a 80 kg student is standing atop a spring in an elevator that is accelerating upward at 3.0m/s2. the spring constant is 2700 n/m .

The value of m is 0.534 kg

f1 =0.92  Hz

f2 = 0.58  Hz

Δm = m2 - m1 =  800 g kg

Mass-spring oscillation occurs with a frequency of:

f = (1/2π)√(k/m)

k = m(2πf)²

When we have: we may conclude that k is constant for both trials.

k = k

m1(2πf1)² = m2(2πf2)²

m1 = m2(f2/f1)²

m1 = (m1+Δm)(f2/f1)²

m1 = Δm/((f1/f2)²-1)

m 1 = 0. 800 g/ (0.92/0.58)^2 – 1

= 0.534 kg or 0.53kg or 534 g

A mass m linked to a spring produces an oscillation with a period of 4 s. A spring's time period lengthens by 1 s when a 2 kg additional mass is added to it.

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The inductor's resistance, R, is 1550.38.

1.05 H is the inductance L.

A capacitance opposes a variation in voltage, while an inductance opposes a changes in current. This is one of the key distinctions between the two components. Additionally, the capacitor and inductor both store energies with in type of either a magnetic charge and a magnetic force, respectively.

Briefing-

Given:

Emf, E=15.5V

Current, i = 4.86mA

Time, t = 0.940 ms

Maximum current, imax Calculation: 6.45mA

a) The resistance is given by,

Ꭱ= V/Imax = 10/6.45×10⁻³= 1550.38Ω

b) The inductance is given by,

L= -Rt/(1-i/imax)= 1550.38×0.940×10⁻³/In(1-4.86/6.45)

The inductance L is 1.05 H.

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The Lagrange's equations of motion for the system is d(ml³Ф2 + ml²Ф1 cos (Ф1-Ф2)) − (−ml³Ф1Ф2 sin (Ф1-Ф2)-mgl sinФ2 )/dt = 0.

Newton's method of developing the equations of motion requires element decomposition. If the forces on the connections are not the primary concern, it is more advantageous to consider the energies in the system to derive the equations of motion.

A double pendulum exhibits simple harmonic motion when the non-equilibrium displacement is small. However, when large displacements are imposed, the behavior of nonlinear systems becomes dramatically chaotic indicating that deterministic systems are not always predictable. There are several possible variations of the double pendulum.

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Inversely proportional to the rectangular of the angular velocity inversely proportional to kinetic energy no longer depends on the mass of the rotating item.

The kinetic energy  of a rotating body is given as

K=1/ 2 Iω

The moment of inertia relies upon the distribution of mass.

subsequently, the kinetic energy relies upon each distribution of mass and angular pace.

Kinetic energy is the energy an object has due to its movement. If we want to accelerate an object, then we need to apply a force applying a force calls for us to do paintings. After paintings have been accomplished, energy has been transferred to the object, and the object might be shifting at a new steady pace.

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A viewing window 30 cm in diameter is erected 3 m below the surface of an aquarium tank filled with sea water. The force the glass must endure is roughly 8562 N.

Given,

Diameter = 30 cm

= 0.3 m

radius = 0.3/2

= 0.15

Total pressure = 1atm + hρg

= 10⁵ N/m + 1000 × 9.8 × 3

= 101325 + 29400

= 130725 Pa

therefore Force = 130725 × π × 0.15²

= 9235.721 N that is approximately 8562 N

An object experiences a push or pull as a result of interacting with another item. Each item is subject to a force whenever two things interact. The two items no longer feel the force after the interaction ends. Only by interaction do forces come into being.

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It is true that if the tank is a reusable tank, there are no check valves and system refrigerant can enter the tank as long as the system pressure is higher than the pressure in the tank.

A fundamental valve type dispersed generously all through a modern refrigeration framework is a manual shutoff valve. In the totally vacant position, this valve ought to permit a free progression of refrigerant and when shut totally block the stream. The standard capability of the shutoff valve is to confine a part or a segment of the framework.

Air conditioning Valves are such parts without which we have no control over stream in pipes .Valves are required for each medium whether it is water, gas, air or some other fluid. Valves would have been required for solids in the event that they could have capacity to stream. Like different regions, valves track down its broad use in air conditioning.

