A record has an angular speed of
38.9 rev/min.
What is its angular speed?
Answer in units of rad/s.

pt 2

Through what angle does it rotate in 1.9 s?
Answer in units of rad

If you know the apparent and intrinsic brightness of a star, you can find the distance to the star by using the inverse square law of brightness.

The apparent brightness of a star is the amount of light received from the star at a given distance from Earth, while the intrinsic brightness is the actual amount of light the star emits. By comparing the apparent and intrinsic brightness of a star, we can calculate the distance to the star using the inverse square law of brightness, which states that the intensity of light decreases as the square of the distance from the source increases. Therefore, the distance to a star can be determined by using the equation: distance = square root (intrinsic brightness / apparent brightness).

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The magnitude of the force is 366,250 N, which is the average force that the EMAS must exert on the jetliner to stop it within the 132-m long bed of crushable cement blocks.

First, we need to calculate the initial kinetic energy of the jetliner:

[tex]= KEi = (1/2)mv^2 \\= (1/2)(55,000 kg)(37 m/s)^2[/tex]

= 48,372,500 J

Next, we can calculate the final kinetic energy of the jetliner:

[tex]= KEf = (1/2)mv^2= (1/2)(55,000 kg)(0 m/s)^2[/tex]

[tex]= 0 J[/tex]

The change in kinetic energy is then:

ΔKE = KEf - KEi = -48,372,500 J

Since the EMAS acts over a distance of 100 m, the average force it exerts is:

[tex]F = \Delta KE/d \\= (-48,372,500 J) / (132 m) \\= -366,250 N[/tex]

The negative sign indicates that the force is acting in the opposite direction to the motion of the jetliner, as it is slowing it down.

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Taking the positive direction to be to the right,  the total momentum of this system is - 14kg-m/s

Option B is correct.

momentum is described as the product of the mass and velocity of an object and a vector quantity possessing a magnitude and a direction.

momentum = mass x velocity

momentum 1  = 5 x 8kg = 40 kg-m/s

momentum 2 = 4 x 15 kg = 60 kg-m/s

momentum 3 = 2 x 3kg = 6 kg-m/s

Taking the positive direction to be to the right,  the total momentum of this system is momentum 1  - momentum 2 + momentum 3

total momentum =  40 kg-m/s - 60 kg-m/s + 6 kg-m/s

total momentum  = -20kg-m/ + 6 kg-m/s

total momentum =  - 14 kg-m/s

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The amount of time which the impetus was implemented is 3.04 seconds.

The momentum of the automobile is 34124.26 kg*m/s.

In order to figure out the time, the following formula for impulse can be applied: impulse = force x time. Reformulating and rearranging this equation, we reach the derivative of time = impulse / force. With the provided calculations of 536.49 N*s divided by 176.32 N, these figures conclude that the amount of time which the impetus was implemented is 3.04 seconds.

Additionally, we can use the formula of momentum = mass x velocity to further determine the vehicular testament of import. When applying these specified numbers of 2546.9 kg and 13.4 m/s respectively, the momentum of the automobile is 34124.26 kg*m/s.

momentum = 2546.9 kg x 13.4 m/s

= 34124.26 kg

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The angle of the free surface relative to the horizontal direction after deceleration is approximately 20.2 degrees.

Let's assume that the tank has a mass of m, the angle of the inclined surface is θ, and the height of the inclined surface is h. The initial kinetic energy of the tank is given by:

KE = (1/2)mv²

where v is the initial velocity of the tank. When the tank reaches the top of the inclined surface, its potential energy is given by:

PE = mgh

where g is the acceleration due to gravity (9.81 m/s²). Since there is no change in the total energy of the system (tank + water), we can equate the initial kinetic energy to the final potential energy:

(1/2)mv² = mgh

Solving for v, we get:

v = √(2gh)

When the tank decelerates with an acceleration of a, its velocity decreases at a rate of a m/s². The time taken for the tank to come to a complete stop is given by:

t = v/a

The distance traveled by the tank during this time is:

s = (1/2)at²

[tex]=\dfrac{1}{2} (\dfrac{v}{a})^2a = \dfrac{v^2}{2a}[/tex]

