State each of Newton's Laws of Motion and explain how each can be observed during the flight of a space craft, from liftoff until the craft enters space.

The reduction in the potential energy of the water is approximately 7.5 J.

option 1

We can use the principle of conservation of energy to determine the reduction in potential energy of the water.

Initially, the water in vessel A has a certain amount of potential energy due to its height above the bottom of the vessel. When the water flows through the tube and reaches vessel B, its height above the bottom of vessel B is lower than that of vessel A, which means that its potential energy has decreased.

The potential energy of the water in vessel A is given by:

PE_A = mgh_A

The mass of the water in vessel A is given by:

m = density x volume

volume = A x h_A

Substituting for m and simplifying, we get:

PE_A = density x A x h_A x g

Similarly, the potential energy of the water in vessel B is:

PE_B = density x A_B x h_B x g

At equilibrium, the height of the water in the two vessels will be the same, so we can set h_A = h_B = h.

Also, since the water is in equilibrium, the pressure at the bottom of both vessels must be the same. This means that the pressure difference between the top and bottom of the water column in vessel A (due to the weight of the water) must be balanced by the pressure difference between the top and bottom of the water column in vessel B.

The pressure difference in vessel A is:

P_A = density x g x h_A

and the pressure difference in vessel B is:

P_B = density x g x h_B

Since the pressure difference must be balanced, we have:

P_A - P_B = density x g x h_A - density x g x h_B = 0

which simplifies to:

h_A = h_B x A_B / A

Substituting for h_A and h_B in the expressions for PE_A and PE_B, we get:

PE_A = density x A x h x g

PE_B = density x A_B x h x g x A / A_B

The reduction in potential energy of the water is:

ΔPE = PE_A - PE_B = density x g x h x (A - A_B x A / A_B)

which simplifies to:

ΔPE = density x g x h x (A - A_B)

Substituting the given values, we get:

ΔPE = 1000 kg/m³ x 9.8 m/s² x 0.3 m x (50 cm² - 25 cm²)

Converting the area units to m², we get:

ΔPE = 1000 kg/m³ x 9.8 m/s² x 0.3 m x (0.005 m² - 0.0025 m²)

Simplifying, we get:

ΔPE = 7.4 J

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A telescope with a 40-inch primary lens has four times the light-gathering power compared to a telescope with a 20-inch lens. Space telescope data is important for studying celestial objects across the electromagnetic spectrum and provides comprehensive information. Telescopic data helps determine distances between objects through techniques like redshift measurement and the cosmic distance ladder.

The relative light-gathering power of a telescope is determined by the area of its primary lens or mirror. In this case, the telescope with the 40-inch primary lens has four times the light-gathering power compared to the telescope with the 20-inch lens. This is because the area of the 40-inch lens is four times larger than the area of the 20-inch lens.

Space telescope data is important across the electromagnetic spectrum because it allows astronomers to study celestial objects in different wavelengths, revealing information that is not accessible through visible light observations alone. By using data from telescopes that operate in various parts of the electromagnetic spectrum, astronomers can gather more comprehensive information about the universe.

One way telescope data helps determine distances between celestial objects is through the measurement of redshift. Redshift occurs when light from distant objects is stretched to longer wavelengths due to the expansion of the universe. By analyzing the amount of redshift in the light from a celestial object, astronomers can estimate its distance. This method is a part of the cosmic distance ladder—a set of techniques used to determine distances to different objects in the universe.

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Answer:

Explanation:

The empirical equation y = 9.8x represents the relationship between the displacement y of an object and the time x it has been falling under the influence of gravity.

On the other hand, the equation V = gT + V0 represents the relationship between the velocity V of an object, the time T, the initial velocity V0, and the acceleration due to gravity g.

To compare the two equations, we can equate the displacement y in the first equation with the expression for displacement in terms of velocity and time, which is y = (1/2)gt^2 + V0t, where t is the time.

Substituting this into the empirical equation, we get:

9.8x = (1/2)gt^2 + V0t

We can see that this equation has three variables: g, V0, and t. We can't determine all three variables from this equation alone.

