Please help me in this question

To resolve the star-planet system at a distance of 4 light-years, a telescope on Earth would need an aperture with a minimum diameter of 55.88 mm.

In optical microscopy, the Rayleigh criterion is frequently used to estimate the resolution of the microscope. The resolution limit imposed by this criterion has long been regarded as a roadblock to using an optical microscope to study biological phenomena at the nanoscale.

We can use the Rayleigh criterion,

θ = 1.22 λ / D

θ = angular resolution

λ = wavelength of light

D = diameter of the telescope's aperture

θ = arctan (r / d)

r = radius of the planet's orbit

d = distance to the star

Now, we use the given values,

r = 149.6×106 km = 149.6×109 m

d = 4 × 9.461×1015 m = 3.7844×1016 m

λ = 550 nm = 550×10-9 m

θ = arctan (r / d)

   =arctan (149.6×109 / 3.7844×1016) = 0.000012 radians

we can use the Rayleigh criterion,

θ = 1.22 λ / D

D = 1.22 λ / θ

D = 1.22 × 550×10-9 / 0.000012

D = 55.88 mm

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Answer:A

Explanation:

Isotopes are members of a family of an element that all have the same number of protons but different numbers of neutrons. The number of protons in a nucleus determines the element's atomic number on the Periodic Table.

The top surface of the oil on that side of the tube is 0.6 times higher than the surface of the water on the other side of the tube.

The principle of hydrostatics, also known as Pascal's principle, states that when an external pressure is applied to a fluid in a container, that pressure is transmitted uniformly in all directions within the fluid, regardless of the shape or volume of the container. In other words, the pressure applied to a confined fluid will be distributed evenly throughout the fluid and will not change in magnitude at any point within the fluid. This principle is important in a number of applications, such as hydraulic systems, which use fluids to transmit force and pressure from one point to another. It is also used to explain how liquids exert pressure on the walls of their container and how objects can float or sink in fluids.

We can use the principles of hydrostatics to solve this problem. Let's call the height difference between the two water surfaces h. We can assume that the oil completely covers the water on one side of the tube and does not mix with it, so the oil and water form two separate liquid columns with a common interface. Let's call the height difference between the oil and water surfaces on the same side of the tube H.

The pressure at any given point in a fluid depends only on the depth of that point below the surface of the fluid and the density of the fluid. Since the two water columns are at the same height, they experience the same pressure from the atmosphere. Similarly, the two oil columns experience the same pressure from the atmosphere.

Now consider a point on the interface between the oil and water on the same side of the tube. This point is at a depth of h+H below the water surface on the other side of the tube, so the pressure at this point is greater than atmospheric pressure by an amount equal to the product of the density of water, the acceleration due to gravity, and the total depth (h+H):

P = Patm + ρwatergh

where P is the pressure at the interface, Patm is atmospheric pressure, ρwater is the density of water, g is the acceleration due to gravity, and h+H is the total depth.

Similarly, the pressure at this point is less than atmospheric pressure by an amount equal to the product of the density of oil, the acceleration due to gravity, and the depth of the oil column (H):

P = Patm - ρoilgH

Since the interface between the oil and water is at the same pressure, we can equate these two expressions for P:

Patm + ρwatergh = Patm - ρoilgH

Solving for H, we get:

H = h(ρwater/ρoil)

Substituting the given values, we get:

H = 0.6h

Therefore, the top surface of the oil on that side of the tube is 0.6 times higher than the surface of the water on the other side of the tube.

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Both the object's speed and mass affect how much kinetic energy it contains. Motional energy is produced while the roller coaster descends. The roller coaster's bottom of the track position is where the most kinetic energy is produced. Kinetic energy changes to potential energy when it starts to rise.

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a. We can actually see here that the girl have kinetic energy which is respect to the escalator.

b. The kinetic energy does not depend on the chosen reference.

Kinetic energy is a form of energy that an object possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. Kinetic energy is a scalar quantity, meaning it only has magnitude and no direction. The formula for calculating kinetic energy is:

KE = 1/2 × m × v²

Where KE is the kinetic energy, m is the mass of the object, and v is its velocity.

