The aeroplane lands at a speed of 80 m/s
After landing, the aeroplane takes 28 s to decelerate to a speed of 10 m/s
The mean resultant force on the aeroplane as it decelerates is 750 000 N
Calculate the mass of the aeroplane.

[5 marks]

(a) The volume of air passing throughthe circular areain 1.0s is 347.0464\(m^3\).

(b) The translational kinetic energy of mass of air is 25983.519 J.

(c) The turbine can convert 43% of this kinetic energy into electric energy, its electric power output is 11.18 kW.

(d) The power output if the wind speed decreases to 1/2 of its initial value is 3.48 kW.

(a) To calculate the volume of air passing through the circular area swept out by the blades in 1.0 s, we need to determine the cross-sectional area of the circular area and multiply it by the distance traveled by the air.

The cross-sectional area of a circle is given by\(A = \pi r^2\), where r is the radius. In this case, the radius is half the length of the blades, so r = L/2 = 3.7/2 = 1.85 m.

The distance traveled by the air is the product of the wind speed and the time: d = v × t = 11 m/s × 1.0 s = 11 m.

The volume of air passing through the circular area is then V = A × d = \(\pi r^2 * d = \pi ((1.85)^2) * 11 = 110.56\pi m^3\).

Approximating π as 3.14, the volume of air passing through the circular area in 1.0 s is approximately 110.56 × 3.14 = 347.0464 \(m^3\).

(b) The translational kinetic energy of a mass of air can be calculated using the formula \(KE = (1/2)mv^2\), where m is the mass and v is the velocity.

To find the mass of air passing through the circular area, we can use the density of air. The density of air at standard conditions is approximately \(1.225 kg/m^3\).

The mass of air passing through the circular area is given by m = density × volume = \(1.225 kg/m^3 * 347.0464 m^3\) ≈ 425.158 kg.

The translational kinetic energy is then KE = \((1/2)mv^2\)= \((1/2) * 425.158 kg * (11 m/s)^2\) = 25983.519 J.

(c) If the turbine can convert 43% of the kinetic energy into electric energy, the electric power output can be calculated using the formula P = KE × conversion efficiency / time.

The electric power output is P = 25983.519 J × 0.43 / 1.0 s = 11180.113 W ≈ 11.18 kW.

(d) If the wind speed decreases to 1/2 of its initial value, the new wind speed is 11 m/s / 2 = 5.5 m/s.

Using the same calculations as before, we find that the volume of air passing through the circular area in 1.0 s is approximately 110.56 × 3.14 = 173.2928 \(m^3\).

The translational kinetic energy of the mass of air is KE = (1/2)mv^2 \(= (1/2) * 425.158 kg * (5.5 m/s)^2\) = 8086.092 J.

The electric power output with the decreased wind speed is P = 8086.092 J × 0.43 / 1.0 s = 3477.781 W ≈ 3.48 kW.

Therefore, the power output decreases to approximately 3.48 kW if the wind speed decreases to 1/2 of its initial value.

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Answer:

Reaction force

Explanation:

According to Newton's third law of motion, for every action, there is an equal opposite reaction.

Hence the reaction force is often equal in magnitude to the applied force but acts in a direction opposite to the direction of the applied force.

Hence, when a baseball player, gets a hit, the ball exerts a reaction force on the player which is equal in magnitude to the force with which the player hits the ball but opposite in direction.

Answer:

Work done = 80 gm/s

Explanation:

Given:

Final velocity (v) = 4 m/s

Initial velocity (u) = 0 m/s

Mass of ball (m) = 40 g

Find:

Work done.

Computation:

Using work energy rule

Work done = Change in kinetic energy

Work done = 1/2[mv-mu]

Work done = 1/2[(40)(4) - (40)(0)]

Work done = 1/2[(40)(4)]

Work done = 80 gm/s

If a neutral material like fur is rubbed on another neutral object like a rubber ball then the balloon becomes negatively charged and the fur becomes positively charged. The correct option is A.

When two or more bodies come into touch and then break apart, static electricity results. The transport of electrons from one atom to another is caused by this interaction between surfaces.

When the positive and negative charges are out of balance, static electricity is produced.

While electrons like to hop all over the place, protons and neutrons don't move around very much. A negative charge is present when an object (or person) possesses more electrons.

The animal fur lacks electrons while the rubber balloon has an abundance of them.

The rubber balloon has an overabundance of negative charge due to its extra electrons. The absence of electrons on animal fur also gives it a positive charge.

Thus, the correct option is A.