However, if we know the time it takes for an object to fall a certain distance, we can use this equation to solve for g and V0. For example, if we know that an object falls 1 meter in 0.45 seconds, we can substitute x=1 and t=0.45 into the equation:

9.8(1) = (1/2)g(0.45)^2 + V0(0.45)

Simplifying this equation, we get:

g = 19.62 m/s^2

V0 = 0.45(9.8) = 4.41 m/s

So the acceleration due to gravity is 19.62 m/s^2 and the initial velocity is 4.41 m/s. Note that these values may not be exactly equal to the true values, as the empirical equation y=9.8x is only an approximation and there may be other factors affecting the motion of the object.

The answer is:

D. 7.6m

The final velocity of the cylinder is 1.22 m/s when it reaches the bottom of the ramp.

To solve this problem, we need to use conservation of energy and rotational kinematics.

Calculate the gravitational potential energy (GPE) of the cylinder at the top of the ramp:

GPE = mgh = (2.9 kg)(9.81)(0.75 m) = 21.39 J

Calculate the final kinetic energy (KE) of the cylinder when it reaches the bottom of the ramp:

[tex]KE = 1/2 mv^2 + 1/2 Iω^2[/tex]

where v is the linear velocity, I is the moment of inertia, and ω is the angular velocity.

Since the cylinder rolls without slipping, we know that v = ωr, where r is the radius of the cylinder.

[tex]KE = 1/2 mv^2 + 1/4 mv^2 = 3/4 mv^2 = 3/8 mgh[/tex]

Substituting the values we have:

KE = 3/8 (2.9 kg)(9.81)(0.75 m) = 63.56 J

Finally, we can use conservation of energy to find the final velocity of the cylinder:

GPE = KE

[tex]mgh = 3/8 mgh + 1/2 mv^2 + 1/2 Iω^2[/tex]

Solving for velocity:

[tex]v = \sqrt (2gh/5) = \sqrt(29.81 m/s^20.75 m/5) = 1.22 m/s[/tex]

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the complete question is:

At the top of a ramp, a 2.9 kg solid cylinder (radius = 0.20 m, length = 0.70 m) is released from rest and allowed to roll without slipping. The ramp measures 0.75 m in height and 5.0 m in length. calculate the final velocity when it reaches the bottom of the ramp

The Large Hadron Collider is a product of and is used for

The Large Hadron Collider (LHC) was designed and built for scientific investigations in the field of particle physics. Its primary purpose is to collide particles at very high energies and observe the resulting interactions to gain insights into the fundamental nature of matter and the universe.

However, the construction and operation of the LHC have also contributed to technological development in fields such as superconductivity, cryogenics, and data processing.

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The mass of water that undergoes a change in temperature from 10 degrees celsius to 60 degrees celsius is 24.9 g.

Mass is the quantity of matter a body contained.

To calculate the mass of  the water, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the mass of water is 24.9 g.

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The speed of the wave with the period given above would be = 3m/s

The wave length generated by the rope = 6m

The period of the wave = 2s

But the formula use for calculate the speed of a wave = v=λf

Where v = speed

λ= wavelength = 6m

f = Frequency.

Also F = 1/T

Where T = period = 2s

F = 1/2 = 0.5 Hz

V = 6× 0.5

V = 3m/s

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The force that acts upon a projectile launched into the air is gravity.

Gravity is a fundamental force of nature that causes all physical objects to attract each other. It is the force that pulls objects towards each other, and it is the reason why objects with mass are attracted towards the center of the Earth.

When an object is launched into the air, it is subject to the force of gravity, which pulls the object down towards the Earth. As the object moves through the air, the force of gravity causes it to follow a curved path, known as a trajectory, until it eventually hits the ground. While other forces such as air resistance may also act upon the projectile, gravity is the primary force that determines the path of the projectile.

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Answer:

Explanation:

The process can be broken down into two steps:

Heat required to raise the temperature of ice from -20°C to 0°C.