The concept of kinetic energy was first introduced by the French mathematician Gaspard-Gustave de Coriolis in 1829. It was later developed by other scientists such as James Prescott Joule and Hermann von Helmholtz.

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Aproximately 1.09 m/s was the locust's first speed.

In engineering mechanics, vectors are used to express values with both a magnitude and a direction. For analysis, vector representations of a variety of engineering quantities—including forces, displacements, velocities, and accelerations—are required.

Δy = vsin(θ)t - 0.5gt²

0 = v*sin(55°)t - 0.5(-9.81 m/s²)*t²

t = 2vsin(55°)/g

Now, we can use the horizontal motion of the locust to find the initial velocity v. The horizontal distance traveled by the locust is given by:

Δx = v*cos(55°)*t

Substituting the expression for t that we just found:

0.750 m = vcos(55°)2vsin(55°)/g

Solving for v:

v = √(0.750 mg/(2sin(55°)*cos(55°)))

v ≈ 1.09 m/s

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C. 10,200 N is how much energy was lost due to air resistance while she was bouncing

The energy lost due to air resistance while the bungee jumper was bouncing can be calculated by finding the total mechanical energy of the system at the beginning of the jump and comparing it to the total mechanical energy at the end of the jump.

At the beginning of the jump, the total mechanical energy is given by:

Ei = mgh

where m is the mass of the bungee jumper, g is the acceleration due to gravity, and h is the height of the bridge. Therefore, at the beginning of the jump:

50 x 30 x 10 - 1/2 x 30^2 x 10

= 15000 - 4500

= 10,200 N

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a.) The evidence for planets orbiting the Sun might be :

b.  Evidence for potentially habitable planets might come in the form of

A planet is described as a celestial body that is in orbit around the Sun, has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and  has cleared the neighborhood around its orbit.

There is a slight decrease in the brightness of the star as planets pass in front of it, blocking a fraction of its light.

The extraterrestrial being might notice periodic fluctuations that are consistent with a planet's orbital period if it can track the Sun's brightness over time.

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Answer:

[tex]80\; {\rm m\cdot s^{-1}}[/tex].

Explanation:

The frequency [tex]f[/tex] of a wave is the number of cycles completed in unit time ([tex]1\; {\rm s}[/tex] in this example.) In this question, [tex]f = 40\; {\rm s^{-1}}[/tex] ([tex]1\; {\rm Hz} = 1\; {\rm s^{-1}}[/tex]) means that the wave would complete [tex]40[/tex] cycles in every [tex]1\; {\rm s}[/tex].

The wavelength [tex]\lambda[/tex] of a wave is the distance the wave travels in each cycle. It is given that [tex]\lambda = 2\; {\rm m}[/tex].

The goal is to find the wave speed, which is the distance that this wave travels in unit time ([tex]1\; {\rm s}[/tex].)

In this question, it is given that [tex]\lambda = 2\; {\rm m}[/tex] and [tex]f = 40\; {\rm s^{-1}}[/tex]. Thus, this wave would travel a total of [tex]40\, (2\; {\rm m}) = 80\; {\rm m}[/tex] for the [tex]40[/tex] cycles completed in each unit time of [tex]1\; {\rm s}[/tex] ([tex]\lambda = 2\; {\rm m}[/tex] for each cycle.) The speed of this wave would be [tex]80\; {\rm m\cdot s^{-1}}[/tex].

Formally, the speed [tex]v[/tex] of this wave can be found by multiplying the wavelength [tex]\lambda[/tex] of this wave by its frequency [tex]f[/tex]:

[tex]\begin{aligned}v &= \lambda\, f \\ &= (2\; {\rm m})\, (40\; {\rm s^{-1}) \\ &= 80\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].

