discuss whether any work is being done by each of the following agents and, if so, whether the work is posi- tive or negative. (a) a chicken scratching the ground (b) a person studying (c) a crane lifting a bucket of concrete (d) the gravitational force on the bucket in part (c) (e) the leg muscles of a person in the act of sitting down

The pair of work and energy is similar.

Among all the given pairs the pair of work and energy are similar because they have similar units.

According to the work energy theorem, the total work done on a body by all the forces combined is equal to the change in kinetic energy of the body.

W = ∆K

According to the principle of homogeneity,

If two quantities are equal then they must have similar units.

In the case of energy and work both of them has the unit Joule. Because there equal as per the work energy theorem.

Work and power, Momentum and energy, force and power all have different units so they are not similar pairs.

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When two dice are rolled there are 36 possible outcomes. The sample for two diced named A and B can be written as follows:

S= {(1,1), (1,2), (1,3),(1,4),(1,5),(1,6), (2,1),(2,2),(2,3),(2,4), (2,5),(2,7),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

This question can be solved using concept of probability and sample space.

a) probability of rolling a 7

Possible outcomes: (6,1),(1,6),(2,5),(3,4),(4,3),(5,2)

Probability= 6/36=1/6

b) Probability of a double

possible outcomes: (1,1),(2,2),(3,3),(4,4),(5,5),(6,6)

probability= 6/36= 1/6

c) probability of rolling a 7 or 8

= probability of rolling 7+ probability of rolling 8

= [tex]\frac{6}{36} +\frac{5}{36}= \frac{11}{36}[/tex]

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The ratio of the three circles they draw is equal to the distances from the stations to the epicenter.

Scientists use triangulation to find the epicenter of an earthquake. If seismic data are collected from at least three different locations, their intersection can be used to determine the epicenter. Each earthquake is recorded by numerous seismometers placed in different directions.

The epicenter is the point on the surface directly above the earthquake. A seismic station uses seismometer recordings to detect earthquakes. Determining the epicenter of an earthquake requires records from three separate seismic stations. Triangulation is a method of uniquely identifying earthquakes using distance information determined from three seismic stations.

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Sherwin's resulting velocity after the collision is  18.94m/sec. if his initial velocity is 12m/sec and mass of 150kg.

It is given that Sherwin has initial velocity and Lia is going to start the bumper car. It means that initial velocity of Sherwin is 12m/sec and initial velocity of Lia is 0m/sec. Since, the collision is elastic, it means that energy will not lost during the collision and momentum will remain conserved.

So, applying the law of conservation of momentum which is

Initial momentum =Final momentum

=>Initial momentum of Sherwin is=mass × velocity

=>Initial momentum of Sherwin=150 × 12m/sec

Now, initial momentum of Lia is =mass × velocity

=>Initial momentum of Lia is =95×0=0m/sec

Now, final momentum of Sherwin=0m/sec since collision is elastic

Also, final momentum of Lia is =95×v

According to the formula, we get

=>150 × 12 +0 =0  + 95×v

=>95×v=150 × 12

=>v=(150 × 12)/95

=>v=1800/95

=>v=18.94m/sec

Hence,  Sherwin velocity is 18.94m/sec.

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The heat transfer into this engine is 52.7%.

Solution:

9.5 + 8.5

Hi = 18KJ

n = w/Hi

= 9.5/18 x 100

= 52.7%

Heat transfer is the field of thermal engineering concerned with the production use conversion and exchange of thermal energy between physical systems. Heat transfer is classified into different mechanisms such as. Conduction convection radiation and energy transfer through a phase change.

There are three ways heat is transferred conduction convection and radiation. Heat transfer between states of matter occurs whenever there is a temperature difference, and heat transfer only occurs in the direction of decreasing temperature, that is, from a hot body to a cold body.

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The location of the resultant force of the water on the vertical end of the pool is 1.67 m from the top.