Heat required to melt ice at 0°C and raise the temperature of water from 0°C to 10°C.

Step 1:

The heat required to raise the temperature of ice can be calculated using the specific heat capacity of ice, which is 2.09 J/g°C.

Heat required = mass × specific heat capacity × change in temperature

Heat required = 10 g × 2.09 J/g°C × (0°C - (-20°C))

Heat required = 418 J

Step 2:

The heat required to melt ice and raise the temperature of water can be calculated using the heat of fusion of ice and the specific heat capacity of water.

Heat required to melt ice = mass × heat of fusion of ice

Heat required to melt ice = 10 g × 334 J/g

Heat required to melt ice = 3340 J

Heat required to raise the temperature of water can be calculated using the specific heat capacity of water, which is 4.18 J/g°C.

Heat required = mass × specific heat capacity × change in temperature

Heat required = 10 g × 4.18 J/g°C × (10°C - 0°C)

Heat required = 418 J

Total heat required = Heat required in Step 1 + Heat required to melt ice + Heat required in Step 2

Total heat required = 418 J + 3340 J + 418 J

Total heat required = 4176 J

Therefore, 4176 J of heat is required to change 10 g of ice at -20°C into water at 10°C.

Therefore, the potential difference of the circuit is 30 volts.

The external effort required to move a charge from one position to another in an electric field is known as an electric potential difference, or voltage. A test charge that has an electric potential differential of +1 will experience a shift in potential energy.

To calculate the potential difference (V) of the circuit, we can use Ohm's Law, which states that V = IR, where I is the current flowing through the circuit and R is the resistance of the circuit.

In this case, the current (I) is given as 0.5 A and the resistance (R) is given as 60 Ω. Therefore, we can substitute these values into Ohm's Law to find the potential difference:

V = IR

V = 0.5 A × 60 Ω

V = 30 volts

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Real, inverted, and same size are the features of the image. when A concave mirror with a curvature of 8 is displayed on a ruler with a range of 0 to 14 cm.

The mirror formula may be used to calculate the image distance for an item located 4 cm from a 1.5 cm focal length mirror.

1/f = 1/u+1/v

f is the focal length

u is the object distance

v is the image distance

Keep in mind that the concave mirror's image distance and focal length are both positive.

Given:

u = 4cm

f = 1.5cm

1/v = 1/1.5-1/4

1/v = 0.67-0.25

1/v = 0.42

v = 1/0.42

v = 2.38cm

The picture is Genuine and INVERTED since the image distance value is positive.

We shall find its magnification and see if it is magnified or lessened. It is amplified if the magnification is larger than 1, and it is decreased if it is less.

Magnification = v/u

Magnification = 2.38/4

Magnification = 0.595 or. 0.6

The picture is reduced in size since the magnification is less than one (SMALLER).

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Answer:

Explanation:

Since the spherical shell has a net charge of -2 µC, it will create an electric field outside the shell. Within the shell, the electric field is zero due to symmetry.

a) To find the electric field 0.1 m from the center, we can use Gauss's law and consider a Gaussian surface in the shape of a sphere with a radius of 0.1 m centered at the center of the spherical shell. The electric field at a distance r from the center of the spherical shell is given by:

E = kq / r^2

where k is Coulomb's constant (9.0 x 10^9 N*m^2/C^2) and q is the charge enclosed by the Gaussian surface.

In this case, the charge enclosed by the Gaussian surface is the point charge of +2 µC at the center of the spherical shell. Therefore, we have:

E = kq / r^2 = (9.0 x 10^9 N*m^2/C^2) * (2 x 10^-6 C) / (0.1 m)^2 = 1.8 x 10^6 N/C

So the electric field 0.1 m from the center is 1.8 x 10^6 N/C.

b) To find the electric field 0.5 m from the center, we can again use Gauss's law and consider a Gaussian surface in the shape of a sphere with a radius of 0.5 m centered at the center of the spherical shell. The charge enclosed by this Gaussian surface is the sum of the point charge of +2 µC at the center and the charge of -2 µC on the spherical shell. Therefore, we have:

q_enclosed = q_center + q_shell = 2 x 10^-6 C - 2 x 10^-6 C = 0 C

Since there is no charge enclosed by the Gaussian surface, the electric field at a distance of 0.5 m from the center is zero.