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Statement about saturn's rings is not true is that the rings must look much the same today as they did shortly after saturn formed.

Saturn, the most beautiful planet in our solar system, is famous for its dazzling rings. These rings extend far into space and engulf many of Saturn’s moons. The brightest rings, visible from Earth in a small telescope, include the D, C and B rings, Cassini’s Division.

The A ring. Just outside the A ring is the narrow F ring, shepherded by tiny moons, Pandora and Prometheus. Beyond that are two much fainter rings named G and E. Saturn's diffuse E ring is the largest planetary ring in our solar system, extending from Mimas' orbit to Titan's orbit, about 1 million kilometers.

The particles in Saturn's rings are composed primarily of water ice and range in size from microns to tens of meters. The rings show a tremendous amount of structure on all scales. Some of this structure is related to gravitational interactions with Saturn's many moons, but much of it remains unexplained.

One moonlet, Pan, actually orbits inside the A ring in a 330-kilometer-wide (200-mile) gap called the Encke Gap. The main rings (A, B and C) are less than 100 meters (300 feet) thick in most places. The main rings are much younger than the age of the solar system, perhaps only a few hundred million years old.

Hence, the correct option is A.

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If the mass of one of the objects were to be doubled, then the gravitational force between the two masses would be 2 times greater than it was originally.

The gravitational force between two masses is given by the equation:

F = G x (m1 x m2) / r^2

where F is the gravitational force, G is the gravitational constant (equal to 6.67 x 10^-11 Nxm^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between them. If the mass of one of the objects is doubled, the gravitational force between the two masses will also be doubled. This is because the gravitational force is directly proportional to the masses of the two objects. Therefore, if the mass of one of the objects is doubled, the gravitational force between the two masses will be 2 times greater than it was originally.

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In 3.5 minutes, the electromagnetic energy of the signal stated above, 71.45 pJ, is reflected to the main receiver.

Intensity = 0.75 x 10⁻¹² W/m²

Intensity = Power / Area

here, Area = A = π r = π (0.38)² = 0.4536 m²

so, Power = 0.75 x 10⁻¹² x 0.4536 = 3.402 x 10⁻¹³ W

Energy = Power x time

here, time = 3.5 minutes = 3.5 x 60 seconds

therefore, energy reflected = 3.402 x 10⁻¹³ x 3.5 x 60 = 71.45 x 10⁻¹² J = 71.45 pJ

this is the energy reflected the central receiver in 3.5 minutes.

Radiation with electromagnetic properties is electromagnetic energy. The energy connected to electromagnetic waves is commonly referred to by this phrase. Energy is what causes these waves to move through any medium. Photons, a unit of light energy that electromagnetic radiation travels in, are free of charge and mass. One of the most significant elements in the cosmos is electromagnetic energy. The force behind the electromagnetic waves is it.

When a force outside of the electrical charge accelerates it, electromagnetic energy is released. As a result of the acceleration, a wave of alternating magnetic and electric fields is created. This wave separates from the charge and flows independently through the medium.

The discrete energy packets known as photons make up electromagnetic waves.

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Think about a single Rb atom held at t0. if allowed (from rest). See McIntyre 6.40 for a hint. There, the solution is (x, t) = (2p) TTT, with 9-2h/m. (You must determine dimensionless constant .)

Rubidium-87 has a positive scattering length at low temperatures, making it mutually repulsive despite rubidium-85's greater abundance. This prevents all condensates bar the tiniest ones from collapsing.

As a getter, rubidium is a substance that mixes with and extracts trace gases from vacuum tubes. Additionally, it is utilized in the creation of specialty glasses and photocells. It is easily ionized, 

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On the surface of the Moon, the free-fall acceleration is roughly one-sixth that of the Earth. Their average densities are 0.667 apart.