The angle of the free surface relative to the horizontal direction after deceleration is given by:

[tex]\theta' = tan^{-1}\dfrac{s}{h}[/tex]

Substituting the values of v and s, we get:

[tex]\theta' = tan^{-1}\dfrac{\sqrt{2gh}^2}{2ah}\\\\ = tan^{-1}\dfrac{2h}{3a}[/tex]

Substituting the given values of h and a, we get:

[tex]\theta' = tan^{-1}\dfrac{2(9.81)sin(15)}{3.83}\\ = 20.2[/tex]

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Gender inequality in mechanical engineering can manifest through biased hiring practices, limited opportunities for women to advance to leadership roles, and a lack of representation in the industry.

Despite efforts to promote gender equality, women are still underrepresented in the field of mechanical engineering. This can be due to a variety of factors, including biased hiring practices, limited opportunities for career advancement, and a lack of representation in the industry.

To address these issues, it is important for companies and organizations to promote diversity and inclusion initiatives, such as actively recruiting women and people of diverse backgrounds, providing mentorship and networking opportunities, and advocating for policies that support work-life balance and equal pay. By creating a more inclusive environment, the field of mechanical engineering can attract and retain more talented individuals and foster innovation and growth.

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--The complete question is, How does gender inequality manifest in the field of mechanical engineering, and what are some potential solutions to address this issue?--

The plant structure that increases the probability of successful reproduction is flower. So, option B.

The reproductive organs of flowering plants are flowers. The possibility of successful pollination and fertilization is increased by the presence of both male and female reproductive structures in them.

In the flowers, the pollen is considered as the male sex cells. The female part, i.e., the pistil, consists of the ovary, which produces female sex cells or eggs.

There are specialized plant structures in flowers, such as brightly colored petals to attract potential pollinators and extended stamens that require animals to brush against the plants in order to receive the nectar.

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A marathon runner is running the race with a speed of 15 m/s. She completed the race within 15 minutes.

We can start by using the formula

Distance = speed x time

We know that the marathon runner is running with a speed of 15 m/s and completed the race in 15 minutes, which is equivalent to 900 seconds (15 min x 60 s/min). Therefore, we can calculate the distance covered by the athlete as

Distance = 15 m/s x 900 s = 13,500 meters

Now, we need to find the distance covered by the athlete if the speed is doubled. Let's call this new distance d' and new speed s'.

s' = 2 x 15 m/s = 30 m/s

We can use the same formula to calculate the new distance covered

d' = s' x t

Where t is the same for both distances, as the runner completed the race in the same amount of time.

t = 900 s

d' = 30 m/s x 900 s = 27,000 meters

Hence, if the speed of the marathon runner is doubled, she would cover a distance of 27,000 meters.

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The coefficient of static friction between the block of wood and the table is 0.449.

The weight of the block of wood is Mg = 4.0 kg × 9.81 m/s^2 = 39.24 N.

The coefficient of static friction μs is given by the equation μ_s = fs/N, where N is the normal force from the table.

Since the block is not accelerating vertically, we know that N = Mg, so we have:

μs = fs/N = 17.64 N / 39.24 N = 0.449

Therefore, the coefficient of static friction between the block of wood and the table is 0.449.

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Answer:

equator

Explanation:

in south & north pole you could have 20+ hours daylight or night, everyday!

The wavelength of the wave in the spring is 0.357 m.

Wavelength is the length of a complete revolution of a wave.

To calculate the wavelength of the wave in the spring, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for λ

Hence, the wavelength is 0.357 m.

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Information technology has greatly impacted the economy, leading to increased productivity, efficiency, and innovation across industries.

The widespread adoption of information technology in the business world has led to a significant transformation in the way companies operate. Through the use of computers, software, and other digital tools, businesses are now able to streamline their operations, automate processes, and access vast amounts of data that can inform decision-making.

