Jane, looking for Tarzan, is running at top speed (4.5 m/s) and grabs a vine hanging vertically from a tall tree in the jungle. How high can she swing upward?
Does the length of the vine affect your answer?

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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There is a flow of electrons from charged to uncharged whenever a charged capacitor is connected to an uncharged capacitor, and this flow continues until a steady state is reached. As a result, there is no further charge transfer and both capacitors are in equilibrium.

When we say a capacitor is uncharged, we imply that there are an equal amount of positively and negatively charged ions and electrons on each of its plates.

The capacitor's starting voltage is zero.

The capacitor's charge Q and voltage across it are both 0 before the switch is closed.

The charge has not had a chance to accumulate before the switch is closed.

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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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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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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.]

The ratio of intensities of the signal and the background noise for each device is 7943.2 and 316.2 respectively.

The signal-to-noise ratio (SNR) is a measure of the strength of the desired signal relative to the background noise. It is usually expressed in decibels (dB).

A higher SNR indicates a stronger signal relative to the background noise, and therefore a higher quality of sound. To find the ratio of intensities of the signal and the background noise for each device, you can use the formula:

Intensity ratio = 10^(SNR/10)

For the cassette player with an SNR of 62 dB, the intensity ratio would be:

Intensity ratio = 10^(62/10) = 316.2

This means that the intensity of the signal is 316.2 times stronger than the intensity of the background noise.

For the CD player with an SNR of 98 dB, the intensity ratio would be:

Intensity ratio = 10^(98/10) = 7943.2

This means that the intensity of the signal is 7943.2 times stronger than the intensity of the background noise. Therefore, the CD player has a much higher intensity ratio and a higher quality of sound compared to the cassette player.

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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 distinction in top among the pinnacle floor of glycerin and the pinnacle floor of ethyl alcohol is 0.0432 meter or 4.32 centimeter the difference in height between the top surface of glycerin and the top surface of alcohol is 4.32 centimeter.

Given the subsequent data:

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The magnitude and direction of the electric field at x = 3.5 cm is 85.75V/m and is towards the plate 1.

Given the electric potential in the space between two flat parallel plates 1 and 2 is (V) = 1270x^2

the perpendicular distance from plate 1 is = xm = 3.5cm

We know that changing electric field is given as :

E(x) = -dV/dx

By differentiating we get :

E(x) = -(d(1270x^2)/dx)

E(x) = - (2*1270*x)

E(x) = -2540x

Here given x = 3.5cm = 0.035m

Then E(x) = -2450*0.035 = -85.75V/m

Hence  the magnitude and direction of the electric field is 85.75V/m and is towards the plate 1

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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 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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The potential gradient along the wire is 0.208Vm⁻¹

We are given that,

Resistance of wire = R = 20Ω

Internal resistance = r = 18Ω

length of wire = L = 10m

E.M.F = ∈ =5V

Thus to find the value of potential gradient of the wire, we can use the equation,

i =  (∈)/(R+r)

i = 5v/ (20Ω +18Ω)

i = 0.104 A

Vr = iR =(0.104 A)(20Ω) =

Vr = 2.08 volt

Thus the potential gradient of the wire is given as,

potential gradient = V/L =  (2.08volt)/(10m)

potential gradient = 0.208Vm⁻¹

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Answer: To solve this problem, we can use the equations of static equilibrium to determine the forces acting on the particle P. In equilibrium, the sum of the forces and the sum of the moments must be zero.

Explanation:

(i) The normal component of the contact force on P is 0.58 N.

(ii) The frictional component of the contact force on P is 0.11 N.

(iii) The coefficient of friction between P and the plane is 0.19.

The forces operating on the particle P can be ascertained using the equations for static equilibrium. The total of the moments and the forces must be zero in an equilibrium state.

The contact force on P has a normal component of 0.58 N.

The 0.11 N frictional component of the contact force on P.

P and the plane experience 0.19 coefficient of friction.

Friction between two surfaces causes kinetic energy to be converted into thermal energy when they move in relation to one another (that is, it converts work to heat). The utilization of friction produced by rubbing pieces of wood together to start a fire serves as an example of how this attribute can have dramatic effects.

