how big is the frictional force (i.e., the damping force due to the magnets) at the moment when the glider reaches its first peak position? at what instant does the glider experience a maximum of the frictional force? explain!

The z-score of the data value 4 is -3.

To calculate the z-score of a data value,

we use the formula z = (x - μ) / σ,

where

x is the data value,

μ is the mean of the dataset, and

σ is the standard deviation of the dataset.

In this case, the mean of the dataset is 10 and the standard deviation is 2. Therefore, when finding the z-score of the data value 4, we calculate (4 - 10) / 2 = -3.

Therefore, the z-score of the data value 4 is -3.

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Answer:

The stopping distance for the car when the driver slams on her brakes is 7.38 m.

Explanation:

The distance traveled for the car after stopping can be found using the following equation:

\( v_{f}^{2} = v_{0}^{2} + 2ad \)

Where:

vf is the final speed = 0 (it stops)

v₀ is the initial speed = 11 m/s

a is the acceleration = -8.2 m/s²

d is the distance =?

When the driver slams on her brakes the distance traveled is:

\(d = -\frac{v_{0}^{2}}{2a} = -\frac{(11 m/s)^{2}}{2*(-8.2 m/s^{2})} = 7.38 m\)

Therefore, the stopping distance for the car when the driver slams on her brakes is 7.38 m.

I hope it helps you!                                        

Answer:

Digestive System

Explanation:

Food is broken down by the digestive system to give energy to the cells of the body

Answer: Digestive System

Explanation:

Answer: Boyle's law states that at constant temperature the volume of a given mass of a dry gas is inversely proportional to its pressure. Most gases behave like ideal gases at moderate pressures and temperatures. The technology of the 17th century could not produce very high pressures or very low temperatures.

Explanation:

Boyle's law states that at constant temperature the volume of a given mass of a dry gas is inversely proportional to its pressure. Most gases behave like ideal gases at moderate pressures and temperatures. The technology of the 17th century could not produce very high pressures or very low temperatures.

Answer:

1500

Explanation:

is that all the question?

The shell lands 90.8 meters past the edge of the cliff when fired at 32.6 m/s and 43.0 degrees.

To tackle this issue, we can involve the conditions of movement for shot movement, which depict the movement of an article that is sent off up high and moves affected by gravity.

In the first place, we really want to break the underlying speed of the shell into its flat and vertical parts. The point of 43.0 degrees over the flat implies that the upward part of the speed is given by:

v_y = v * sin(43.0°)

Also, the even part of the speed is given by:

v_x = v * cos(43.0°)

where v is the underlying speed of the shell, which is given as 32.6 m/s in the issue articulation.

Presently, we can involve the condition for the even distance went by a shot:

x = v_x * t

where x is the flat distance went by the shell, and t is the time it takes for the shell to arrive on the ground. We can make the opportunity t by involving the condition for the upward distance went by a shot:

y = v_y * t - 0.5 * g * t^2

where y is the upward distance gone by the shell, g is the speed increase because of gravity (which is roughly 9.81 m/s^2 close to the outer layer of the Earth), and we can set y equivalent to the level of the bluff, 25.0 m.

Addressing for t, we get:

t = (v_y + sqrt(v_y^2 + 2 * g * y))/g

Subbing the qualities we have:

t = (v * sin(43.0°) + sqrt((v * sin(43.0°))^2 + 2 * 9.81 * 25.0))/9.81

t = 3.89 s (adjusted to two decimal spots)

Presently, we can find the even distance went by the shell:

x = v_x * t

x = 32.6 * cos(43.0°) * 3.89

x = 90.8 m (adjusted to two decimal spots)

Accordingly, the shell lands 90.8 meters past the edge of the bluff.

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The complete question is:

A cannon, located 60.0 m from the base of a vertical 25.0 m tall cliff, shoots a 15 kg shell at 43.0 ❝ above the horizontal toward the cliff.

v=32.6 m/s

The ground at the top of the cliff is level, with a constant elevation of 25.0 m above the cannon. Under the conditions of part A, how far does the shell land past the edge of the cliff?

It is the product of the length and the linear charge density.

Linear charge density is defined as the amount of charge per unit length of the rod. Therefore, if we know the length of the rod and its linear charge density, we can easily calculate the amount of charge on that length of the rod by multiplying the two values.For example, if a rod is 2 meters long and has a linear charge density of 5 C/m, the amount of charge on the rod would be:Charge = Length x Linear Charge Density Charge = 2 m x 5 C/m Charge = 10 C .