Given the radius of the Moon is (Rm) = 0.250 RE

The radius of the earth (RE) = 6.4 x 10^6 m

Let freefall acceleration of the moon = gm

Let freefall acceleration of the earth = ge

Given gm = ge/6

We know that g = Gm/r^2 where G is the gravitational constant

Let mass of moon = m1 and mass of earth = m2

Gm1/Rm^2 = Gm2/6xRE^2

mass = densityxvolume

let density of moon = d1 and density of earth = d2

d1 x (4/3Rm^3)/Rm^2  =  d2x (4/3RE^3)/6xRE^2

d1xRm = d2xRE/6

d1/d2 = RE/6X0.250RE

d1/d2 = 0.667

Hence the ratio of densities of moon and earth is 0.667

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The current concentration of carbon dioxide in the atmosphere is far higher than the natural range over the last 650,000 years, and is increasing rapidly for several reasons. Some of the main factors that have contributed to this increase include:

Overall, the current high levels of carbon dioxide in the atmosphere are the result of human activities, such as the burning of fossil fuels and deforestation, which have released large amounts of carbon dioxide into the atmosphere. These activities have led to a rapid increase in the concentration of carbon dioxide in the atmosphere, far beyond the natural range of concentrations over the last 650,000 years.

The flux of a vector g into this sphere 0.00004pi. estimate div g at the point (2, 3, -1) is the divergence at the point  is 0.03.

Calculation :

Divergence of a vector field G at a point p is defined as:

div(G)p=Fluxp/Volumep

A point p=(3,3,−1) has a radius of 0.1 units and the flux entering p is 0.00004π

.Volume of point p = (4/3)π 0.1³=0.0043π

Therefore, the divergence at the point is given by:

div(G)p=−0.00004π/(0.004/3)π=−0.03

divergence, in mathematics, the differential operator applied to a vector-valued function in three dimensions. The result is a function representing the rate of change. The divergence of vector v is given by . where v1, v2, and v3 are the vector components of v, typically the fluid flow velocity field.

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The moment arm for each force is 0.218 m and 0.0287 m , and the joint is a flex .

In the question ,

it is given that ,

quad force is ([tex]F_{q}[/tex]) = 500 N

weights at the ankle is wₐ ,

So , wₐ = (10 Kg)(9.8 m/s²)

= 98 N

given

the distance from knee joint to weight(a) = 0.38 m

the distance from knee joint to quad force (q) = 0.05 m

From the diagram , we can see that ,

the moment arm for the weight is ([tex]a_{t}[/tex]) = a*cos55° = (0.38)*cos55° = 0.218 m

and

the moment arm for equal force([tex]q_{t}[/tex]) = q*cos55° = (0.05)*cos55° = 0.0287 m

Now , torque (net) = ([tex]F_{q} \times q_{t}[/tex]) - ([tex]w_{a} \times a_{t}[/tex])

After substituting the values , we get

Net Torque = 500×0.0287 - 98×0.218

= 14.35 - 21.364

we can see that as the net torque is negative , its weight will pull down the leg ,

So , the joint will flex not extend .

Therefore , The joint will Flex .

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The tension in the string is = 0.118

Given the values in the question,

The volume of the plastic ball = 75 [tex]cm^{3}[/tex]

Density ( ρ ) = 840 kg / [tex]m^{3}[/tex]

Let the tension on the ball = T

Since the density is given in centimeters so convert volume also in meters,

⇒ 75 [tex]cm^{3}[/tex] = 0.000075 [tex]m^{3}[/tex]

The ball is following the principle of buoyant force, so the ball is stable in the water the force that the ball is exerting into the water is equal to the force the water is exerting on the ball.

The forces could be represented as -

∑ [tex]F_{y}[/tex] = [tex]F_{b}[/tex] - T - [tex]W_{b}[/tex] = 0

T = [tex]F_{b}[/tex] - [tex]W_{b}[/tex]

T = ρ x g x [tex]V_{w}[/tex] - ρ x g x [tex]V_{b}[/tex]

T = ( 1000 x 9.8 x 0.000075 ) - ( 840 x 9.8 x 0.000075 )

T = 0.735 - 0.617

T = 0.118

Therefore, The tension in the string is = 0.118

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Pressure and mass flow relationship It follows that increasing the pressure supplied to the intake section will increase the pressure differential between the inlet and outlet valves.

