A heat engine takes in 330 J of energy from a hot reservoir and performs 22.0 J of work in each cycle. Find (a) the efficiency of the engine and (b) the energy expelled to the cold reservoir in each cycle.

Ranking in order, from largest to smallest, their wave speeds : [tex]v_{a}=v_{b}=v_{c}[/tex]

What is Wave speed?

The amount of space a wave covers in a certain length of time, such as the number of metres it covers in a second, is known as its wave speed. Speed = Wavelength x Frequency is an equation that describes how wave speed relates to wave wavelength and wave frequency.

Wave pulses in stretched string, wave speeds, and medium are notions that must be understood in order to answer the provided issue.

Find the factors that impact the medium's wave speed first. Next, evaluate the three waves and order them by speed.

Given by, is the wave speed,

ν=nλ

Here, v is the wave speed, n is the frequency, and λ is wavelength.

The same stretched string is being followed by all three waves. Therefore, the medium is the same for all three strings.

Only the wave medium has the ability to alter a wave's speed.

The wave speed for the same medium is unaffected by the frequency and wavelength of any of the three waves. The criterion to evaluate the waves would be frequency and wavelength if the medium were different for each of the three waves.

Due of their shared medium of motion, all three waves will move at the same pace. thus only the characteristics of the medium have an impact on wave speed.

[tex]v_{a}=v_{b}=v_{c}[/tex]

The three waves use the same medium. The wave velocity will thus be the same. The wave speed will vary depending on the medium, and it may be rated.

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The speed at which the ball must be shot at the point p for it to land at the distance 6 cm is 6.635 m/s.

Given that,

Height h₁ = 5 cm

Height h₂ = 1.6 cm

Distance d = 6 cm

We know, t = √(2 h₂/g) = √(2* 1.6)/9.8 = 0.57 s

We know that, distance is nothing but speed multiplied by time.

According to the above statement, expression can be written as d = V₁* t

V₁ = d/t = 6/0.57 = 10.52 m/s

Using work energy theorem, we have

mg(h₁ - h₂) = 1/2* m * V₁² - 1/2* m * V₂²

Eliminating 'm' on both sides, g(h₁ - h₂) = 1/2* V₁² - 1/2* V₂²

9.8 (5 - 1.6) = 1/2* 10.52² - 1/2* V₂²

33.32 = 1/2(10.52² - V₂²)

(10.52² - V₂²) = 66.64

V₂² = 44.03

V₂ = 6.635 m/s

Thus, the speed of the ball with which it should be shot is 6.635 m/s.

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YES, Many consumers have concerns about changing their incandescent bulbs because they are unsure of how LED light bulbs operate. Using dimmable LED light bulbs in sockets without a dimmer switch is one often requested query.

Compared to conventional incandescent bulbs, LED light bulbs have many benefits. The key benefits are longer life, less heat, and less electricity usage. Non-dimmable LED lights are becoming less and less available from shops. As a result, it is almost certain that you will need to use a conventional socket to install a dimmable LED light.

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The volume of water that will be pumped from the lower to the upper reservoir to generate the energy is 93,790.7 m³.

The volume of water needed to generate the given power is calculated by applying the law of conservation of energy as shown below.

gravitational potential energy of water or work done by the water = energy generated

Mathematically, the equation is given as;

W = PV

where;

W = (ρgh)V

where;

(ρgh)V  = Pt

where;

V = Pt / ρgh

The given parameters include;

The volume of water needed to generate the energy is calculated as follows;

V = (120 x 10⁶ x 3600) / (1000 x 9.8 x 470)

V = 93,790.7 m³

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A distance-time graph can be used to see the distance traveled by an object when it moves in a straight line. A distance-time graph's line gradient corresponds to the object's speed. The gradient's magnitude determines how quickly an object is travelling.

Acceleration is the rate at which velocity, both in terms of speed and direction, varies over time. Whenever something moves either quicker or slower in a horizontal path, it is referred to as pushed.

An object's velocity is altered by a net force, and acceleration increases with net force. To accelerate at the same rate as less massive objects, more massive objects need greater net forces.

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A)  The constant of proportionality, K is 840 B) The current when the resistance is 12 ohms is 70 amperes.

The resistance R and the current I are inversely related.