This has resulted in increased productivity, efficiency, and cost savings for companies. Additionally, information technology has facilitated the rise of new industries, such as e-commerce and digital marketing, while also enabling existing industries to adapt and innovate in response to changing market conditions.

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--The complete question is, How has information technology impacted the economy?--

A spring scale with a spring constant of 120 N/m would stretch by 0.14 meters if it had 3.75 J of work done on it.

The work done on a spring can be calculated using formula:

[tex]W = (1/2) * k * x^2[/tex]

where W is the work done in joules (J), k is spring constant in Newtons per meter (N/m), and x is displacement of the spring from its equilibrium position in meters (m).

Rearranging the formula, we get:

x = sqrt(2W/k)

Plugging in given values, we get:

x = sqrt(2 * 3.75 J / 120 N/m) = 0.14 m

Therefore, a spring scale with a spring constant of 120 N/m would stretch by 0.14 meters if it had 3.75 J of work done on it.

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The ball will strike the ground after 8.04 seconds.

Using the kinematic equation for displacement:

y = y0 + v0t - 1/2g*t^2

where:

We want to findt, let's substitute the values:

0 = 58.52 + 19.50t - 1/2(9.81)*t^2

4.905t^2 - 19.50t - 58.52 = 0

Using the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where:

t = (-(-19.50) ± sqrt((-19.50)^2 - 4(4.905)(-58.52))) / 2(4.905)

t = (19.50 ± 31.37) / 9.81

The two possible solutions are:

t1 = 5.61 s (ball on the way up)

t2 = 8.04 s (ball on the way down)

Since the question is asking for when the ball strikes the ground, we take the larger solution, which is:

t = 8.04 s

In other words, the ball will strike the ground after 8.04 seconds.

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1.00 kg of ice at -24.0°C is placed in contact with a 1.00 kg block of a metal at 5.00°C. They come to equilibrium at -8.88°C.

We can use the principle of conservation of heat to solve this problem. The heat lost by the metal must equal the heat gained by the ice.

The heat lost by the metal is given by

Q1 = m1c1ΔT1

Where m1 is the mass of the metal, c1 is its specific heat, and ΔT1 is the change in temperature.

The heat gained by the ice is given by

Q2 = m2c2ΔT2

Where m2 is the mass of the ice, c2 is its specific heat, and ΔT2 is the change in temperature.

Since the two objects come to thermal equilibrium, we can set Q1 equal to Q2

m1c1ΔT1 = m2c2ΔT2

Solving for c1, we get

c1 = m2c2ΔT2 / (m1ΔT1)

By putting these values we get

c1 = (1.00 kg)(2.06 kJ/kg·K)(-24.0°C - (-8.88°C)) / [(1.00 kg)(5.00°C - (-8.88°C))]

c1 = 0.902 kJ/kg·K

Hence, the specific heat of the metal is 0.902 kJ/kg·K.

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A student measured the length of a wire four times using a meter rule, then average length will be 18.55 cm

A student measured the length of a wire four times using a meter rule and obtained the following reading 18.6,18.5,18.6,18.5.

To determine the length of the wire, we need to calculate the average of the four measurements.

Wadding up all the readings and dividing by the number of readings.

Average length = (18.6 + 18.5 + 18.6 + 18.5) / 4

Average length = 74.2 / 4

Average length = 18.55 cm

Therefore, the length of the wire is approximately 18.55 cm.

The question is incomplete and the complete question is

'' A student measured the length of a wire four times using a meter rule and obtained the following readings: 18.6 cm; 18.5 cm and 18.6 cm. Determine the length the length the student should record''.

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The sacrifice involved in making one decision over another  is known as opportunity cost.

The opportunity cost of a choice is described as  the value of the best alternative forgone where, given limited resources, a choice needs to be made between several mutually exclusive alternatives.

When talking about an opportunity cost, it is referred to as those benefits that exist when making a decision which  could either be in business or a personal decision.

The law of increasing opportunity cost sates that as you increase the production of one good, the opportunity cost to produce the additional good will increase . It is always recommended to make a cost-benefit analysis to contemplate all the benefits.  