More people will attempt to hurry past the segment as a result. As a result, we may state that pressure and mass flow rate are directly related (gradient). Mass flow rate is the amount of a substance that moves per unit of time in physics and engineering. In SI units, it is measured in kilograms per second, and in pounds or slugs per second in US customary units. Although occasionally (Greek lowercase mu) is used, the typical symbol is (, pronounced "m-dot"). The force that is delivered perpendicular to an object's surface and expressed as a symbol (p or P) is known as pressure.

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Hubble's law is a statement of a direct correlation between the distance to a galaxy and its recessional velocity as determined by the red shift. It states that all galaxies are moving away from the Earth and from each other.

Edwin Hubble discovered that most of the galaxies are moving away from the Earth and away from each other. He also discovered that there is a relationship between the distance to a galaxy and its speed. He stated that the farther away a galaxy is, the faster it is moving away from us. Hence, Hubble’s law, also known as the Hubble–Lemaître law, refers to the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance.

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The force that results when a liquid under pressure acts on surfaces that are submerged is known as a hydrostatic force. Fundamental concepts in fluid mechanics include the calculation of the hydrostatic force and the location of the centre of pressure.

suppose that a plate is immersed vertically in a fluid with den- sity and the width of the plate is at a depth of meters beneath the surface of the fluid. if the top of the plate is at depth and the bottom is at depth ,[tex]$$F=\int_a^v \rho g x w(x) d x,$$[/tex]

where [tex]$g$[/tex] stands for the acceleration of gravity.

Solution. Pick a point [tex]$x \in[a, b]$[/tex] and consider a horizontal section of the plate through [tex]$x$.[/tex]

Suppose this section defines a thin rectangle of height [tex]$\Delta x$[/tex] and width [tex]$w(x)$[/tex]whose area is [tex]$w(x) \Delta x$[/tex]. The pressure on this thin rectangle is then [tex]$\rho g x$[/tex], and therefore the hydrostatic force is given by

[tex]$$F=P A=\rho g x w(x) \Delta x$$[/tex]

The total force is then approximated by adding over different horizontal sections:

Taking the[tex]limit Delta x 0 yields[/tex]

[tex]F=\int_a^b \rho g x w(x) d x .$$[/tex]

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The gravitational force of attraction between the satellite and the moon is 1.44 x 10^22 N.

To calculate the gravitational force of attraction between the satellite and the Ganymede moon, you can use the formula:

where F is the gravitational force, G is the gravitational constant (which is approximately 6.67 x 10^-11 N*m^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between them.

Plugging in the values provided, we get:

F = (6.67 x 10^-11 N*m^2/kg^2) * (200 kg) * (1.48 x 10^23 kg) / (300 km)^2

  = 1.44 x 10^22 N

This is the gravitational force of attraction between the satellite and the Ganymede. It is a very strong force, due to the large mass of the moon and the relatively close distance between the satellite and the moon.

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Two balls of the same mass are thrown towards a wall and collide with it moving with a speed of 5 m/s. Ball A hits the wall and rebounds with a speed of 4 m/s. Ball B hits the wall and stops. Assume that the collisions times are the same for each ball. Compared to ball B, ball A has a greater  velocity change a greater change, and  a greater  impact force.

The term "impact force" refers to a circumstance in which effort is expended to move a target object a certain distance. When two objects collide, it can be understood as the force that results. The coming together of two objects is known as an object collision. A lot happens to an object as a result of the impact force quickly. F serves as a symbol to represent it. The dimensions are specified by [M1L1T-2] and the Newton (N) unit of measurement is used. Its equation is the twice-taken time divided by the product of a body's mass and velocity. In other words, it is the proportion of kinetic energy that a body has to its total distance traveled.

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Force needed to push  the couch 4 m to the other side of the room is 70.8 N.

Kinetic friction is described as a force that acts among transferring surfaces. A body transferring at the surface reports a pressure within the contrary direction of its movement. The value of the pressure will depend on the coefficient of kinetic friction among the two materials.

Calculation:-

mass = 90 Kg

force = 600 N

coefficient of the friction is 0.6

F = μN

  = 0.6 × 90 × 9.8

   = 529.2 N

force needed = 600 - 529.2

                       = 70.8 N

F = ma

a = f/m

   = 70.8/90

   = 0.78 m/s²

Static friction is what maintains the box from transferring without being driven, and it need to be conquer with a sufficient opposing pressure before the field will pass. Kinetic friction (additionally known as dynamic friction) is the force that resists the relative motion of the surfaces as soon as they may be in motion.