Given that, length of the swimming pool is 16 m

Width of the swimming pool is 6 m

Depth of the pool (h) is 2.5 m

Area of the pool (A) = 6* 2.5 = 15 m²

Moment of inertia (I) = bh³/12 = 6* 2.5³/12 = 7.82 m⁴

x = h/2 = 1.25 m

The expression for location of force is

H = x + I/(A*x) =  1.25 + 7.82/(15* 1.25) = 1.25 + 7.82/18.75 = 1.67 m

Thus, the location of the resultant force of the water on the vertical end of the pool is 1.67 m from the top.

The question is incomplete. A swimming pool is 16 m long and 6 m wide.

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A moon has more mass than the planet it circles and less mass than a star.

Do planets have a greater mass than stars?

By this definition, "stars" must be larger than planets in terms of mass. The size of a white dwarf would be comparable to that of a moon or small planet, but its mass would be approximately 200–1300 times that of Jupiter. Even more extreme are neutron stars, which are about the size of an asteroid but have a mass of several thousand Jupiters.

Why is the weight of the same object different on different planets Class 7?

The weight of an object is determined by its mass and the gravitational force that it experiences. The separation between two objects affects how strong gravity is. Because of this, an object weights differently on many planets.

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Upon calculation A=[tex]\left[\begin{array}{ccc}3&5\\0&0\\\end{array}\right][/tex]    and A'= [tex]\left[\begin{array}{ccc}0&1\\0&3\\\end{array}\right][/tex]

This question can be solved using the concept of matrices.

A matrix is a rectangular array of integers divided into rows and columns. In mathematics, a matrix is an array of integers that is arranged in a rectangular pattern and split into rows and columns. They are often expressed by enclosing all of the numbers included between square braces.

According to the question given here

T₁(x,y)= (x-3y,3x+5y)

and

T₂(x,y)= (y,0)

Now it is clearly mentioned that T= T₁*T₂

T(x,y)= T₂[T, (x,y)]

T(x,y)= T₂(x-3y,3x+5y)

T(x,y)= (3x+5y,0)

T(1,0)= (3*1+5*0,0)= (3,0)

T(0,1)= (3*0+5*1,0)= (5,0)

which means A=[tex]\left[\begin{array}{ccc}3&5\\0&0\\\end{array}\right][/tex]

Now to find A'

T'= T₁*T₂

T'(x,y)= T₁[T₂(x,y)]

T'(x,y)= T₁(y,0)

T'(x,y)= (y-3*0,3y+5*0)

T'(x,y)= (y,3y)

T'(1,0)= (0,0)

T'(0,1)= (1,3)

which gives us A'= [tex]\left[\begin{array}{ccc}0&1\\0&3\\\end{array}\right][/tex]

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8.1 * [tex]10^{5}[/tex] Hz is a frequency of this light when predominant wavelength emitted by an ultraviolet lamp is 370 nm .

fλ = c

where f- Frequency

          λ - Wavelength

          c- speed of light

 f= c/ λ

  = 3 * [tex]10^{8}[/tex]/ 370

  = 8.1 * [tex]10^{5}[/tex] Hz

A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is typically defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm).

The wavelength, which will also apply to troughs, is the separation between two wave crests. The number of vibrations that span a particular area in a second is known as the frequency, which is measured in cycles per second (Hz) .

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A pendulum requiring exactly one second for each swing in either direction or two seconds for a complete vibration and having a length between centers of suspension and oscillation of 99.353 centimetres at sea level in latitude 45 degrees.

The absorption coefficient ,[tex]\beta[/tex] of PMMA is [tex]0.3\ m^{-1}[/tex] when 0.97 fraction of light is transmitted through 10 mm panel of PMMA.

The absorption coefficient determines how far light of a specific wavelength can penetrate before being absorbed. Light is only poorly absorbed in a material with a low absorption coefficient, and if the material is thin enough, it will appear transparent to that wavelength.

Given,

The fraction of light transmitted through PMMA panel = 0.97

Thickness of PMMA panel = 100 mm = 0.1 m

The absorption of coefficient, [tex]\beta[/tex]can be determined by the relation,

[tex]I=I_oe^{-\beta x}\\\\\frac{I}{I_o}=e^{-\beta x}\\\\[/tex]

applying natural log on both sides

[tex]ln(\frac{I}{I_o})=ln(e^{-\beta x})\\\\ln(\frac{I}{I_o})=-\beta x\\\\\beta = -\frac{1}{x}ln(\frac{I}{I_o})[/tex]

Here, x is the thickness of the PMMA panel; [tex]\frac{I}{I_o}[/tex] is the fraction of light transmitted; I is the initial intensity of light before transmitting through panel and [tex]I_o[/tex] is the final intensity of light after passing through the panel.

