Through action and reaction, a rocket engine generates thrust. Hot exhaust gases from the engine exit via the back of the engine. In response, the opposing reaction produces a propelling force.

Forces always act in pairs that are equal but opposite, according to Newton's third law of motion. Another way to put it is that there is an equal but opposing reaction to every action. In other words, when you push against a wall, the wall pushes back at you with a force equal to your own.

There is an equal and opposite reaction to every action, according to Newton's third law. The implication of the statement is that there are always two forces acting on the two interacting objects. The force acting on the first object is equal in size to the force acting on the second.

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It is closest to 0.17 MPa when gas is first under pressure.

To find R, the gas constant, the ideal gas law can be modified. R=PiViniTi under initial conditions, and R=PfVfnfTf under final conditions. Both expressions are equal to each other because they both equal R. In situations where one or more of the variables are constant, this equation is frequently utilised.

The average number is 8.314 J K-1 mol-1. It is a typical SI unit. To utilise this value exactly, you must: Use K for the temperature.

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Hence, normal reaction on ball is 4.22N.

Mass,M=1kg

Angular velocity, ϖ=10rad/s

Length of rod, r=0.1m

Angle, α=30o

From the figure,

Horizontal Equilibrium forces.

Tcos30o=mϖ2r=1×102×0.1=10

T=cos30o10​=3

​20​……(1)

Vertical forces in equilibrium.

N=mg−Tsin30o=1×10−3

​20​×21​=4.22N

Hence, normal reaction on ball is 4.22N

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The answers are (a) velocity, v=2.8m/s , mass, m=0.0038kg and x=0.055m.

(b) v=2.7m/s.

Any object or system that has stored energy as a result of its position or component arrangement is said to have potential energy. Nevertheless, it is unaffected by external factors like air pressure or altitude. On the other hand, kinetic energy is the force that propels a moving object or group of particles.

(a) By equating the compressed spring's potential energy to the cork's kinetic energy at release, we have

The formula is :

k = [tex]\frac{1}{2} mv^2[/tex]

v = [tex]\sqrt{\frac{2k}{m} }[/tex]

And potential energy of spring = [tex]\frac{1}{2}mx^2[/tex]

On equating these two equations we get ;

v = x[tex]\sqrt{\frac{k}{m}[/tex]

After substituting the value of x = 5.5 cm and m = 3.8g we would get

v=2.8m/s m=0.0038kg and x=0.055m.

(b) In the novel scenario, there is some potential energy present just before release. Energy conservation changes when d=0.015m.

Similarly solving the question we get :

v = 2.7 m/s

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She ignores the above average quality of the most of Lian's work, focusing exclusively on what she does incorrectly. Instance of FITB bias is this.

When people's perceptions of the likelihood of an outcome are clouded by similarities between objects or events, this phenomenon is known as the representativeness heuristic bias. People frequently believe that two related things or events are more closely correlated than they actually are. The Stanford Prison Experiment is frequently used as an example of unethical research. She disregards the above average quality of the majority of Lian's work, focusing solely on what she does incorrectly. As a result, the experiment cannot be replicated by researchers today because it does not adhere to the standards established by numerous ethical codes, including the Ethics Code of the American Psychological Association. This is an illustration of FITB bias.

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The magnitude of the net force on the bicycle as it crosses the finish line is 1.26 N.

Here, we have been told that the radius of the course, r is = 140 m (i)

The time taken to cover the entire course is = 60 s (ii)

The mass of the bicycle is = 76 kg (iii)

We know the formula = a = v²/r. Using this formula and the values of (i), (ii), and (iii), we get -

= a = Δv/Δt = v - 0/60

= v = 1.53 m/s

Nt force due to weight and normal force are canceled. But the force due to the centripetal acceleration is -

= mv²/r

= 76*(1.53)²/140

= 1.26 N

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A force of friction on a box going down an incline is 3 lbs (N)

Frictional force is the force created when two surfaces come into contact and slide against one another. The following variables impact the frictional force: Surface roughness and the amount of force pressing them together have the biggest an impact on these forces. friction, a force that prevents two solid objects from rolling or sliding over one another. Although frictional forces, such as the traction required to walk without slipping, can be advantageous, they also pose a significant amount of resistance to motion.

The resistive force of friction (Fr) divided by normal or perpendicular force (N) pushing the objects together yields the coefficient of friction (fr), which is a numerical value. Equation fr = Fr/N serves as a representation of it.

The force that prevents one solid item from moving across another is known as friction. The four basic types of friction are fluid friction, rolling friction, sliding friction, and static friction.