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The smaller wavelength is 121.49515 nm and the larger wavelength is 121.4956866 nm.

It is the series of spectral lines which results in emission of UV radiations.

It happens when electron goes from n≥ 2 to n = 2

where, n = principle quantum number

The first line of Lyman series occur due to transition of electrons from n=1 to n=2

If we consider the '2p' level

The first transition of Lyman series

Energy:

-3.4015 eV ; n=2

-13.606eV ; n=1

ΔE = 4.5 * 10⁻⁵eV

Given

hc = 1239.8 eV(nm)

We know wavelength of radiation emitted is

\lambda = hc / (E₂-E₁)

If e⁻ transition occurs from n = 2P(3/2) to n = 1

E₂ - E₁ = -3.4015 eV + ΔE/2 + 13.606 eV

E₂ - E₁ = 10.2045225 eV

If e⁻ transition occurs from n = 2P(1/2) to n = 1

E₂ - E₁ = -3.4015 eV + ΔE/2 + 13.606 eV

E₂ - E₁ = 10.2044775 eV

Smaller value of wavelength = hc/E₂-E₁ = 1239.8/10.2045225 = 121.49515 nm

Larger value of wavelength = hc/E₂-E₁ = 1239.8 / 10.2044775 = 121.4956866 nm

Therefore the smaller wavelength is 121.49515 nm and the larger wavelength is 121.4956866 nm.

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a. Spring constant which has a maximum mass velocity of 25.0 cm/s and a period of 0.450 s = 17.49 N/m.

b. The amplitude of the motion of the spring = 0.0179 m.

c. Frequency of oscillation of the spring = 2.22 Hz.

Briefly, angular velocity is the angular speed accompanied by the direction. The unit of angular speed is rad/s or rad/minute or rad/hour.

Some of the equations that are often used are:

ω = [tex]\sqrt{\frac{k}{m}}[/tex]

ω = 2π/T

ω = angular velocity (rad/second)

k =  the spring constant

m = mass of the object

f = frequency (rev/second)

T = period (second)

The question is incomplete, it should be:

Find the

a. constant of the spring?

b. amplitude of the motion?

c. frequency of oscillation?

We have,

Mass of the object = 90.0 g

The maximum speed = 25.0 m/s

The period = 0.450 s

Determine the angular velocity first,

ω = 2π/T

= 2π/0.450

= 4.44 π rad/s

So,

a. Spring constant:

ω = [tex]\sqrt{\frac{k}{m}}[/tex]

k = ω²m

= (4.44 π rad/s)² (0.09)

= 17.49 N/m.

b. The amplitude:

vm = (xm) (ω)

So, xm = vm/ω

= 0.25/4.44 π

= 0.0179 m

c. The frequency:

f = 1/T

= 1/0.450

= 2.22 Hz.

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Form the given annual revenue and expenses the payback period of the new equipment is closest to 4 years .

What is Payback Period ?

Payback Period is defined as amount of time the company will have to wait before it recovers its investment.

the net annual cash flow can be calculated using the formula .

Net annual cash flow = (Net income) + (Non-cash items (i.e. depreciation))

From the table we get , net income = $60000

depreciation = $30000

So ,

Annual Cash Flow = 60000 + 30000 = $90000

We know that , Payback period is = (Initial investment)/(Annual cash flow)

= 365000/90000

= 4.055555 years

≈ 4 years .

Therefore , The payback period of the new equipment is closest to 4 years .

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The period of oscillation T of the scale is T = 0.37 sec .

In the question ,

it is given that ,

weight of the Italian ham (m₁) = 0.300 Kg = 0.3 Kg

weight of the slices of ham are (m₂) = 0.400 kg = 0.4 Kg

the force constant of the vertical spring is(k) = 200 N/m .

Let oscillation period be = T ,

the plates make a totally inelastic collision ,

We know that , In inelastic collision, momentum is conserved but the kinetic energy is not conserved.