I=k/R   (k is the constant of proportionality)

A) I=210 amperes

    R=4 ohms

    I=k/R

    k=I×R

    k=210×4=840

B)   R=12 ohms

      k=840

      I=k/R

      I=840/12=70 amperes

Another significant characteristic in electrical systems that can be measured is resistance. Ohms. are the units. used to measure. resistance. The forces that hinder an electrical current's ability to travel through a conductor are referred to as resistance. All materials have some inherent impedance to the movement of electron current. We haven't figured out how to create conductors without any resistance.

Consider a hose that is partially clogged with sand if we are using our water analogy from the voltage lesson to help visualize resistance. The water in the hose will flow more slowly due to the sand. We can claim that a blocked hose has more water flow resistance than an unconnected hose.

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All the prompts indicated above are related to the qualities of light in Physics parlance.

1) When the left hand is lifted in front of the mirror, the picture depicts the right hand rising. This is due to the picture being reversed laterally. In the case of a flat mirror, it is produced.

2) Keep in mind that convex mirrors are commonly employed in shop security mirrors because the reflective surface bulges outwards toward the light source, resulting in a distorted picture but an increased range of view. This broad perspective is ideal for visually covering a large area.

3) A piece of paper appears white in the sunshine because it reflects all colors of light. When seen in red light, it appears red.

4) A rainbow is created by the interaction of sunlight and atmospheric circumstances. As light reaches a water droplet, it slows and bends as it transitions from air to denser water. The light bounces off the interior of the droplet, splitting it into wavelengths (or colors).

5) One effect of refraction is the bending of light as it passes through a medium with a different refractive index. For example, when light travels from air into water, it is bent, or refracted, causing objects to appear distorted or shifted. This is why objects underwater may appear closer or larger than they actually are.

6) The Newton disc, also known as the Disappearing Color Disc, is a well-known physics experiment in which a revolving disc with multiple colored parts becomes white when spun very quickly.

Some of the qualities of light are as follows:

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There is no difference in the shape of 2p and 3p orbitals since the azimuthal quantum number, which defines the shape of the orbital, is the same for both.

The electron orbital energy levels are listed in the following order, from lowest to highest: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, and 7p. Because electrons all have the same charge, they try to stay as far apart as possible due to repulsion. We only need three hybrid orbitals, aka sp2, because the carbon has no lone pairs and is connected to three hydrogens. Don't forget to account for any lone pairings. Every solitary pair need its own hybrid orbital.

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a. At the time [tex]\rm \(t = 0\)[/tex], the magnetic field at the location of detector #1 is in the +z direction.

b. At [tex]\(t \approx 2 \times 10^{-8}\)[/tex] seconds, detector #2 will detect the electric and magnetic fields.

(a) To determine the direction of the magnetic field at the location of detector #1, we can use the right-hand rule, which relates the direction of the magnetic field [tex]\rm (\(B\))[/tex], the direction of the electric field [tex]\rm (\(E\))[/tex], and the direction of propagation [tex]\rm (\(+y\))[/tex].

Since the pulse of electromagnetic radiation is propagating in the +y direction and detector #1 detects an electric field in the -x direction, the magnetic field [tex]\rm (\(B\))[/tex] must be in the +z direction.

This is because electromagnetic waves are transverse waves, and the electric and magnetic fields are perpendicular to each other and the direction of propagation.

So, at time [tex]\rm \(t = 0\)[/tex], the magnetic field at the location of detector #1 is in the +z direction.

(b) To determine the time at which detector #2 will detect electric and magnetic fields, we need to consider the distance between the two detectors and the speed of propagation of the electromagnetic wave.

Let's assume that the speed of light [tex]\rm (\(c\))[/tex] is [tex]\rm \(3.00 \times 10^8\)[/tex] m/s.

The distance between the two detectors is [tex]\rm \(d = 6\)[/tex] m (distance between the y-coordinates of the detectors).

The time [tex]\rm (\(t\))[/tex] it takes for the electromagnetic wave to travel from detector #1 to detector #2 is given by:

[tex]\[ t = \frac{d}{c} \]\\\\\ t = \frac{6 \, \text{m}}{3.00 \times 10^8 \, \text{m/s}} \]\\\\\ t \approx 2 \times 10^{-8} \, \text{s} \][/tex]

So, in [tex]\rm \(t \approx 2 \times 10^{-8}\)[/tex] seconds, detector #2 will detect the electric and magnetic fields.

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Answer:

Therefore, the approximate value of y for x = 4 is approximately 0.97.