[tex]\beta = -\frac{1}{0.1}ln(0.97)\\\\\beta = -10*(-0.03)=0.3 m^{-1}[/tex]

Thus, the absorption coefficient is [tex]0.3\ m^{-1}[/tex]

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Answer:

Electromagnetic induction was discovered by Micheal Faraday.

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An electrical circuit refers to the combination of various electrical components that are connected together. - True

An electrical circuit refers to the combination of various electrical components that are connected together in a closed loop, thereby allowing electrons to flow through the circuit. Electrical circuits are essential for the operation of most electronic devices and are made up of a variety of components such as resistors, capacitors, inductors, and transistors.

These components are connected together using conductive materials. The conductive material is generally the copper wire which is used to create the circuit. The flow of electrons through the circuit can be controlled and manipulated using various techniques, such as switching and modulation, to perform a wide range of functions.

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When the students close the circuit and the fan blades start to spin, energy is transformed from electrical energy to mechanical energy.

Electrical energy is energy generated from the flow of electric charge through a conductor. This energy is utilized in virtually all modern-day appliances, from lightbulbs to cell phones to electric cars. It is created in power plants, harnessed through transmission lines, and distributed to consumers. Electrical energy can be converted into other forms of energy, such as heat or light, and can be used to power machines and equipment.

This is done by the battery supplying electrical energy to the switch and the fan, which then converts the energy into rotational energy. This is what causes the fan blades to spin and produces mechanical energy. The mechanical energy produced by the fan is then used to create air movement, which is another form of mechanical energy.

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The heat absorbed if the efficiency of the engine is 55% is determined as 1,000 J.

The heat absorbed by the system is the positive heat gain by the system or  the useful energy of the system.

From the fist law of thermodynamics, when heat is added to a system or absorbed by the system, the system gains heat.

Mathematically, the first law of thermodynamics is given as;

ΔU = q + w

where;

The heat absorbed by the system is calculated as follows;

q = ΔH / ( 1 - e )

where;

q = 450 J / ( 1 - 0.55 )

q = 450 J / 0.45

q = 1,000 J

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1.33m/s^2 is the acceleration. when a billiard ball is decelerating at a constant rate. its initial velocity is 8m/s. after 1.5 seconds it is travelling at 6m/s.

The rate at which a moving object's velocity changes is known as acceleration. It gauges the speed of velocity changes. Examples of acceleration include riding a carousel and traveling at a constant speed around a bend on a road.

The equation a = v/t denotes acceleration (a), which is the change in velocity (v) over the change in time (t).

a = (v_f - v_i) / Δt

a= 6m/s  - 8m/s / 1.5 seconds

a=-1.33m/s^2

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Dog is seated 1.25 metres from the centre and rotates at a tangential speed of 2.0 metres per second. If the dog weighs 19.3 kg, the centripetal force acting on it will be 61.76 N.

A total net force  acting on an object moving in a circular motion is known as a centripetal force.

It is given that radius(r) of the merry go round = 1.25m

tangential speed of the merry go round (v) = 2m/s

Mass of the dog (m) = 19.3kg

Centripetal acceleration (ac) is calculated as = v^2/r

So ac = (2x2)/1.25 = 3.2m/s^2

According to centripetal force(Fc) = mxac

Then Fc = 19.3 x 3.2 = 61.76N

Hence the centripetal force acting on the dog is 61.76N

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Water falls at a flow rate of 0.250 l/s into a 0.750-kg bucket on a scale. After 3 seconds, the weight shown on the scale is 14.7 N

The relation between the accumulated volume and the volume flow rate is given by:

V = Q x t

Where:

V = accumulated volume of water

Q = volume flow rate

t = time period

In the given problem:

Q = 0.25 l/s

t = 3 s

Hence,

V = Q x t = 0.25 x 3 = 0.75 liter

The density of the water is 1 kg per liter, therefore 0.75 liter of water is equal to 0.75 kg of water.