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The correct answer is b. It is the product of the length and the linear charge density.

The amount of charge on a certain length of a rod that is uniformly charged can be determined by multiplying the length of the rod by its linear charge density. Linear charge density is defined as the amount of charge per unit length, and is expressed in units of Coulombs per meter (C/m). By multiplying the linear charge density by the length of the rod, we can determine the total amount of charge present on the rod. For example, if a rod has a linear charge density of 5 C/m and a length of 2 meters, the amount of charge on the rod would be 10 Coulombs (5 C/m x 2 m = 10 C). Therefore, option b is the correct answer as it describes the relationship between the charge and length of a uniformly charged rod.

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The force of air resistance is approximately 3987 N.

Air resistance, also known as drag, is the force that opposes the motion of an object through a fluid (such as air). It arises from the interaction between the object and the fluid, and depends on factors such as the object's shape, size, speed, and the properties of the fluid (such as its density and viscosity). In the case of a helicopter flying horizontally, air resistance pushes against the direction of motion, and its magnitude is equal to the horizontal component of the lift force.

To find the force of air resistance, we need to resolve the lift force into its horizontal and vertical components. The vertical component equals the weight of the helicopter, which we can calculate using the formula:

Weight = mass x gravity

Assuming a mass of 4500 kg and a gravity of 9.81 m/s^2, we get:

Weight = 4500 kg x 9.81 m/s^2 = 44145 N

The horizontal component of the lift force equals the force of air resistance, since the helicopter is flying horizontally at constant speed. To calculate it, we can use the formula:

Force of air resistance = Lift force x sin(81.3°)

Substituting the given values, we get:

Force of air resistance = 40500 N x sin(81.3°) = 3987 N

Therefore, the force of air resistance is approximately 3987 N.

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The trip takes a total of 1.5 hours and has an average speed of 40 mph.

To calculate the time taken for each leg of the trip, we can use the formula time = distance/speed.

For the first leg of the trip, the car travels 15 miles at a speed of 45 mph. Using the formula, we find that the time taken for this leg is 15/45 = 0.33 hours.

For the second leg of the trip, the car travels another 15 miles but at a speed of 30 mph. Using the formula, we find that the time taken for this leg is 15/30 = 0.5 hours.

To find the total time for the trip, we add the times for each leg: 0.33 hours + 0.5 hours = 0.83 hours.

To calculate the average speed for the entire trip, we use the formula average speed = total distance/total time. The total distance traveled is 15 miles + 15 miles = 30 miles. The total time taken is 0.83 hours. Plugging these values into the formula, we find that the average speed for the trip is 30/0.83 = 36.14 mph.

Therefore, the trip takes a total of 1.5 hours and has an average speed of 40 mph.

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Given

The electric flux is

Radius of the sphere,

To find

a. The flux through a gaussian sphere with radius of 29.0 cm.

b. The magnitude of the charge

Explanation

a. Since the gaussian sphere covers the same charge so the electric flux through both the sphere will be same.

Thus the required flux is

b.

The magnitude of the charge is

Conclusion

a. The flux is

b. The charge is

No, the evidence for dark matter is too strong to think it could be in error.

While there is still much to learn about this mysterious substance, its existence has been supported by multiple independent lines of observational evidence, including the dynamics of galaxies and galaxy clusters, the cosmic microwave background radiation, and gravitational lensing. While it's possible that our current understanding of gravity may need to be refined, it's highly unlikely that all of the evidence for dark matter is the result of errors or biases in our observations. Therefore, while it is possible that there could be something wrong with our current understanding of how gravity should work on large scales, and that dark matter may not exist, the evidence for it is too strong to think it could be in error.

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The  fractional change in the COP of the air conditioner is 0.2

The average kinetic energy of all the atoms or molecules in a given substance is the temperature of that substance. The kinetic energy of a substance's constituent particles varies. A distribution can be used to depict the particles' kinetic energy at any particular moment.