Explanation:

To determine the approximate value of y for x = 4, we need to use the values in the table to find a mathematical relationship between x and y. This can be done by performing a linear regression analysis on the data.A linear regression model is a statistical model that represents the relationship between two variables as a linear equation. The equation of the line is given by:y = mx + bWhere m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).We can use the values in the table to calculate the values of m and b. Using the formula for the slope of a line:m = (Σ(xy) - (Σx)(Σy)/n) / (Σ(x^2) - (Σx)^2/n)Where Σ(xy) is the sum of the products of the x and y values, Σx is the sum of the x values, Σy is the sum of the y values, Σ(x^2) is the sum of the squares of the x values, and n is the number of data points.Plugging in the values from the table, we get:m = (1146.07 - (69.7)(625.99)/5) / (1152.64 - (69.7)^2/5)m = 0.68The y-intercept can be calculated using the formula:b = (Σy - m(Σx)) / nPlugging in the values from the table and the value of m that we just calculated, we get:b = (625.99 - 0.68(69.7)) / 5b = -1.75We can now use the values of m and b to write the equation of the line:y = 0.68x - 1.75To determine the approximate value of y for x = 4, we can substitute this value into the equation:y = 0.68 * 4 - 1.75y = 2.72 - 1.75y = 0.97

The tension on the rope is 300 n. when the block is fully submerged in a fluid of density 600 kg/m3 ,The tension on the rope is 2940.

T = buoyancy force - weight of block = 600 x 9.8 - 300 x 9.8 = 2940

When two opposing pressures pull on a rope, string, or wire, the force communicated through the object is known as tension. The energy is pulled equally on the bodies at the ends by the tension force, which is applied over the entire length of the wire.

Each physical object that comes into contact with another applies force to that other. Names are given to these contact forces based on the types of objects. The term "tension" can be used to describe one of the forces acting on an object that is a rope, cable, or chain.

Since they effectively convey a force over a predetermined distance, cables and ropes can be utilized to apply forces (e.g. the rope length). Remember that since ropes cannot effectively push, tension acts as the pulling force.

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The average power supplied by the voltage source is given by

Pavg = Irms * Vrms

Pavg = 1/2 I₀² R = I²rms * R

Pavg = 1/2 V₀²/R = V²rms /R

where, Pavg is average power

Irms is rms current

Vrms is rms voltage

I₀ is the peak value of alternating current

V₀ is the peak value of alternating voltage

Root mean square current of the alternating current represents the DC current that dissipates the same amount of power as the average power dissipated by the alternating current.

The RMS value of alternating current is given by the direct current which flows through a resistance.

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Richard Feynman was the scientist who first suggested partons to study high-energy hadron collisions before quarks were suggested.

The elementary particle known as the quark is a fundamental component of matter. Hadrons, which are composite particles made of these quarks and neutrons and protons, the building blocks of atomic nuclei, are the most stable of these hadrons.

A strong contact between two or more quarks holds together hadrons, which are composite subatomic particles. Simply put, hadrons are like molecules that the electric force holds together. Protons and neutrons combine to form hadrons, which are particles.

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The spaceship's pendulum experiences fewer oscillations in a given time period than the pendulum on Earth.

Because of the effect of time dilation, a clock moving with respect to an observer appears to run more slowly than a clock that is at rest in the observer's frame. When observed from earth, the pendulum on the spaceship takes longer to complete one oscillation. Therefore, the clock associated with that pendulum will run slower (gives fewer oscillations as seen from the earth) than the clock associated with the pendulum on earth.

Oscillations is the process of any quantity or measure repeatedly varying its equilibrium value in time. Another definition of oscillation is the periodic variation of a substance between two values or around its core value.

An object's mechanical oscillations are referred to as vibrations. However, oscillations also happen in dynamic systems, or to be more precise, throughout all of science. Even our heartbeat generates vibrations. Oscillators, meanwhile, are described as having motion toward an equilibrium point.

To put it simply, oscillation motion is the word used to describe a mechanical system's item swinging from side to side.

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Binding energy for Fe is 8.52 MeV and for nickel is 554.3 MeV.

Binding energy :  It is the minimum amount of energy required to disassemble or break down an atom's nucleus into the subatomic particles, which are protons and neutrons.

The average energy required to release a nucleon from a nucleus is called binding energy per nucleon.