Answer:

A) P.E = 138.44 J

B) The velocity of swing at bottom, v = 3.33 m/s

C) The work done, W = -138.44 J

Explanation:

Given,

The mass of the child, m = 25 Kg

The length of the swing rope, L = 2.2 m

The angle of the swing to the vertical position, ∅ = 42°

A) The potential energy at the initial position ∅ = 42° is given by the relation

                               P.E = mgh joule

Considering h  = 0 for the vertical position

The h at ∅ = 42° is  h = L (1 - cos∅)

                              P.E = mgL (1 - cos∅)

Substituting the given values in the above equation

                              P.E = 25 x 9.8 x 2.2 (1 - cos42°)

                                     = 138.44 J

The potential energy for the child just as she is released, compared to the potential energy at the bottom of the swing is, P.E = 138.44 J

B) The velocity of the swing at the bottom.

At bottom of the swing the P.E is completely transformed into the K.E

                 ∴                 K.E = P.E

                                    1/2 mv² = 138.44

                                    1/2 x 25 x v² 138.44

                                           v² = 11.0752

                                            v = 3.33 m/s

The velocity of the swing at the bottom is, v = 3.33 m/s

C) The work done by the tension in the rope from initial position to the bottom

            Tension on string, T = Force acting on the swing, F

                           =

                           = - 2.2 x 25 x 9.8 [cos0 - cos 42°]

                           = - 138.44 J

The negative sign in the in energy is that the work done is towards the gravitational force of attraction.

The work done by the tension in the ropes as the child swings from the initial position to the bottom of the swing, W = - 138.44 J

According to the question the length of the river span of the bridge in meters is 853.3232 m.

Length is a physical quantity that measures the distance between two points. It is one of the fundamental units in the International System of Units (SI). It is usually measured in meters, although it can also be measured in other units such as centimeters, kilometers, feet, yards, miles, and so on.

The length of the river span of the bridge is 2799.0 ft. To convert this length to meters, we need to use a conversion factor. There are 0.3048 meters in one foot, so the conversion factor we will use is 1 ft
= 0.3048 m.

To convert 2799.0 ft to meters, we multiply by the conversion factor:
2799.0 ft * 0.3048 m/ft
= 853.3232 m

Therefore, the length of the river span of the bridge in meters is 853.3232 m.

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Protons, neutrons, and electrons are the three main subatomic particles that make up atoms.

An oxygen atom has 8 protons, 8 electrons, and its number of neutrons may vary depending on the isotope of oxygen. The more frequently encountered isotope of oxygen is oxygen-16, with 8 neutrons.

The element with 13 protons is aluminum (Al). To find the mass number, we add the number of protons and neutrons in the nucleus. Therefore, the mass number of this aluminum isotope would be 13 + 14 = 27.

If an atom has 7 electrons, it must be nitrogen (N), which has an atomic number of 7.

Number of neutrons = Mass number - Atomic number

Thus, we obtain the number of neutrons by the equation: 14 - 7 = 7

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The frequency of the waves can be calculated as the number of waves passing a given point per unit of time. In this case, the frequency is:

f = (number of waves) / (time)

f = 12 waves / 45 s

f = 0.267 Hz

The wavelength is the distance between two adjacent wave crests, which is given as 9.0 m in the problem.

The speed of the wave can be calculated using the formula:

v = f × λ

where v is the wave speed, f is the frequency, and λ is the wavelength.

Substituting the values given, we get:

v = 0.267 Hz × 9.0 m

v = 2.40 m/s

Therefore, the speed of the waves is 2.40 m/s (to two significant figures).

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The power being provided to the propeller 3.0 seconds after it starts rotating is approximately 21.8 MW and the moment of inertia of the propeller is approximately 0.55 kg⋅m².

In hydraulic systems, forces are transferred from one area to another inside an incompressible fluid, such as water or oil. Most aircraft's landing gear and braking systems are hydraulic. In order to function, pneumatic systems need a compressible fluid like air.

I = (τt²) / (2πΔθ)

Substituting the given values, we get:

I = (2.0×10³ N⋅m × (6.0 s)²) / (2π × (1000 rev/min) × (1 min/60 s) × 2π)

I ≈ 0.55 kg⋅m²

P = τω

ω = ω₀ + αt

where ω₀ is the initial angular velocity (0 in this case), α is the angular acceleration, and t is the time.