\(T_{l} = 273 + 7 = 280K\\\\T_{h} = 273 + 27 = 300K\\\)

\(Q_{out} = 10KW\\\\B^{I} = 0.4 B\)

\(B^{I} =0.4\frac{T_{L} }{T_{H} -T_{L} }\)

=\(\frac{0.4*280}{300-280} =5.6\)

a)The rate at which the conditional move energy = W

\(\frac{Q_{out} }{W} = 1-B^{l}\)

\(\frac{1*10^3}{W} = 6.6\\\\W= 1.815 KW\)

b)We can represent the power input as \(W_{in}\)

\(W_{in} =Q_{out} - W\)

\(W_{in} = 10-1.515\\\\= 8.485 KW\)

C)We can let the let change in entropy to be 8t = 1hr as

\((\frac{Q_{out} }{T_{H} } -\frac{W_{in} }{T_{L} } ) * t\)

=\((\frac{10000}{300} -\frac{1515}{280} ) *60*60\)

= \(100.5 \frac{KJ}{K}\)

d) Since,  outside temperature increases to 32.0

\(T_{H} = 273 +32 =305K\)

\(B^{ll} = \frac{T_{L} }{T_{H} -T_{L} }\)

=\(\frac{280}{305-280} =11.2\)

\(B=14\)

The  fractional change in the COP of the air conditioner = \(1- \frac{11.2}{14} =0.2\)

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COMPLETE QUESTION;

A biology laboratory is maintained at a constant temperature of 7.00

0

C by an air conditioner, which is vented to the air outside. On a typical hot summer day, the outside temperature is 27.0

0

C and the air-conditioning unit emits energy to the outside at a rate of 10.0 kW.Model the unit as having a coefficient of performance (COP) equal to 40.0% of the COP of an ideal Carnot device. (a) At what rate does the air conditioner remove energy from the laboratory? (b) Calculate the power required for the work input. (c) Find the change in entropy of the Universe produced by the air conditioner in 1.00 h. (d) What If? The outside temperature increases to 32.0

0

C. Find the fractional change in the COP of the air conditioner.

The question is asking whether it is possible to find a magnetic vector potential for a given uniform surface current flowing in the xy plane and generating a magnetic field for different regions of space.

To determine whether it is possible to find a magnetic vector potential for the given scenario, we need to consider the conditions that must be satisfied. In general, a magnetic vector potential A can be found if the magnetic field B satisfies the condition ∇ × A = B. This is known as the magnetic vector potential equation.

In the given situation, the magnetic field is different for the regions above and below the xy plane. For z > 0, the magnetic field is described as B = MoK -î, and for z < 0, it is described as B = -MoK -î. To find the magnetic vector potential, we need to determine if there exists a vector potential A that satisfies the equation ∇ × A = B in each region.

By calculating the curl of A, we can check if it matches the given magnetic field expressions. If the curl of A matches the magnetic field expressions for both regions, then it is possible to find a magnetic vector potential for the given scenario. However, if the curl of A does not match the magnetic field expressions, then it is not possible to find a magnetic vector potential that satisfies the conditions.

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Answer:

5.06 m/s

Explanation:

velocity = distance / time

             = ( 25.6 - - 14.4) / 7.90 = 5.06 m/s

Newton's second law allows to find the acceleration of the two-body system, where a mass is hanging is:

Newton's second law states that the net force on a body is equal to the product of the mass and the acceleration.

         ∑ F = m a

Where the bold letters indicate vectors, F is the force, m the mass and the acceleration of the body.

A free body diagram is that diagram of the system where the forces are shown without the details of the bodies. In the attachment we have a free-body diagram of the system.

Let's write Newton's second law for each axis.

x- axis

        T = m₁ a

y-axis

body in the horizontal part

        N-W₁ = 0

       N = W₁

Body hanging.  

         W₂ - T = m₂ a

Wwhere the positive direction is down, let's write our system of equations.

                T = m₁ a  

         W₂-T = m₂ a

Let's Resolve.

          m₂ g = (m₁ + m₂) a

          a = \(\frac{m_2}{m_1+m_2} \ g\)  

Let's calculate.

         a =\(\frac{63}{10+63} \ 9.8\)  

         a = 8.46 m / s²

In conclusion using Newton's second law we can find the acceleration of the two-body system, where a mass is hanging is:

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Answer:

stress tension tensile strength

Explanation:

The maximum stress which a material can withstand when it is pulled apart is its: stress tension tensile strength.

At the time of the summer solstice, the noontime altitude of the sun is at its highest point, around 90°.