Binding Energy , BE=Δmc2,  where Δm is the mass defect

Here , Δm=Mass of nucleon- Mass of nucleus=26 [tex]m_{p[/tex] +30 [tex]m_{n[/tex] -m 56 Fe

Hence,

BE = (26 [tex]m_{p[/tex] +30 [tex]m_{n[/tex] -m 56 Fe) [tex]c^{2}[/tex]

where [tex]m_{n[/tex] = 1.00866 u

[tex]m_{p[/tex]  = 1.00727 u

BE=[26×1.00727+30×1.00866−55.936]×931

=0.51282×931

=477.435 MeV

Binding energy per nucleon = 477.435/56 MeV

                                                =8.52 MeV.

Now we will calculate binding energy for nickel

Then mass defect,

       Δm=28m H +34m n − 28 34 m

       Δm=28×1.008+34×1.0087−61.9237

       Δm=0.5961u

Hence binding energy,

        B.E.=Δm×931

        B.E.=0.5961×930=554.3 MeV

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The force acting on the 2 m wire carrying a 2 A current and placed in a 4 T magnetic field is 16 N.

The subject of this question is Physics, particularly dealing with the concept of magnetic force. In this scenario, we are asked to determine the magnitude of the force acting on a wire that is carrying a current and placed within a magnetic field. The force on a current carrying conductor in a magnetic field can be calculated using the formula F=BIL, where F is the magnetic force, B is the magnetic field strength, I is the current in the wire, and L is the length of the wire.

In this problem, we are given B=4 T, I=2 A, and L=2 m. Substituting these values into the equation, we find that F=BIL=(4 T)*(2 A)*(2 m)=16 N.

Therefore, the correct answer is D. 16 N.

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When a metal is heated, its atoms begin to vibrate more vigorously and move further apart from each other. This increases the distance between the atoms, which in turn causes the metal to expand and become longer.

The amount of expansion that a metal undergoes when heated depends on several factors, including the type of metal, the initial temperature of the metal, and the rate at which it is heated. In general, most metals will expand by a small amount when heated over a wide range of temperatures.

At very high temperatures, some metals may begin to undergo a phase change, such as melting or vaporization. This can cause the metal to undergo a significant change in length, depending on the amount of phase change that occurs.

Overall, the length of a metal will generally increase as the temperature increases, although the exact amount of expansion will depend on the specific conditions and the type of metal involved.

If you traveled for 25 hours with an average speed of 48 miles/hour, the distance traveled is 25 * 48 = 1200 miles. This can be found by multiplying the number of hours traveled by the average speed to get the total distance traveled.

The center of mass is 2.25 which is point C.

A place at which the entire mass of a body or all the masses of a system of particles appears to be concentrated is defined as the center of mass of a body or system of particles.

The center of mass for straightforward stiff objects with homogeneous density is found at the centroid. The center of mass will always rest immediately underneath a shape if it is suspended from a single point. Therefore, the center of mass is where two lines that are drawn down downward from two different places on a shape (one at a time) intersect.

Here, we have 5 masses so the center of mass will be at the third block.

But here we remove a block and the left masses are:

o.5, 1.5, 2.5 and 4.5

X(cm) = m(0.5) + m(1.5) + m(2.5) + m(4.5) / 4m

X(cm) = m(0.5 + 1.5 + 2.5 + 4.5) / (4) m

[m will be cancelled out]

X(cm) = 9 / 4 = 2.25 which is point C

Therefore, the center of mass is 2.25 which is point C.

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The plane of a loop of wire is perpendicular to a magnetic field. Rank from greatest to least, the magnitudes of the loop's induced emf for each situation will be E - B - D - A - C.

The number of magnetic flux lines on a unit area passing perpendicular to the given line direction is known as induced magnetic field strength. It is denoted by B.

The magnitude of the induced EMF in the loop of wire is:

∈ = ΔФ/ Δt

The magnetic flux is given by ФB = ΔBA

∈ = ΔBA / Δt

The above expression shows that the induced emf is proportional to the rate of change of the magnetic field.

ΔB/Δt = (1T-0T)/6 = 0.167 T/sec

ΔB/Δt = (4T-1T)/2 = 1.500 T/sec

ΔB/Δt = (4T-4T)/60 = 0 T/sec

ΔB/Δt = (3T-4T)/4 = -0.25 T/sec

ΔB/Δt = (0T-3T)/1 = -3 T/sec

From the above, it is observed that rank, from the greatest to least, the magnitudes of the loop's induced emf for each situation will be

E - B - D - A - C.