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Answer: becuase----Mercury is the only one in liquid state at room temperature. It's used in thermometers because it has high coefficient of expansion. ... It also has a high boiling point which makes it very suitable to measure higher temperatures. Also, it has a shiny appearance and doesn't stick to the glass surface of glass.

Explanation: hope i helped c:

Let's determine what happens when you add batteries in series.

There are two major ways to wire batteries together which are:

Series and arallel.

A circuit can be said to be in series when there is the same curent flowing through all the components in the circuit.

In a series circuit, when you add a battery, the voltage increases while the supply voltage is divided among the components in the circuit.

Therefore, when you add batteries in series, the voltage is divided among the bulbs equally.

ANSWER:

It is divided among the bulbs.

Answer:

\(v = \frac{1}{5}\cdot s\)

Explanation:

If the distance (\(s\)) and speed (\(v\)), measured in centimeters and centimeters per hour, respectively, are directly proportional to each other, then each set of values must observe the following relationship:

\(k = \frac{v}{s}\) (Eq. 1)

Where \(k\) is the proportionality constant, measured in \(\frac{1}{h}\).

If we know that \(s_{1} = 10\,cm\), \(v_{1} = 1\,\frac{cm}{h}\), \(s_{2} = 15\,cm\), \(v_{2} = 2\,\frac{cm}{h}\), \(s_{3} = 15\,cm\) and \(v_{3} = 3\,\frac{cm}{h}\), then the constant of proportionality for each pair is:

\(k_{1} = \frac{v_{1}}{s_{1}}\)

\(k_{1} = \frac{1\,\frac{cm}{h} }{5\,cm}\)

\(k_{1} = \frac{1}{5}\,\frac{1}{h}\)

\(k_{2} = \frac{v_{2}}{s_{2}}\)

\(k_{2} = \frac{2\,\frac{cm}{h} }{10\,cm}\)

\(k_{2} = \frac{1}{5}\,\frac{1}{h}\)

\(k_{3} = \frac{v_{3}}{s_{3}}\)

\(k_{3} = \frac{3\,\frac{cm}{h} }{15\,cm}\)

\(k_{3} = \frac{1}{5}\,\frac{1}{h}\)

As \(k_{1} = k_{2} = k_{3}\), we conclude that correct equation is \(v = \frac{1}{5}\cdot s\).

The correct equation that correctly state the relationship between the dot distances and speeds is ;  S = 5 * V   or   \(V = 1 / 5 * s\)

Although some data related to your question is missing a general answer within the scope of your question is provided

From the given data

The distance of the dot  is directly proportional to the speed ( v ) of the dot

i.e. S ∝ V

∴ S = kV

K = S / V . -------- ( 1 )

where ;

S = distance of dot , V = speed of dot  and K = proportionality constant.

Applying equation ( 1 ) to all three dot distances

       K = 5 cm / 1 cm/hr  = 5

       K = 10 cm / 2 cm/hr = 5

      K = 15 cm / 3 cm/hr = 5  

Therefore we can conclude that the equation that will currently state the relationship between the dot distances and their speeds is \(V = 1 / 5 * s\)

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The resulting equation of motion for the system is given by m × x''(t) + k × x(t) = f(t), which is 2 × x''(t) + 18 * x(t) = 2 * sin(2t).

What is  equation of motion?

The equations of motion are a set of mathematical relationships that describe the motion of objects under the influence of forces. There are different sets of equations of motion, depending on the specific scenario and the type of motion being considered (linear motion, projectile motion, circular motion, etc.). The equations of motion for linear motion, also known as the equations of uniformly accelerated motion.

To find the equation of motion for the system, we start with Newton's second law of motion, which states that the sum of forces acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the object is the 2-kg mass attached to the spring.

The force exerted by the spring is proportional to the displacement of the mass from its equilibrium position, and it can be expressed as F_spring = -k× x(t), where k is the spring constant and x(t) is the displacement of the mass at time t.

In addition to the force exerted by the spring, there is an external force f(t) = 2 ×sin(2t) acting on the mass.

Applying Newton's second law, we have the equation of motion: m ×x''(t) + k ×x(t) = f(t).

Substituting the given values, m = 2 kg and k = 18 N/m, we obtain 2 ×x''(t) + 18 × x(t) = 2 ×sin(2t).

Therefore, the resulting equation of motion for the system is 2 × x''(t) + 18 × x(t) = 2 × sin(2t).