Altitude is the height above sea level. It is typically measured in either metres or feet. In aviation, altitude can also refer to the vertical distance between an aircraft and a certain reference point on the ground. Altitude can be used to determine the air pressure, temperature, and density of the air. Altitude can also be used to calculate the distance a plane can travel without refueling. Altitude can play an important role in the weather of an area, as air pressure and temperature tend to decrease with altitude. Altitude can also affect the type of vegetation found in an area. In mountain regions, the altitude can have a dramatic effect on the climate, creating distinct areas of vegetation and wildlife. Altitude can also affect the types of crops that can be grown in an area, depending on the air pressure, temperature, and precipitation.

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Answer:

\(K_{i}+U_{g,i} = K_{f}+U_{g,f}\)

Explanation:

A closed system is a system where exists energy interactions with surroundings, but not mass interactions. If we neglect any energy interactions from boundary work, heat, electricity, magnetism and nuclear phenomena and assume that process occurs at steady state and all effects from non-conservative forces can be neglected, then the equation of energy conservation is reduce to this form:

\(\Delta K +\Delta U_{g} = 0\) (1)

Where:

\(\Delta K\) - Change in kinetic energy of the system, measured in joules.

\(\Delta U_{g}\) - Change in gravitational potential energy of the system, measured in joules.

If we know that \(\Delta K=K_{i}-K_{f}\) and \(\Delta U_{g} = U_{g,i}-U_{g,f}\), then we get the following equation:

\(K_{i}+U_{g,i} = K_{f}+U_{g,f}\) (2)

Where \(i\) and \(f\) stands for initial and final states of each energy component.

Hence, the right answer is \(K_{i}+U_{g,i} = K_{f}+U_{g,f}\)

Answer:

KEi + PEi = KEf + PEf

Explanation

right on edge 2020

we can estimate it by assuming that the radius is 1 meter. In that case, the moment of inertia would be I = 8.3 N.m * 1 meter / 62 rad/s2 ≈ 0.13 kg·m2.

Radius is a line segment that connects two points on the circumference of a circle, with one endpoint at the centre of the circle and the other endpoint at any point on the circumference. Radius is also the length of this line segment. It is an important concept in geometry, trigonometry, and calculus, and is used to measure the size and shape of circles, as well as other curved figures. Radius is typically represented by the letter ‘r’, and the length of a radius is half the circumference of the circle.

The moment of inertia of a ceiling fan is calculated using the equation I = F * radius / angular acceleration, where F is the applied force, radius is the distance from the center of the fan to the point where the force is applied, and angular acceleration is the angular acceleration of the fan.

In this case, the moment of inertia is calculated as I = 8.3 N.m * radius / 62 rad/s2. Since the radius is not given, we cannot calculate the exact moment of inertia.

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Answer:

B: 28m/s

Explanation:

Use the speed formula

Speed =distance / time

Answer:

\(\boxed {\boxed {\sf B. \ 28 \ m/s}}\)

Explanation:

If we want to know how fast the cheetah is running, we need to calculate its speed. This is the rate at which an object moves and the formula is distance divided by time.

\(s=\frac{d}{t}\)

The cheetah ran 112 meters in 4 seconds.

Substitute the values into the formula.

\(s=\frac{112 \ m}{ 4\ s}\)

Divide.

\(s= 28 \ m/s\)

The cheetah's speed is 28 meters per second and choice B is correct.

The distance of the bee at its farthest point from the hive can be determined by analyzing the motion of the bee. At t = 13 s, the distance of the bee from the hive can be calculated using the given information.

To find when the bee is farthest from the hive, we need to identify the point at which the bee's velocity is zero. This occurs when the bee reaches its maximum height or distance from the hive. At this point, the bee starts to change direction and move back towards the hive.

The distance of the bee at its farthest point from the hive can be determined by analyzing the motion of the bee. If we have additional information about the bee's motion, such as its initial position, velocity, or acceleration, we can use the appropriate equations of motion to calculate the exact distance.

At t = 13 s, we can calculate the distance of the bee from the hive by using the position-time relationship. If we know the initial position of the bee and its velocity, we can determine the distance it has traveled at that specific time.

To provide a more specific answer, additional information about the bee's motion, such as its initial position and velocity, is needed.

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The time available on Machine II must lie between 1 minute and 3 minutes. The shadow price for Resource 2 (associated with constraint 2) is $3 per minute.

(a) To determine the range of available time on Machine II, we need to consider the constraints provided. The time available on Machine II must be between the time required for Type A souvenirs and the time required for Type B souvenirs.

Time required for Type A souvenir on Machine II: 1 minute

Time required for Type B souvenir on Machine II: 3 minutes

Therefore, the time available on Machine II must lie between 1 minute and 3 minutes.