Total mass on the scale = mass of water + mass of bucket

                                       = 0.75 + 0.75 = 1.5 kg

The scale will read the weight:

Weight = mg = 1.5 x 9.8 = 14.7 N

Your question is incomplete, but most probably your question was:

Water falls without splashing at a rate of 0.250 L/s from a height of 2.60 m into a 0.750 kg bucket on a scale. If the bucket is originally empty , what does the scale read 3 s after water starts to accumulate in it.

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Observations of young stars tell us that when the Sun was young the solar wind was stronger than it is today.

The proto-planetary disc's gas and dust would have been cleaned away by the young Sun's solar wind after three to ten million years, pushing it into interstellar space and putting an end to the planets' formation.

The solar nebular disc model, often known as the solar nebular model, is the most extensively used current variation of the nebular hypothesis.

The planets' almost circular and coplanar orbits, as well as their motion in the same plane as the Sun's spin, were all explained by this theory, along with a number of other features of the Solar System.

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The density of the sphere given it stretches the spring 8 cm from it's equilibrium position is 1.25 g/cm³

First, we shall obtain the mass of the sphere. Details below:

F = mg

F = Ke

Thus,

mg = Ke

Divide both sides by g

m = Ke / g

m = (80 × 0.08) / 9.8

m = 0.653 Kg

Multiply by 1000 to express in grams

m = 0.653 × 1000

m = 653 g

Finall, we shall determine the density of the sphere. Details below:

Density = mass / volume

Density of sphere = 653 / 523

Density of sphere = 1.25 g/cm³

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The effect of doubling the water mass on the temperature change, and why do you think this happened is  doubling the mass will double the temperature change.

It lowers the temperature. Because the water temperature lowers as the bulk of the cylinder grows, it will result in a cooler year. Thermal expansion happens with heating. The mass stays constant. The loudness goes up. And as a result, the density drops. The average kinetic energy of an object's particles rises with increasing temperature. The object's thermal energy grows as the average kinetic energy of its particles rises. As a result, an object's thermal energy rises as its temperature does.

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The cell cycle advances from G1 phase to S phase when the cyclin–CDK complex phosphorylates RB.

The management of eukaryotic cell proliferation depends on the precise transition from G1 phase to S phase of the cell cycle, and its dysregulation encourages oncogenesis. Growth-dependent cyclin-dependent kinase (CDK) activity encourages DNA replication and starts the transition from G1 to S phase during G1 phase.

By causing alterations in transcription across the entire genome, CDK activation sets off a positive feedback loop that drives up CDK activity even more, committing the cell to division. G1-S transcripts produce proteins that control subsequent cell cycle processes. The intricate molecular mechanisms that regulate the temporal order of transcriptional activation and inactivation, identify distinctive functional subgroups of genes, and link cell cycle-dependent transcription are just now starting to come into focus as a result of recent research.

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When a rock on a string is spun in a horizontal circle, the speed is doubled, quadrupling the tension in the string.

When the rope breaks, there is no force in the radial direction, thus the stone flies off tangentially because of inertia. Until the stone is attached to a string, the tension in the string causes centripetal force and centrifugal force along in radial direction of motion.

What is Tension in the string?

Tension is the force that is sent through a rope, string, or wire when two opposing forces pull on it. Along the whole length of the wire, the tension force pulls energy equally on the bodies at the ends.

Every physical object that comes into contact with another one exerts a force on it. These contact forces have names based on the types of things they are applied to. One of the forces exerted on an object, such as a rope, cable, or chain, is tension.

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The orion nebula, m-42,  is a hot, thin cloud of glowing gas, so its spectrum is (d) a few bright lines against a dark background.

The Orion Nebula is it a cloud of gas?

One of the best-known celestial features is the Orion Nebula, often known as M42. This cloud of gas and dust, the middle "star" in Orion's dagger hanging below his belt, is so dazzling that it can be seen with the unaided eye even from a distance of more than 13 quadrillion kilometers (8 thousand trillion miles).