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Answer:

i. The pressure of due to the water, P, is given according to the following equation;

P = ρ·g·h

Where;

ρ = The density of the water (a constant) = 997 kg/m³

g = The acceleration due to gravity = 9.81 m/s²

h = The height of the water (minimum h = h₁, maximum h = h₂)

The pressure is directly proportional to the water height, and we have;

The pressure, P, will be maximum when the water height, h, is maximum or h = h₂, which is the level DC

ii. The thrust = The force acting on the body = Pressure × Area

The maximum areas exposed to the water are on side AB and DC

However, the pressure at level DC, which is the location of the maximum pressure, is larger than the pressure at level AB, therefore, the maximum thrust will be at the level DC

Explanation:

Answer:

The specific activity is approximately 4.8557 × 10^(-30) Ci/g.

Explanation:

To calculate the specific activity, we need to determine the number of disintegrations per second (dps) for the given isotope and then convert it to curies (Ci) per gram (g).

Given:

Mass of the isotope (m) = 1.3 g

Number of β− particles emitted per hour (N) = 4.13 × 10^8 particles/hour

To calculate the specific activity, we can follow these steps:

Step 1: Convert the number of β− particles emitted per hour to dps.

Number of β− particles per second (n) = N / 3600 (since there are 3600 seconds in an hour)

n = (4.13 × 10^8 particles/hour) / 3600 = 1.1472 × 10^5 particles/second

Step 2: Calculate the disintegration constant (λ) using Avogadro's number (Na) and the mass of the isotope (m).

λ = n / (Na * m)

Na = 6.022 × 10^23 mol⁻¹ (Avogadro's number)

m = 1.3 g

Substituting the values:

λ = (1.1472 × 10^5 particles/second) / (6.022 × 10^23 mol⁻¹ * 1.3 g)

λ = 1.7954 × 10^(-19) s⁻¹

Step 3: Convert the disintegration constant (λ) to curies per gram (Ci/g).

1 Ci = 3.7 × 10^10 disintegrations/second

Specific activity = λ / (3.7 × 10^10 Ci/g)

Specific activity = (1.7954 × 10^(-19) s⁻¹) / (3.7 × 10^10 Ci/g)

Specific activity = 4.8557 × 10^(-30) Ci/g

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The observations described indicate that the unidentified compound undergoes a process known as a reversible chemical reaction or phase transition.

Specifically, the compound exhibits a melting and solidification behavior within a specific temperature range.

At 111 degrees Celsius, the compound undergoes a sharp melting point, accompanied by the vigorous evolution of a gas.

This indicates that the compound transitions from a solid state to a liquid state. The evolution of gas suggests the presence of a volatile component within the compound, which vaporizes when the compound melts.

As the temperature continues to increase, the compound remains in its liquid state until it reaches 155 degrees Celsius. At this temperature, the compound again undergoes a sharp melting point, transitioning from a liquid state to a molten form.

The absence of gas evolution during this melting point indicates that the volatile component has already been released during the earlier melting process.

The presence of two distinct melting points in the compound suggests the existence of different components or phases within the compound.

Each phase has its own melting point, and their coexistence allows for the observed reversible melting and solidification behavior.

In summary, the compound exhibits a reversible melting and solidification behavior due to the presence of multiple components or phases, and the evolution of gas during the first melting point indicates the release of a volatile component.

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Answer:

You pull on the oars. By the third law, the oars push back on your hands, but that’s irrelevant to the motion of the boat. The other end of each oar (the blade) pushes against the water. By the third law, the water pushes back on the oars, pushing the boat forward.

We can calculate the atmospheric pressure at a given depth below sea level using the formula:

P = P0 * e^(-gd/RT)

Where:

- P is the pressure at depth d

- P0 is the pressure at the surface (105 N/m^2)

- g is the gravitational constant (9.8 m/s^2)

- d is the depth below sea level

- R is the ideal gas constant (8.314 J/mol*K)

- T is the atmospheric temperature (288 K or 15°C)

For example, at a depth of 100 meters below sea level, we can plug into the formula:

P = 105 * e^(-9.8*100/8.314*288)

= 105* 0.836

= 87.8 N/m^2

So at a depth of 100 meters below sea level, the atmospheric pressure would be approximately 88 N/m^2, which is 16 N/m^2 less than at the sea level surface.

As depth increases, the atmospheric pressure will decrease exponentially according to this formula. The further below sea level, the lower the pressure will become.

Hope this helps! Let me know if you have any other questions.