10 lbf = 44.4822161525 N

0.30 us = 0.30 KJ

Weight = 0.25

0.30us-10lbf=3lbs

1. Decide which natural force is present between the object and the earth. Consider a typical force of 0.10 lbf (N)

2. Establish the frictional factor. We can opt for a friction coefficient of 0.30us.

3. Multiplying these figures by one another: (0.10lbf(N)) x 0.30us = 3 pounds (N)

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Scalability Is the measure of a system's ability to expand.

Scalability is the measure of a system's capability to grow or decrease in performance and fee in response to adjustments in application and gadget processing needs.

Scalability / Extensibility. refers to a machine's potential to make bigger, change, or downsize without problems to fulfill the converting needs of a commercial enterprise corporation. applications. programs that deal with the entry, control the processing common sense, and provide the desired output.

Scalability refers to the potential of a company (or a system, which includes a pc network) to perform properly below an improved or increasing workload.

A system that scales nicely may be capable of preserving or increasing its stage of overall performance at the same time as it is examined by way of larger and large operational demands. Scalability refers back to the potential of a pc, product, or system to make bigger to serve a large number of customers without breaking down.

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Disclaimer:- your question is incomplete, please see below for the complete question.

____________________ Is the measure of a system's ability to expand?

The width of the slit that illuminates by a 650-nm laser is 0.29mm.

It is a long, narrow cut or opening. Slit is used for diffraction process that affecting waves which are amenable to quantitative description and analysis. Such treatments are applied to a wave passing through one or more slits whose width is specified as proportion of the wavelength.

How to calculate the width of the slit?
Distance of second minimum on one right side of central maximum is 1/2 of total distance between the second minimum on left side and right side.

= 1/2 * 11mm

= 5.5mm

θ = the angular position of the second minimum on right side (also same of left side)

tan θ = 5.5mm / 1.2m = 4.6 * 10^-3
θ = arctan 4.6*10^-3

= 0.26rad

Now let's use the condition for the second minimum

αsinθ = 2λ

α * sin0.26 = 2 * 650 * 10^-9

α * 4.5*10^-3 = 2*650*10^-9

slit width is

α = 2 * 650 * 10^-9 / 4.5 * 10^-3

= 0.29 * 10^-3 m

= 0.29mm

Therefore, the width of the slit is 0.29mm.

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If the universe was infinite in both extent and age then we would expect the night sky to be uniformly bright.

The universe can be described as all of space and time including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang Theory has given the cosmological description of the development of the universe.

Space and time emerged together approximately 13 billion years ago, and the universe is expanding ever since the Big Bang. While the spatial size of the universe is unknown and we can only measure the size of the observable universe.

From further observational improvements, the Sun can be defined as one of a few hundred billion stars in the Milky Way, which is one of a few hundred billion galaxies and also many of the stars in a galaxy have planets in the universe.

According to the Big Bang theory, matter and energy initially have become less dense as the universe expanded.

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Dark matter makes up about 27% of the universe.

Quasars and abundant in dark matter, and with over 2,000 quasars identified today, it is clear that the universe contains a lot of dark matter.

All the stars, spheres and galaxies that can be perceived nowadays make up just 5 percent of the universe. The former 95 percent is prepared of stuff stargazers can't see, notice or even understand. These secretive substances are called dark energy and dark matter.

Experts determine their presence grounded on their gravitational influence on what little bits of the universe can be perceived.

Dark energy refers to that energy which acts against gravity, thereby resulting in the expansion of the universe. It's major constituent is current characterized with vacuum fluctuation. It is on this premise that dark matter was theorized to be causing the expansion of the universe to accelerate and itself including dark matter is filled in empty space.

Therefore, from the simple note above, it can be deduced that dark energy of dark matter does not produce electromagnetic radiation.

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The final and initial changes in the potential are Ui = 1.323 J and Uf =0 in the term of variables in the given problem.

The initial and final potential energies are usually calculate by the formula that has mgh terms.

Here we can calculate mgh :

[tex]mgh = 1/2 Iw^2 + mv^2 /2 \\2gh = r^2 w^2 + v^2\\2gh = r^2 v^2/ r^2 +v^2\\v^2 = gh = 9.8 × 0.75= 2.71 m/s\\w = v/ r= 33.9 rad/sec\\initial energy of potential =vi = mgh = 1.323.\\final energy of potential = vf = 0 as the height is = 0.[/tex]

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315 pm is the distance  for the center of mass of carbon monoxide in units of pm

distance= Med/Ms-Me

distance=12×10^5/16-12

distance=315 pm

Distance is the length between two locations or objects, and it is directionless. Since distance is a scalar property, it only takes into account the total magnitude and ignores the start and end locations. Since distance is a scalar characteristic, it can only have a positive or zero value; it cannot be negative.

The most common unit of measurement for distance is the meter (m), but you may also use kilometers (km) to describe greater distances and centimeters (cm) or millimeters to represent lesser distances (mm). When calculating distance, the letter D is usually used to denote the distance traveled.

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