Why is Orion so crucial?

One of the starry sky's most intriguing and significant constellations is Orion. One reason why astronomers are drawn to it is that it contains one of the Milky Way Galaxy's closest and most active star nurseries (the Orion Nebula).

The Orion Nebula's gas glows for what reason?

The Trapezium and Nebula are located in front of a cold, dusty "giant molecular cloud" that contains regions of active star formation, around 1500 light years away. A blister on the molecular cloud's front edge gets electrified by the stars of the Trapezium, making it glow.

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Main sequence is the stage of the star's lifecycle in which hydrogen acts as the primary fuel for nuclear fusion.

These hydrogen and helium elements combine to increase the mass in the centre of the cloud as a result of gravity's contracting force. As mass increases, gravitational pull also expands. All of the molecules and particles in the environment are pulled in by gravity. As the molecules continue to descend into the cloud's core, the cloud's mass rises and the cloud's center begins to heat up. This heated center is known as a protostar.

Now, as additional molecules are drawn to this protostar, the protostar's temperature is rising. The temperature continues to climb until the time comes when the pressure exceeds the point when two hydrogen atoms start to fuse, releasing heat and radiation to create helium.

Nuclear fusion is the process of fusing two hydrogen atoms to create helium by releasing a large amount of energy.

The outward force produced by the radiation and heat emitted now balances the inward force exerted by gravity. The star is born when the force is balanced equally inward and outward.

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The statement 'the system does work on surroundings' is false because the work done is a positive quantity.

This question can be answered using the first law of thermodynamics.

The First Law of Thermodynamics is a thermodynamic adaptation of the law of conservation of energy. "The overall energy in a system remains constant, even when it may be transformed from one form to another," says one basic expression. Another typical phrase is "energy cannot be generated or destroyed" (in a "closed system"). While there are other nuances and consequences that may be better conveyed in more sophisticated formulations, this is the fundamental premise of the First Law.

According to first law,

U= Q+W

U: internal energy of the system

Q: amount of heat

W: work done

Q= -17 kJ, W= 21 kJ

If Q is positive it means heat flows into the system. If Q is negative it means heat flows out of the system.

In the given question heat s negative which means heat flows into the system.

Work done is positive hence work is done on the system.

U= Q+W

U= -17+21= 4kJ

This is an exothermic process since Q is negative.

Complete question:

For a particular process q = –17 kj and w = 21 kj. Which of the following statements is false?

a) heat flows from the system to the surrounding

b) the system does works on the surrounding

c) U= +4kJ

d) the process is exothermic

e) none of the above is false

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A solar day is 0.50001917 times longer than a sidereal day if the earth's orbital period is shortened to six months.

Earth is just a rocky, earthy planet and is home to us. There are mountains, valleys, canyons, plains, and much more on its stable and dynamic surface. Being an ocean planet, Earth is unique. The Earth's surface is 70% covered by water.

1 Sidereal year = 365.256 days

1 Solar year (1 tropical year) = 365.242 days

The length of time inside a sidereal year is equal to 365.256/2 days, or 182.628 days, if the earth's orbital period is six months.

1 Solar day = 182.256/365.242 sidereal days

1 Solar day = 0.50001917 sidereal day

A solar day is 0.50001917 times longer than a sidereal day if the earth's orbital period is shortened to six months.

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The complete question is-

Solar and Sidereal Days. Suppose Earth orbited the Sun in 6 months rather than 1 year but had the same rotation period. How much longer would a solar day be than a sidereal day? Explain.

The force of gravity between the two asteroids will be 125 *10^6 n

From the data,

The mass of the first asteroid is = 1 million kg = 1000000 Kg.

The mass of the second asteroid is = 50000 Kg.

The distance between both the asteroids = 400 m

We know,

The force of gravity between two objects can be determined by using the relationship

[tex]F_g=\frac{M_1M_2}{d}[/tex]

So, for determining the value of the force of gravity we will put the value of m1, m2 and d in the above formula:

Thus we will get:

[tex]F_g=\frac{1000000\times 50000}{400}=125,000,000=125\times 10^6\:N[/tex]

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