ω = 0 + (τ/I)t

ω = (2.0×10³ N⋅m) / (0.55 kg⋅m²) × (3.0 s)

ω ≈ 10,909 rad/s

P = (2.0×10³ N⋅m) × (10,909 rad/s)

P ≈ 2.18×10⁷ W

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Humans would need a breathable environment like that on Earth in the living section of a colony on Venus in order to survive. Nitrogen, oxygen, and trace amounts of other gases, such as carbon dioxide, make up the majority of the atmosphere on Earth.

The clouds are made of sulfuric acid, and the atmosphere is primarily carbon dioxide, the same gas that causes the greenhouse effect on Venus and Earth. And the heated, high-pressure carbon dioxide acts corrosively at the surface.

For instance, compared to Earth, which has 99% nitrogen and oxygen in its atmosphere, Venus and Mars both contain more than 98% carbon dioxide and nitrogen.

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An inductance of 0.0191 H (19.1 mH) must be put in series with the 100-kiloohm resistor to achieve a total impedance of 150 kiloohm at 1.0 MHz.

What is Induction?

Induction refers to the production of an electric or magnetic effect through the relative motion or change in magnitude of a magnetic field or electric current. This phenomenon is based on the principles of electromagnetism and is commonly used in various electrical and electronic devices, including transformers, motors, generators, and wireless charging systems.

The total impedance can be calculated using the following formula:

Z_total = sqrt([tex]R^{2}[/tex] X_[tex]L^{2}[/tex])

where R is the resistance (100 kiloohm) and X_L is the inductive reactance. We can rearrange this formula to solve for X_L:

At 1.0 MHz, the angular frequency is:

w = 2πf = 2π × 1.0 × [tex]10^{6}[/tex] = 6.28 × [tex]10^{6}[/tex]ad/s

The inductive reactance can be calculated using the following formula:

X_L = wL

where L is the inductance in henries. We can rearrange this formula to solve for L:

L = X_L / w

Now we can substitute the given values and solve for L:

X_L = sqrt((150 ×[tex]10^{3}[/tex]) - (100 ×[tex]10^{3}[/tex])) = 120 × [tex]10^{3}[/tex] ohm

L = X_L / w = 120 × [tex]10^{3}[/tex] ohm / 6.28 × [tex]10^{6}[/tex] rad/s = 0.0191 H

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The relationship between a sound wave's intensity and pressure amplitude (also known as pressure variation p) is. I is equal to (p) 2 2 v w, where is the thickness of the substance that the sound is contained in.

Describe a sound wave.

Hence, a sound wave is made up of periodically occurring compressions and compression and rarefaction, or areas of high and low pressure, that are travelling at a specific pace. In other words, it consists of a regular (i.e., oscillating or vibrating) change in pressure that takes place around the optimum pressure that is present at a specific time and location.

A sound wave is created by a speaker in what way?

A speaker creates a sound by vibrating a cone, which causes air molecules to vibrate. A speaker in Figure 17.2. 2 vibrates with a consistent frequency and amplitude, causing motions in the molecules of the surrounding air. The speaker transfers power to the air as it vibrates back and forth, primarily as thermal energy.

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Answer:

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To solve this problem, we can use the formula for heat transfer:

q = mcΔT

where q is the heat transferred, m is the mass of the object, c is its specific heat capacity, and ΔT is the change in temperature.

We know that the mass of the block is 0.35 kg and that its initial temperature is -27.5 ºC. We also know that the mass of water is 0.217 kg and that its initial temperature is 25.0 ºC.

When they come to equilibrium at 16.4 ºC, we can calculate how much heat was transferred from the water to the block:

q = mcΔT q = (0.217 kg)(4186 J/kg ºC)(25.0 ºC - 16.4 ºC) q = 1825 J

This amount of heat was transferred from the water to the block, so we can set it equal to the amount of heat absorbed by the block:

q = mcΔT 1825 J = (0.35 kg)c(16.4 ºC - (-27.5 ºC)) 1825 J = (0.35 kg)c(43.9 ºC) c = 148 J/kg ºC

Therefore, the specific heat capacity of the block is 148 J/kg ºC.