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The explanation for this observation is that the magnetic field distorts the electric field in the band. This distortion creates an electric field component directed from point A to point B which deflects the electrons in the bar toward point B.

The physical field that surrounds an electrically charged particle and exerts a force on all other charged particles in that field, either attracting or repelling them, is called the electric field (or E-field). It can also refer to the physical field system of charged particles.

The negatively charged electrons are directed to the positive electrode or (+) plate. Positively charged protons are directed to the negative electrode or plate (-).

Therefore, ferromagnetic materials bend the lines of magnetic force in space in a static field. The distortion effect on the static magnetic field is disturbed by the deformed material.

The complete questions:

Current is moving through a copper ribbon in the direction shown. The ribbon is suspended between the poles of a magnet as indicated. When the voltage is measured between A and B, it is observed that A is at higher potential than B. Which of the following explains this observation?

A) The electrons in the ribbon behave like magnetic dipoles, thus, they align with the magnetic field of the magnet that deflects electrons in the ribbon toward point A.

B) The electrons in the ribbon behave like magnetic dipoles, thus, they align with the magnetic field of the magnet that deflects electrons in the ribbon toward point B.

C) Electrons moving through the magnetic field experience a magnetic force to the left that deflects electrons in the ribbon toward point A

D) Electrons moving through the magnetic field experience a magnetic force to the right that deflects electrons in the ribbon toward point B

E) The electric field in the ribbon is distorted by the magnetic field. This distortion creates an electric field component directed from point A to point B that deflects electrons in the ribbon toward point B.

The true choice is E

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Galileo and Cassini are the two missions on outer planets that were orbiters. Galileo orbited Jupiter for eight years, while Cassini orbited Saturn for thirteen years.

A total of 9 spacecraft have been launched for missions on outer planets. Two of them are orbiters. Galileo was an American spacecraft to study Jupiter. It was delivered into Earth orbit on October 18, 1989, by Space Shuttle Atlantis,

Cassini was a space mission by NASA and ASI to study the planet Saturn. It was launched on Titan IVB/Centaur, and the date was October 15, 1997. Cassini was active for nearly 20 years which it spent orbiting Saturn for 13 years. It was the first spacecraft to enter Saturn orbit.

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The induced electromotive force is larger in magnitude if the magnetic field is turned off more quickly when the vector points into the page.

We know that, as per faraday's law,

= Induced EMF = d(Ф)dt

where Ф  is magnetic flux

Thus, Ф = BA

so,

Induced EMF = d(BA) / dt

We can see time in inversely related to emf. So if we switch off the magnetic field in less time then EMF will be more.

Therefore, answer should be "The induced electromotive force is larger in magnitude if the magnetic field is turned off more quickly."

Next, the current should follow Lenz's law and t should oppose the change in magnetic flux.

The induced current should flow clockwise.

Now, we know

Induced emf = d(BA)/ dt

where A = pi X r²

So, if radius is doubled then,

= A = π X (2r)²

= A = 4 X pi X r²

Hence,

Emf increases by 4 times ( it quadruples ).

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2.0 m/s is the maximum speed. 200 m/s2 is the maximum acceleration. Calculating the angular frequency is necessary. utilising the angular frequency formula.

Fill out the formula with the value A stretched string is traversed by a sinusoidal wave. A particle on the string can move at a maximum speed of 0.900 m/s and accelerate at a maximum rate of 270 m/s2. What are the wave's frequency and amplitude?

On stretched string, a sinusoidal wave travelling in the right direction has an amplitude of 20 cm, a wavelength of 1, and a speed of 5 m/s. It is assumed that y=0 and dtdy0 at x=0 and t=0. the wave function for y. (x,t).

A particle on the string can move at a maximum speed of 0.900 m/s and accelerate at a maximum rate of 270 m/s2. What are the wave's frequency and amplitude?

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Answer:

Explanation:

happens to me  with some guy names venus he always flaggs me when i even answer a question its  really dificult to even try to answer when someone is on your tail ever now and then

Microbursts are dangerous for commercial aircraft on takeoff or landing because of the associated high wind gusts and turbulence.

Microbursts can create strong and sudden downdrafts that can cause a rapid decrease in airspeed and altitude, leading to a potential loss of lift and control. This can be especially dangerous during takeoff or landing when the aircraft is already at a low altitude and has limited ability to recover.