So the electric field 0.5 m from the center is 0 N/C.

The secondary coil needs 120 turns.The power transmitted to the secondary winding is 0.155 W.

A transformer works by using electromagnetic induction to transfer electrical energy between two circuits. The voltage changes between the primary and secondary coil based on the ratio of the number of turns in each coil. In a step-up transformer, the voltage is increased from the primary to the secondary coil, while in a step-down transformer, the voltage is decreased.

Transformers are commonly used in electronic devices to convert voltage levels, isolate circuits, and match impedances. They are often used in power supplies to step down the voltage from the wall outlet to a level that can be used by the device. They are also used in audio amplifiers to match the impedance of the output to the speaker, and in radio and television receivers to tune in to different frequencies.

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Answer:

To find the density of seawater at a certain depth, we need to use the following equation:

P = P0 + ρgh

where:

P0 = pressure at the surface (given as 1 atm = 101325 Pa)

ρ = density of seawater at the depth we're interested in

g = acceleration due to gravity (9.81 m/s^2)

h = depth below the surface

We also need to use the bulk modulus equation to find the change in pressure with depth:

B = (ρ/ρ0)(P-P0)/P

where:

ρ0 = density of seawater at the surface (given as 1050 kg/m^3)

P = pressure at the depth we're interested in

Combining these two equations, we get:

B = (ρ/ρ0)((P0 + ρgh) - P0)/P

B = ρgh/P

ρ = (BP)/(gh)

Substituting the given values, we get:

ρ = (2.3 x 10^9 N/m^2)(101325 Pa)/(9.81 m/s^2)(1050 kg/m^3)(1 atm)

ρ ≈ 1031.4 kg/m^3

Therefore, the density of seawater at a depth where the pressure is 1 atm and the density at the surface is 1050 kg/m^3 is approximately 1031.4 kg/m^3.

The law of conservation of energy states that energy can neither be created nor destroyed, but it can be transformed from one form to another. Here are some examples of the conservation of energy:

A roller coaster moving up and down a track: As the roller coaster climbs up a hill, it gains potential energy. When it reaches the top and starts to descend, this potential energy is converted into kinetic energy. At the bottom of the hill, the kinetic energy is at its maximum and the potential energy is at its minimum.

A pendulum swinging back and forth: As a pendulum swings, it moves between two points of maximum potential energy, where it is momentarily at rest, and two points of maximum kinetic energy, where it is moving the fastest.

A light bulb converting electrical energy into light: When a light bulb is turned on, electrical energy is converted into light energy and heat energy. The total amount of energy is conserved, but some of it is lost as heat.

A car braking to a stop: When a car brakes, the kinetic energy of the moving car is converted into thermal energy due to friction between the brake pads and the wheels. The total amount of energy is conserved, but the kinetic energy is transformed into a less useful form.

A battery powering a device: When a battery is used to power a device, chemical energy is converted into electrical energy. The electrical energy is then used to perform work, such as lighting a bulb or spinning a motor.

These are just a few examples of the conservation of energy in action. In each case, energy is transformed from one form to another, but the total amount of energy remains constant.

The hammer's centripetal acceleration is therefore 100.59 m/s².

An object has positive acceleration when it is going faster than it was previously. Positive acceleration was demonstrated by the moving car in the first scenario. Positive forward motion is being made by the car.

Hammer mass, m, is 6.55 kg. chain length, including the length of the arms, r = 1.3 m, Hammer's angular velocity is given by the formula: = 1.4 rev/s = 8.79646 rad/s (1 rev = 6.28 rad).

The formula a = V2/r, where V is the transverse velocity of the hammer, yields the centripetal acceleration.

V = r, hence

As a result, a = r²

A = 1.3 x 8.796462, or 100.59 m/s², is obtained by substituting the supplied numbers in the equation above.