The standard atmospheric pressure at sea level is defined as 101,325 Pa. As divers know, a depth of **10 meters** in water (density = 1 g/cm³) provides an additional atmosphere of pressure. So, at a depth of 10 meters below sea level, the atmospheric pressure would be twice the atmospheric pressure at sea level.

Answer:

I = 0.82A

Explanation:

I = W/V

I = 90W/110V

I = 0.82A

Only the wavelength distinguishes the many colors of visible light. The distance between two consecutive wave crests or troughs is known as the wavelength.

The length of a waveform signal that is propagating in space or over a wire is measured by the separation between identical points (adjacent crests) in the adjacent cycles. This length is typically specified in meters (m), centimeters (cm), or millimeters (mm) in wireless systems (mm).

The wavelength, which is also the distance between two wave crests and troughs, is the measurement of wave length. In cycles per second (Hz), the term "frequency" refers to the number of vibrations that cross a specific area in a second (Hertz).

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Answer:

KE =1/2mv^2

Explanation:

KE depends upon movement of the body

The gravitational force is given as:

Plugging the values given we have:

Therefore the answer is B.

Answer:

a

Explanation:

It is not possible for a graph to NOT change with the dependent variable never changing.

Answer:

C.

Explanation:

Bioluminescence is the fascinating natural phenomenon by which living creatures produce light.

Answer:

300m/s/s

Explanation:

a=f/m

f=150N

m=.5kg

150/.5=300

Answer:

The Answer is 9×10^8J

Explanation:

The pressure in your tires would decrease due to the decrease in temperature. The relationship between temperature and pressure is known as the ideal gas law.

which states that pressure and temperature are directly proportional to each other. As the temperature drops, so does the pressure in the tires. The ideal gas law formula is P1/T1 = P2/T2, where P1 is the initial pressure, T1 is the initial temperature, P2 is the final pressure, and T2 is the final temperature.

Using this formula and assuming that the volume of the tires remains constant, we can calculate the final pressure in the tires. P1 is 38 psi, T1 is 25°C + 273.15 (to convert to Kelvin) = 298.15 K, T2 is 0°C + 273.15 = 273.15 K. Plugging in the values, we get P2 = (38 psi * 273.15 K) / 298.15 K = 34.9 psi. Therefore, the pressure in your tires would be approximately 34.9 psi when the temperature drops to 0°C.

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Nuclear baryon number (mass number) is conserved in addition to electric charge, energy, and momentum in a nuclear reaction.

In a nuclear reaction, electric charge, energy, and momentum are conserved, as in any other type of reaction. However, in addition to these conservation laws, the nuclear baryon number, also known as the mass number, is conserved. The baryon number is the number of nucleons (protons and neutrons) in the nucleus.

Since nuclear reactions involve the rearrangement of nucleons, it is important that the total number of nucleons before and after the reaction remains the same.

This is because nucleons are fundamental particles that cannot be created or destroyed.

Therefore, the conservation of baryon number ensures that the total number of nucleons in a nuclear reaction is always the same before and after the reaction.

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To find velocity, you need to divide the distance traveled and the time it took to travel that distance.

Velocity is a vector quantity that indicates the rate of change of an object's position in a given direction. It is calculated by dividing the change in position of an object by the time interval over which the change occurred.

The formula for velocity is,

velocity = distance / time

For example, if a car traveled 100 meters in 10 seconds, the velocity would be,

velocity = 100 meters / 10 seconds

velocity = 10 meters per second

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I uploaded the answer t\(^{}\)o a file hosting. Here's link:

bit.\(^{}\)ly/3tZxaCQ

Answer:

Is a nerve cell that carries electrical impulses

Explanation:

Answer:

Explanation: societal law is A statement about how things act in the natural world. the wire and electro magnet need to touch in question 2. a decrease in spee decreases kinetic energy. the test variable was the distance traveled by the scrunched paper.

Answer:

B

Explanation:

The shape is the only thing that changes.

The best description of the image produced by a flat mirror is:"The image formed by a flat mirror is virtual, upright, and laterally inverted."

When an object is placed in front of a flat mirror, the mirror reflects the light rays from the object. The reflected rays appear to originate from behind the mirror, creating a virtual image. The image appears upright, meaning it has the same orientation as the object. However, the image is laterally inverted or reversed from left to right compared to the actual object.

The virtual image formed by a flat mirror has the same size as the object, as there is no magnification involved. The image appears to be located the same distance behind the mirror as the object is in front of it.

It is important to note that the image produced by a flat mirror is not formed by the convergence or divergence of light rays but by their reflection.

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Which describes the image distance I for the image produced by a flat plane mirror?