So , when the slice of ham land on the plate, then the kinetic energy of system equal to maximum potential energy of spring.

that means , T = 2π√(m₁ + m₂)/k

Substituting the values ,

we get ,

T = 2π√(0.3 + 0.4)/200

Simplifying further ,

we get ,

T = 0.37 seconds .

Therefore , If the collision is inelastic then the Period of oscillation is 0.37 s .

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More than 1 billion is a credible estimate of the number of habitable planets, or NHPs, in our galaxy based on current scientific knowledge.

Out of the eight planets, three (Venus, Earth, and Mars) may be able to support life. One in five planets outside of our Solar System are thought to be capable of supporting life, according to recent findings of extrasolar planets: Planetary lifespan on average. Scientists estimate that the closest such planet may be 12 light-years away. There have been discovered 59 possible inhabited exoplanets as of June 2021. On K2-18b, an estimated 110 light years away super-Earth that may be habitable, water vapor has been found. The exoplanet was previously discovered by NASA's Kepler satellite in 2015, but data processing has uncovered new information that has never been seen on a super-Earth.

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The spring constant k is (1/k₁ + 1/k₂ + 1/k₃)⁻¹.

The effective spring constant k of the two-spring system will be equal to (1/k₁ + 1/k₂)⁻¹, while the spring constant k′ of the three-spring system will be equal to (1/k₁ + 1/k₂ + 1/k₃)⁻¹.

Since only one force F acts, the force on spring with spring constant k₁ is F = k₁x₁ where x₁ is its extension

the force on spring with spring constant k₂ is F = k₂x₂ where x₁ is its extension

Let F = kx be the force on the equivalent spring with spring constant k

We must consider the variable x as the extension of each spring.

The total extension , x = x₁ + x₂

x = F/k = F/k₁ + F/k₂

1/k = 1/k₁ + 1/k₂

k = (1/k₁ + 1/k₂)⁻¹

B

The force on spring with spring constant k₃ is F = k₃x₃ where x₃ is its extension

Let F = kx be the force on the equivalent spring with spring constant k and extension x.

The total extension , x = x₁ + x₂ + x₃

x = F/k = F/k₁ + F/k₂ + F/k₃

1/k = 1/k₁ + 1/k₂ + 1/k₃

k = (1/k₁ + 1/k₂ + 1/k₃)⁻¹

Therefore, the value of spring constant k is (1/k₁ + 1/k₂ + 1/k₃)⁻¹.

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[NOTE: THIS IS AN INCOMPLETE QUESTION. THE COMPLETE QUESTION IS: Consider two massless springs connected in series. Spring 1 has a spring constant k1, and spring 2 has a spring constant k2. A constant force of magnitude F is being applied to the right. When the two springs are connected in this way, they form a system equivalent to a single spring of spring constant k.

(A) What is the effective spring constant k of the two-spring system? Express the effective spring constant in terms of k1 and k2.

(B) Now consider three springs set up in series as shown. (Figure 2) The spring constants are k1, k2, and k3, and the force acting to the right again has magnitude F. Find the spring constant k′ of the three-spring system. Express your answer in terms of k1, k2, and k3.]

Answer:

Explanation:

1) Conduction - 100% (C)

2) Convection can take place in vacuum is incorrect - 100% (A)

3) Remains same - 100% (D)

Considering the Boyle's law, if the pressure is increased to 1.80 atm, the gas will ocuppy a volume of 11.04 L.

Boyle's law establishes the relationship between the pressure and the volume of a gas when the temperature is constant.

Boyle's law states that the pressure of a gas in a closed container is inversely proportional to the volume of the container, when the temperature is constant: if the pressure increases, the volume decreases, while if the pressure decreases, the volume increases.

Mathematically, Boyle's law states that if the amount of gas and the temperature remain constant, the product of the pressure and the volume always has the same value:

P× V= k

where:

Considering the initial state 1 and the final state 2, it is fulfilled:

P₁× V₁= P₂× V₂

In this case, you know:

Replacing in Boyle's law:

737 torr× 20.5 L= 1368 torr× V₂

Solving:

(737 torr× 20.5 L)÷ 1368 torr= V₂

11.04 L= V₂

Finally, the new volume is 11.04 L.

Learn more about Boyle's law:

brainly.com/question/4147359

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