The hammer's centripetal acceleration is therefore 100.59 m/s².

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The insect  appears 3cm away from the image shown.

The refractive index is the ratio of the speed of light in a vacuum to the speed of light in a given medium. However, when light passes through a medium with a different refractive index than the surrounding medium, it appears to change direction at the boundary between the two media. This phenomenon is called refraction.

Refractive index = Real depth/ Apparent Depth

3/2 = 9/A

A = 18/3

A = 6 cm

Displacement = 9 cm - 6 cm = 3cm

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If the wind bounces backward from the sail, the boat will not be set in motion as no forward force is generated. For the boat to move forward, the sail must be positioned to catch the wind and create lift in the desired direction.

If the wind bounces backward from the sail, the craft will not be set in motion. In order for a sailboat to move forward, the wind must push on the sail, creating a force that propels the boat forward through the water. When the wind hits the sail, it creates lift in a direction perpendicular to the sail's surface, which results in a forward force that propels the boat.

However, if the wind bounces backward from the sail, it does not create lift and therefore does not result in a forward force on the boat. Instead, the wind is redirected in a different direction, and the boat remains stationary. In order for the boat to move forward, the sail must be positioned to catch the wind and create lift in the desired direction, propelling the boat forward.

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A. 90°C, NMWU (Nylon-coated Metal Clad) is a type of electrical wire commonly used in residential and commercial wiring applications.

It is composed of a metal conductor, such as aluminum or copper, wrapped in a protective layer of nylon. The advantage of this type of wire is that it is easier to work with than other types of wire, is highly resistant to corrosion, and can withstand temperatures up to 90°C.

The insulation rating of a wire is a measure of its ability to withstand heat or cold without being damaged. This rating is determined by the maximum temperature that the insulation can withstand before it begins to degrade or break down. For NMWU wire, the maximum allowable conductor temperature insulation rating is 90°C. Other types of wire may have lower or higher ratings.

The insulation rating of the wire must be taken into account when selecting a wire for an application. If a wire is subjected to temperatures greater than its rated insulation temperature, the insulation can be damaged and the wire may become unsafe.

Therefore, it is important to ensure that the insulation rating of the wire is appropriate for the application. For NMWU wire, the maximum allowable conductor temperature insulation rating is 90°C, so it should only be used in applications.

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Answer:

The student use 2400 Joules

Explanation:

From the formula E = pt

p = 800W

t = 3 seconds

=> E = 800*3 = 2400J

Answer:

a. Chemical energy from the battery is converted to electrical energy in the flashlight.

Thank you for reaching out to me with your question. From what I understand, you are curious about the importance of an assignment or exam that is worth 20% of your grade.

To put it simply, any assignment or exam that is worth a certain percentage of your grade is an indicator of how much weight that particular task carries in determining your overall grade for the course. In other words, if you were to score poorly on an assignment that is worth 20% of your grade, it could significantly impact your final grade.
It is important to note that each assignment or exam may be worth a different percentage, and it is up to the instructor to determine the weight of each task. Generally, assignments and exams that are worth a higher percentage of your grade carry more weight and have a greater impact on your final grade.
Therefore, it is crucial to take each assignment or exam seriously and give it your best effort, especially those that carry a higher percentage of your grade. It is also important to keep track of your grades throughout the semester and identify any areas that may need improvement, so you can work towards improving your overall grade.
I hope this explanation helps clarify the importance of an assignment or exam that is worth a certain percentage of your grade. Please let me know if you have any further questions or concerns.

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w is 1.07 × 10^4, expressed in scientific notation with the correct number of significant figures.

The equation given is:

Ψ = w/(yz^2)

We Substitute the given values, we get:

Ψ = w/(y × z^2) = 1.1 × 10^3 × 2.48 × 10^-2 × 6.000 = 1.6464

solving  for w and rearranging  the equation as:

w = Ψ × y × z^2

We Substitute the given values, we get:

w = 1.6464 × 37 × (14)^2 = 10,722.7584

we  round the value of w to three significant figures, since the values of y, z, and Ψ are given with three significant figures, in order to express the result in scientific notation with the correct number of significant figures,

Rounding 10,722.7584 to three significant figures gives 10,700. Therefore, the value of w is:

w = 1.07 × 10^4

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Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics.