Explanation:

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Answer:

Explanation:

The frequency of the waves produced in the glass of water will depend on the frequency of the sound wave produced by the guitar string.

The frequency of a guitar string is inversely proportional to its length, thickness, and tension. Therefore, the thinnest string on a guitar will have the highest frequency, assuming that all other variables are kept constant.

Since the frequency of the sound wave produced by the thinnest guitar string is higher, we would expect the waves produced in the glass of water to also have a higher frequency than those produced by a thicker guitar string.

The two risk factors that can affect the ability of a child to learn in school is poor parenting and malnutrition.

A risk factor can be defined as any predisposing factor that can expose an individual to harm.

A risk factor that affects a child is an aspect of the child or environment that increases the probability of poor outcomes.

The two risk factors that can affect the ability of a child to learn in school include the following:

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The researcher did not find strong evidence to support the idea that job applicants with popular names are viewed more favorably than equally qualified applicants with less popular names.

It sounds like the researcher conducted an experiment to investigate whether job applicants with popular names are viewed more favorably than equally qualified applicants with less popular names.

Based on the information provided, the researcher found that the differences in the evaluations of the applicants by the two groups were not significant at the .001 level.

The factors that play an important role in the hiring process for a job:

(1) Qualifications and experience: Employers typically look for candidates who possess the necessary qualifications and experience for the job. This includes education, training, certifications, and work experience.

(2) Skills and abilities: Employers also consider a candidate's skills and abilities related to the job. These may include technical, interpersonal, communication, and problem-solving skills.

(3) Personal characteristics: Personal characteristics, such as motivation, work ethic, and adaptability, can also play a role in the hiring process. Employers may look for candidates who demonstrate a positive attitude, a willingness to learn, and the ability to work well with others.

(4) Fit with company culture: Companies may also consider whether a candidate fits with their company culture, values, and mission. This can include factors such as teamwork, creativity, and innovation.

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Mice that ate sunflower seeds gained an average of 2.1 grams that Raphael can determine from his experiment. Each group is given a different type of feed.

Grams (g) is a unit of measurement for mass in the International System of Units (SI). It is the base unit of mass in the SI, and is defined as being equal to the mass of a physical prototype, which is kept at the International Bureau of Weights and Measures. In practical terms, 1 gram is equal to 0.0352739619 ounces, or 0.00220462262 pounds. Grams are often used to measure the weight of food, medicines, and other small objects.

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The net force on particle q₁ is 9.22 × 10^-13 N, and it points to the left.

The net force on particle q₁ due to particles q2 and q3 can be found using Coulomb's law.

Coulomb's law states that the force between two charged particles is given as

F= k * (q₁ * q₂) / r^2

Since q₁ and q₂ have the same charge, the force between them is repulsive, i.e., it points to the left. Using Coulomb's law, we can find the magnitude of this force:

F₁₂ = k * (q₁ * q₂) / r₁₂^2

F₁₂ = (9 × 10^9 Nm^2/C^2) * (-2.35 × 10^-6 C)^2 / (0.100 m)^2

F₁₂ = -4.61 × 10^-13 N

Here,  the force between q₁ and q₂ points to the left, and its magnitude is 4.61 × 10^-13 N.

The  force between q₂ and q₃ also points to the left, and its magnitude is given as

F₂₃ = k * (q₂ * q₃) / r₂₃^2

F₂₃ = (9 × 10^9 Nm^2/C^2) * (-2.35 × 10^-6 C)^2 / (0.100 m)^2

F₂₃ = -4.61 × 10^-13 N

Here,  the force between q₂ and q₃ also points to the left, and its magnitude is 4.61 × 10^-13 N.

F_net = -F₁₂ - F₂₃

F_net = -(-4.61 × 10^-13 N) - (-4.61 × 10^-13 N)

F_net = 9.22 × 10^-13 N

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The temperature of the electric fire element is 18.3 K

We use the formula at:

P = σAT^4

where P=  power radiated,

A = surface area of the black body,

σ =Stefan-Boltzmann constant (5.67 × 10^-8 W/m^2K^4),

T = temperature in Kelvin.