When a viscous fluid is agitated, for instance, kinetic energy is transformed into thermal energy. Wear, which can result in component damage or performance degradation

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In a black hole, the pull of gravity is so great that not even the most powerful electromagnetic waves can make their way out. According to general relativity, a black hole can arise if a massive object is so compact that it warps spacetime.

The event horizon is the threshold beyond which it is impossible to travel. According to general relativity, there are no locally observable features despite the fact that crossing them might drastically change the course of an object's life. A black hole is very similar to a perfect black body in that it does not reflect any light.

What's more, the same spectrum as a black body with a temperature inversely proportional to its mass is predicted by quantum field theory in curved spacetime for the radiation that event horizons generate. Stellar black holes have temperatures on the order of billionths of a Kelvin, making direct observations nearly impossible.

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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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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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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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Jupiter: largest planet Saturn: has the most conspicuous rings Uranus: has the most highly inclined rotation axis Neptune: has the medium-sized moon Triton in orbit

Jupiter is the largest planet in the Solar System, with a diameter of over 140,000 kilometers and a mass about 318 times that of Earth. It is the fifth planet from the Sun and is known for its strong magnetic field and large number of moons, including the four Galilean moons - Io, Europa, Ganymede, and Callisto - which were discovered by Galileo Galilei in the 17th century.

Saturn is the second-largest planet in the Solar System and is known for its beautiful and prominent ring system, which is composed of ice, rock, and dust particles. The rings are tilted relative to the planet's equator, and the width of the rings varies from about 10 meters to over 20,000 kilometers.

Uranus is the seventh planet from the Sun and is notable for its unusual orientation, with its axis of rotation tilted at an angle of about 98 degrees relative to its orbit around the Sun. This means that Uranus experiences extreme seasons, with each hemisphere experiencing about 42 years of daylight and darkness.

Neptune is the eighth and outermost planet in the Solar System and is known for its bright blue appearance and strong winds. It has a medium-sized moon called Triton, which orbits the planet in a retrograde direction (opposite to the planet's rotation). Triton is thought to be a Kuiper Belt object that was captured by Neptune's gravity and is the only large moon in the Solar System that orbits in this direction.

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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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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.

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When a paperweight and tray are placed together and put into a horizontal oscillating motion, the coefficient of static friction between them is 0.2

Given  frequency of motion (f) = 1.22 Hz.

the amplitude of the motion (A) =  5.00 x 10^-2 m

The coefficients of the normal force applied by the surface are determined as friction force.

Force of friction (Fr) = μ x normal force (F)

coefficient(μ) = F/Fr

we know that Fr = kx = mω^

2A anf F = mg

mω^

2A  = μmg

μ = ω^

2A/g  and ω = 2πf

μ = (2x3.14x1.22)^2 x 5x10^-2/9.8 = 0.2

Hence the coefficient = 0.2

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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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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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Maximum height could a person jump and land rigidly upright on both feet without breaking his legs: h = 0.30 m

Briefly:

Potential energy = m g h would be present in a jumper at height h, and as the jumper hits the ground, this potential energy will totally transform into kinetic energy. Now, the human can only absorb a maximum of 200 J of energy.

m = 67 kg

g = 9.8 m/s²

⇒ m g h = 200 J

⇒ h = 200 J / (67 kg × 9.8 m/s²) = 0.30 m

Therefore, a person can only fall from a height of 0.30 m safely and without breaking both of their legs.

In metabolic processes, lipids provide the most energy. On reduction, lipids turn into fatty acids. As a result, fat has a higher energy content than both glycogen and proteins together.

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Question:-

the maximum energy a bone can absorb without breaking is surprisingly small. for a healthy human of mass 67 kg , experimental data show that the leg bones can absorb about 200 j . part a from what maximum height could a person jump and land rigidly upright on both feet without breaking his legs?

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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Answer:

Explanation:

1) Conduction - 100% (C)

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

3) Remains same - 100% (D)

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 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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