Rμν−12gμνR=8πGT^μν.

This is Einstein’s field equation. Essentially, this equation is general relativity. The left-hand side represents the geometry of spacetime. The right-hand side, the energy, momentum, and stresses of matter.

What this equation describes, in the words of Wheeler, is this: Spacetime tells matter how to move; matter tells spacetime how to curve.

But look closely. That T

on the right-hand side. It has a hat.

It has a hat because it is a quantum-mechanical operator. Because we know that matter consists of quantum fields. So it is described by operator-valued quantities (Dirac called them q-numbers). They are unlike ordinary numbers. For instance, when you multiply them, the order in which they appear matters. That is, when you have two operators p^

and q^

, p^q^≠q^p^

most of the time. So they are definitely not like numbers.

When Einstein wrote down his field equation over 100 years ago, the T

did not have a hat. But that’s because they didn’t know about operator-valued quantities at the time. Now we do. So I have to put the hat there.

But there are no hats on the left-hand side. And because of that, my equation might as well say something like, some apples = some oranges. It makes no sense. The stuff on the left-hand side (which consists of numbers) can never equal the stuff on the right-hand side (which definitely does not consist of numbers.)

I can make it work, though. I can replace that operator with its so-called expectation value:

Rμν−12gμνR=8πG⟨Tμν⟩.

This is called semiclassical gravity. And it works well, very well indeed. A little too well, as a matter of fact. Gravity is so weak, quantum effects are so irrelevant, this equation accurately describes Nature everywhere we can look. But we still don’t like it, because using that expectation value trick is a cheat, a cop-out.

Now you might wonder, why don’t I put hats on top of the things on the left-hand side? I would… if I knew how to quantize spacetime. That is, how to turn the numbers that describe gravity into quantum-mechanical operators.

But I do not. And nobody does. The standard methods all fail, leading to equations that make no sense at all.

So we are kind of stuck… we don’t know how to quantize gravity, and our observations don’t help us, don’t offer any hints as to how to get beyond semiclassical gravity. Theorists keep trying to come up with new ideas (or recycle old ones) but basically, we’ve been pretty much just spinning our wheels for decades.

The statement that correctly defines an evolutionary stage of a star like the sun is that after leaving the main sequence, its core is stable due to electron degeneracy. That is option C.

The stages of the life cycle of a star include the following:

The evolutionary stage is also called the main sequence stage of the life cycle of the star.

In this stage, the core temperature reaches the point for the fusion to occur whereby the protons of hydrogen are converted into atoms of helium. This leads to the stability of the core of the newly formed start due to electron degeneracy.

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Answer:

Explanation:

We can use the inverse-square law of universal gravitation to determine the weight of the missile at an altitude of 6.4 x 10^6 m. The law states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Let M be the mass of the Earth and m be the mass of the missile. At the Earth's surface, the weight of the missile is:

F1 = mg

where g is the acceleration due to gravity on the Earth's surface, which we assume to be 9.81 m/s^2.

At an altitude of 6.4 x 10^6 m, the distance between the center of the Earth and the missile is:

r = R + h

where R is the radius of the Earth (6.4 x 10^6 m) and h is the altitude of the missile (6.4 x 10^6 m).

The weight of the missile at this altitude can be calculated using the inverse-square law of universal gravitation:

F2 = G * M * m / r^2

where G is the gravitational constant (6.6743 x 10^-11 N * m^2 / kg^2).

Substituting the given values, we get:

F2 = (6.6743 x 10^-11 N * m^2 / kg^2) * (5.97 x 10^24 kg) * (400 N) / (6.4 x 10^6 m + 6.4 x 10^6 m)^2

F2 = 39.61 N

Therefore, the weight of the missile at an altitude of 6.4 x 10^6 m is approximately 39.61 N.