Microbursts are intense, short-lived downdrafts that can cause severe turbulence and strong winds in a localized area. They occur during thunderstorms and can last from a few seconds to a few minutes.

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Wavenumber (and frequency) drop from left to right, and peaks in an IR spectrum grow downward.

An absorption technique that is frequently used in both qualitative and quantitative investigations is infrared (IR) spectroscopy. The electromagnetic radiation in the infrared area of the spectrum has the ability to change the rotational and vibrational states of covalent bonds in organic molecules.

In addition to a variety of other uses, infrared spectroscopy (IR) is used to determine chemical species, identify chemical species, quantify chemical species, and determine molecular structure. Utilizing this method, scientists may examine matter in its solid, liquid, and gaseous phases.

An atom or group of atoms inside a molecule that exhibits a comparable set of chemical characteristics across a variety of compounds is referred to as a functional group.

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The length of the can above the water level is 5.22 cm.

First determine the height of the can.

355cm3 = pi * r2 * l     Volume of cylinder formula where l is length of can.

355=pi * (3.1)2 * l       Where 3.1 is half of the diameter.

l = 11.76cm

Now determine the total mass of the can including the water inside.

Total mass = 20g + (355ml)/2 * 1g/ml = 177.5g,    where 1g/ml is the density of water, therefore since we know half the can is full of water we take the volume of water inside, multiply it by the density and determine the mass of water. This, in addition to the weight of the can itself gives us the total mass of the floating object.

Total mass=197.5g

According to Archimedes' principle the mass of a floating object equals the mass of fluid displaced by the object.

197.5=mass of water displaced

197.5=density of water * volume of water

197.5= 1g/ml * (pi * (3.1)2 * l)      where l is the length of can inside the water

6.54cm=l

So take total length of can and subtract the submerged length to retrieve the above water length.

11.76cm - 6.54cm = 5.22cm

5.22 cm of water level.

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If a wooden plank 2 m long, 30 cm wide, and 40 mm thick floats in water with 10 mm of its thickness above the surface, the mass of the board is 18 kg.

Calculation:-

mass of board = density of water x volume of water displaced

= 1000 x 2x0.3x0.03

= 18 kg.

A property of a body that is a measure of inertia is usually viewed as a measure of the amount of matter contained in the body that causes it to have weight in a gravitational field. Mass is a dimensionless quantity that describes the amount of matter in a particle or object.

The mass of an object is a measure of its inertial properties or the amount of matter it contains. The weight of an object is a measure of the force exerted on it by gravity, or the force required to support it. Mass can best be understood as the amount of matter present in an object or body. Everything around us has mass.

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The period of oscillation of the building will be=13 s

During strong winds, the pendulum moves when it passes through the equilibrium position with a speed of = 0.36 m/s

(a)

Let us assume that the time period of oscillations of the building be [i 0]

So, the expression for time period will be: [tex]$$T=2 \pi \sqrt{\frac{l}{g}}$$[/tex]

Where, l is the length of the pendulum and g is the acceleration due to gravity.

So, the value of time period of oscillations will be:

[tex]T & =2 \pi \sqrt{\frac{(42 \mathrm{~m})}{\left(9.8 \mathrm{~m} / \mathrm{s}^2\right)}}[/tex] =13.0 seconds.

(b)

As we have, the relation between angular frequency and time period, which is [tex]$$\omega=\frac{2 \pi}{T}$$[/tex]

So, the value of the linear velocity of the pendulum will be

[tex]$$\begin{aligned}v & =A \omega \\& =A\left(\frac{2 \pi}{T}\right) \\& =\frac{2 \pi A}{T} \\& =\frac{2 \pi(0.75 \mathrm{~m})}{(13.0 \mathrm{~s})} \\& =0.36 \mathrm{~m} / \mathrm{s}\end{aligned}$$[/tex]

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The complete question should be:

Taipei 101 (a 101-story building in Taiwan) is sited in an area that is prone to earthquakes and typhoons, both of which can lead to dangerous oscillations of the building. To reduce the maximum amplitude, the building has a tuned mass damper, a 660,000 kg mass suspended from 42-m-long cables that oscillates at the same natural frequency as the building. When the building sways, the pendulum swings, reaching an amplitude of 75 cm in strong winds or tremors. Damping the motion of the mass reduces the maximum amplitude of oscillation of the building.

What is the period of oscillation of the building?

During strong winds, how fast is the pendulum moving when it passes through the equilibrium position?