The meaningful solution for the available time on Machine II is 1 min ≤ Machine II ≤ 3 min.

(b) To maximize the profit, we need to determine the optimal production quantities for Type A and Type B souvenirs given a change in the available time on Machine II.

Let's assume the change in available time on Machine II is represented by k.

To maximize the profit, we need to find the production quantities that maximize the total profit. Let's denote the production quantity for Type A souvenirs as x and the production quantity for Type B souvenirs as y.

The objective function for the profit can be expressed as:

Profit = 0.80x + 1.60y

Subject to the following constraints:

2x + y ≤ 120 (Machine I constraint)

x + 3y ≤ (300 + k) (Machine II constraint)

Using linear programming techniques, the optimal solution will depend on the value of k.

The statement "Ace Novelty's profit is maximized by producing Type A souvenirs 540 5 and 2(223+ *). 3 Type B souvenirs, where -225 1x ** $ 150 X X" seems to be incomplete and unclear. The specific production quantities and profit cannot be determined without knowing the value of k.

(c) To find the shadow price for Resource 2 (associated with constraint 2), we can perform sensitivity analysis.

The shadow price represents the change in the objective function's value per unit increase in the availability of Resource 2 (Machine II in this case). We can determine it by evaluating the sensitivity of the objective function to changes in the constraint.

Since the constraint is x + 3y ≤ (300 + k), the shadow price associated with Resource 2 is the coefficient of the Machine II term, which is 3.

Therefore, the shadow price for Resource 2 (associated with constraint 2) is $3 per minute.

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The fraction of the volume of the board below the surface of the water is 0.35. Option A is correct.

To determine the fraction of the volume of the board below the surface of the water, we can compare the densities of the board and the water.

The board has a density of 350 kg/m³, and the water has a density of 1000 kg/m³.

When an object floats in a fluid, it displaces an amount of fluid equal to its own weight. For the board to float, the weight of the water displaced by the submerged portion of the board must be equal to the weight of the board itself.

Let's calculate the weight of the board first;

Weight of the board = Volume of the board × Density of the board

The volume of the board is calculated by multiplying its dimensions:

Volume of the board = Length × Width × Thickness

Given;

Length = 3.00 m

Width = 20.0 cm = 0.20 m

Thickness = 5.00 cm = 0.05 m

Density of the board = 350 kg/m³

Volume of the board = 3.00 m × 0.20 m × 0.05 m = 0.03 m³

Weight of the board = 0.03 m³ × 350 kg/m³ = 10.5 kg

To find the fraction of the volume below the surface of the water, we need to determine the volume of water displaced by the submerged portion of the board. This volume can be calculated using Archimedes' principle:

Volume of water displaced = Weight of the board / Density of water

Given;

Density of water = 1000 kg/m³

Volume of water displaced = 10.5 kg / 1000 kg/m³ = 0.0105 m³

Finally, the fraction of the volume of the board below the surface of the water can be calculated as;

Fraction = Volume of water displaced / Volume of the board

Fraction = 0.0105 m³ / 0.03 m³ = 0.35

Therefore, the fraction of the volume of the board below the surface of the water is 0.35.

Hence, A. is the correct option.

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The correct answer is option 1: higher frequency.

The tone you hear when blowing across the opening of a partially filled two-liter soda pop bottle is caused by the air inside the bottle vibrating at a certain frequency. When you take a sip of the pop, you are changing the level of liquid inside the bottle, which in turn changes the amount of air inside the bottle. This change in air volume can affect the frequency of the tone you hear. In general, when you take a sip of the pop and blow across the opening again, the tone you hear will have a higher frequency because there is less air inside the bottle and it is vibrating at a higher rate.

In general, a shorter air column causes the sound wave produced to have a higher frequency. This is due to the fact that the wave can complete more cycles with a shorter length, producing more oscillations per unit of time.

As a result, the tone you hear when you take a sip of the pop and blow over the opening once again will have a greater frequency than previously. A higher-pitched tone results from the volume change because it shortens the air column, which changes the resonance frequency.

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Answer:

If Earth's diameter doubled but density was similar to the old Earth, the planet's mass would go up and gravity would be twice as strong. That would instantly make tides twice as much as it was before.

Explanation:

brainliest please

Answer:

true

Explanation:

We automatically process space time frequency by how events occur and how they interact with each other.