P = 1500 W

The surface area of a cylinder is gotten by:

A = 2πrh + 2πr^2

A = 2π(0.04 m)(0.3 m) + 2π(0.04 m)^2

A = 0.0902 m^2

Substituting the values into the Stefan-Boltzmann law, we have:

1500 W = (5.67 × 10^-8 W/m^2K^4)(0.0902 m^2)T^4

T^4 = 4196.9

T = 18.3 K

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The value of the charge on each particle is [tex]1.05 x 10^-8 C[/tex].

Coulomb's law is a fundamental principle of electrostatics that describes the interaction between electric charges. It states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. We can use Coulomb's law to solve this problem. Mathematically,

[tex]F = k(q1q2)/r^2[/tex]

where F is the force of attraction or repulsion between the two charged particles,[tex]q1[/tex] and [tex]q2[/tex] are the magnitudes of the charges on the two particles, r is the distance between them, and k is Coulomb's constant, which has a value of [tex]9.0 x 10^9 Nm^2/C^2.[/tex]

In this problem, we know that the charges are equal and the distance between them is 10.0 cm. We also know that the force between them is 0.5 N. Therefore,

[tex]0.5 N = k(q^2)/(0.1 m)^2[/tex]

Solving for q, we get:

[tex]q = \sqrt{[(0.5 N)(0.1 m)^2/k]}[/tex]

[tex]q = \sqrt{(0.5 N)(0.01 m)/(9.0 x 10^9 Nm^2/C^2)}[/tex]

[tex]q = 1.05 x 10^-8 C[/tex]

Therefore, the value of the charge on each particle is [tex]1.05 x 10^-8 C.[/tex]

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part a.  the wavelength of this wave  is 26 cm

part b. The amplitude (A) of a wave is 9 cm

The wavelength (λ) of a wave is described as the distance between two consecutive points on the wave that are in phase.

In this scenario, the distance between two corresponding points on the wave will be equal to the horizontal distance from crest to trough, which is 26 cm.

Hence, the wavelength of the wave is: λ = 26 cm

The amplitude (A) of a wave is described as the maximum displacement of a particle from its rest position as the wave passes through it.

In this scenario, the vertical distance from crest to trough is 18 cm, which is equal to twice the amplitude.

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The time takes the kid to remain in the air is 0.735 s.

Time is the duration of an events. The s.i unit of time is seconds.

To calculate how long the kid will be in the air, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the time is 0.735 s.

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The force needed to lift the 1800 kg car with the small piston is 2,649 N or approximately 270 kg (since 1 kg is equal to 9.81 N).  

The hydraulic lift works based on Pascal's principle, which states that the pressure applied to a confined fluid is transmitted equally in all directions throughout the fluid.

Assuming there is no loss of energy due to friction or other factors, the force exerted on the small piston will be equal to the force exerted on the large piston. This can be expressed as:

F1/A1 = F2/A2

where F1 is the force exerted on the large piston, A1 is the area of the large piston, F2 is the force exerted on the small piston (which we want to find), and A2 is the area of the small piston.

We can rearrange this equation to solve for F2:

F2 = (F1/A1) x A2

Given that the area of the large piston is 100 cm², we can calculate the force exerted on the large piston by using the weight of the car and the gravitational acceleration:

F1 = m x g = 1800 kg x 9.81 m/s² = 17,658 N

Substituting the values into the equation, we get:

F2 = (17,658 N / 100 cm2) x 15 cm² = 2,649 N

Therefore, the force needed to lift the 1800 kg car with the small piston is 2,649 N or approximately 270 kg (since 1 kg is equal to 9.81 N).

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The mass of Brachiosaurus moves with a momentum of 134,054 kgm/s  and the velocity is 3.9 m/s, which is 34.37 kg.

The momentum is the product of mass and velocity. The momentum is the vector quantity and the unit of momentum is Kgm/s.

Momentum = mass × velocity

 mass    = momentum/velocity

momentum =  134,052 kgm / s

velocity = 3.9 m/s

mass = 134052 / 3.9

         = 34.37 kg

Thus, the mass of Brachiosaurus is 34.37 kg.

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