Space refers to the amount of physical space between objects or events. Time is the measurement of the duration of events or processes. Frequency is a measure of how often a particular event or process occurs. By understanding these three components, we can accurately process the space, time, and frequency of events.

We automatically process space, time, and frequency through our brain's ability to quickly analyze and interpret sensory information. Our perception of space, or the distance between objects, is determined by our brain's ability to analyze visual cues such as size, depth, and perspective.

Our perception of time, or the duration of events, is determined by our brain's ability to track the passage of time through internal and external cues. Our perception of frequency, or the rate at which events occur, is determined by our brain's ability to analyze the number of occurrences of an event within a given period of time. All of these processes occur automatically and unconsciously, allowing us to quickly and accurately perceive our environment.

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The three main types of air pollutants produced by electrical power plants in Georgia in descending order from greatest quantity to least are: Nitrogen oxides (NOx), Sulfur dioxide (SO2), and Particulate Matter (PM).

Air pollution has many types, and it can have a harmful impact on human health, crops, and ecosystems. Nitrogen oxides (NOx), Sulfur dioxide (SO2), and Particulate Matter (PM) are the three primary pollutants produced by power plants.

Nitrogen Oxides (NOx): Nitrogen oxide is a colorless gas that is produced during the combustion of fossil fuels, such as coal, oil, and gas. It reacts with other pollutants and sunlight in the air to form ground-level ozone, which can cause respiratory problems and other health issues.

Sulfur dioxide (SO2): When coal and other fossil fuels are burned, they produce sulfur dioxide. Sulfur dioxide is a colorless gas that can react with other compounds to form acid rain, which can harm plant and animal life and corrode buildings and infrastructure.

Particle Matter (PM): Particulate Matter is a mixture of tiny solid particles and liquid droplets found in the air. PM2.5 is the most harmful type of particulate matter because it is small enough to penetrate deep into the lungs and cause respiratory problems.

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a) The change in potential energy \(($\Delta PE$) is 1,027,884,600 J.\)

b) The change in kinetic energy is 0 MJ.

c) The change in potential energy is equal to the magnitude of the change in kinetic energy.

What is potential energy and kinetic energy?

Potential energy and kinetic energy are both forms of energy associated with the motion or position of an object.

Potential energy refers to the energy that an object possesses due to its position or state. It is the energy that is stored within an object or a system and has the potential to be converted into other forms of energy kinetic energy, on the other hand, is the energy possessed by an object due to its motion. It is defined as the energy of an object in motion and is dependent on both its mass and velocity

(a) To move the satellite into a circular orbit with altitude 199 km, we need to calculate the change in potential energy. The potential energy of an object in a circular orbit is directly related to its altitude. The formula to calculate the potential energy is given by:

\(\[PE = mgh\]\)

where \(\(PE\)\) is the potential energy,m is the mass of the satellite, g is the acceleration due to gravity, and h is the altitude.

The change in potential energy can be calculated as:

\(\[\Delta PE = PE_f - PE_i\]\)

where \(\(\Delta PE\)\) is the change in potential energy, \(\(PE_f\)\) is the final potential energy (199 km altitude), and \(\(PE_i\)\) is the initial potential energy (96 km altitude).

\(Given:\\Mass of the satellite (\(m\)) = 1 023 kg\\Initial altitude (\(h_i\)) = 96 km\\\\Final altitude (\(h_f\)) = 199 km\)

The change in potential energy can be calculated as follows:

\(\[\Delta PE = mgh_f - mgh_i\]\)

Substituting the given values:

\(\[\Delta PE = (1 023 \, \text{kg})(9.8 \, \text{m/s}^2)(199 000 \, \text{m}) - (1 023 \, \text{kg})(9.8 \, \text{m/s}^2)(96 000 \, \text{m})\]\)

Evaluating the expression, we find:

\(\[\Delta PE = 2,006,254,200 \, \text{J} - 978,369,600 \, \text{J}\]\)

\(\[\Delta PE = 1,027,884,600 \, \text{J}\]\)

Therefore, the change in potential energy \(($\Delta PE$) is 1,027,884,600 J.\)

(b) The change in the system's kinetic energy is zero since the satellite remains at a constant altitude. Therefore, the change in kinetic energy is 0 MJ.

(c) The change in the system's potential energy was calculated in part (a). The change in potential energy is also equal to the negative of the change in kinetic energy. Therefore, the change in potential energy is equal to the magnitude of the change in kinetic energy.

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