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#complete question:

What is the sacrifice involved in making one decision over another ?

a) The order in which the objects reach the bottom of the slope depends on their moments of inertia, b) All three shapes will reach the bottom of the slope in approximately the same amount of time, which is around 0.42 seconds, c) The solid cylinder has the greatest moment of inertia, d) All three objects have the same linear acceleration of approximately 1.52 m/s^2, and e) All three objects have the same tangential (linear) velocity of approximately 1.52 m/s.

A slope is a slanted surface that connects two different levels or elevations.

a) The order in which the objects reach the bottom of the slope depends on their moments of inertia. The object with the smallest moment of inertia will reach the bottom first, followed by the object with the next smallest moment of inertia, and so on.

b) The time it takes each shape to reach the bottom of the slope can be calculated using the formula:

t = sqrt(2h/(g*sin(theta)))

where h is the height of the slope (1 m), g is the acceleration due to gravity (9.81 m/s^2), and theta is the angle of the slope (20°).

For the given values, we have:

t_ring = sqrt(21/(9.81sin(20°))) ≈ 0.42 s

t_sphere = sqrt(21/(9.81sin(20°))) ≈ 0.42 s

t_cylinder = sqrt(21/(9.81sin(20°))) ≈ 0.42 s

Therefore, all three shapes will reach the bottom of the slope in approximately the same amount of time.

c) The moment of inertia of a ring, sphere, and solid cylinder can be calculated using the formulas:

I_ring = m*r^2

I_sphere = (2/5)mr^2

I_cylinder = (1/2)mr^2

where m is the mass of the object and r is its radius.

Since all three objects have the same mass and are made from the same material, their radii must be different in order for their moments of inertia to be different. Therefore, the object with the greatest radius will have the greatest moment of inertia. In this case, the solid cylinder has the greatest radius, so it has the greatest moment of inertia.

d) The linear acceleration of each object can be calculated using the formula:

a = gsin(theta)(1 - mu*cos(theta))

where mu is the coefficient of static friction between the object and the slope.

For the given values, we have:

a_ring = 9.81sin(20°)(1 - 0.3cos(20°)) ≈ 1.52 m/s^2

a_sphere = 9.81sin(20°)(1 - 0.3cos(20°)) ≈ 1.52 m/s^2

a_cylinder = 9.81sin(20°)(1 - 0.3*cos(20°)) ≈ 1.52 m/s^2

Therefore, all three objects have the same linear acceleration.

e) The tangential (linear) velocity of each object can be calculated using the formula:

v = r*omega

where omega is the angular velocity of the object, which can be calculated using the formula:

omega = a/r

where a is the linear acceleration of the object and r is its radius.

For the given values, we have:

v_ring = r*omega = r(a/r) = a ≈ 1.52 m/s

v_sphere = r*omega = r(a/r) = a ≈ 1.52 m/s

v_cylinder = r*omega = r(a/r) = a ≈ 1.52 m/s

So, all three objects have the same tangential (linear) velocity.

Therefore, a) The order in which the objects reach the bottom of the slope depends on their moments of inertia, b) All three shapes will reach the bottom of the slope in approximately the same amount of time, which is around 0.42 seconds, c) The solid cylinder has the greatest moment of inertia, d) All three objects have the same linear acceleration of approximately 1.52 m/s^2, and e) All three objects have the same tangential (linear) velocity of approximately 1.52 m/s.

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The mass of the Ball B is 1.35 x 10⁻⁶ kg.

Gravitational Force is described by Newton's law of universal gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The law of universal gravitation is important in many fields, including astronomy, physics, and engineering.

The gravitational force F between two objects of masses m1 and m2 separated by a distance r is given by:

F = G(m₁m₂)/r²

where G is the gravitational constant.

We can rearrange the equation to solve for the mass of Ball B:

m₂ = Fr²/Gm₁

Substituting the given values, we get:

m₂ = (8.7 x 10⁻¹⁰ N)(3.0 m)²/(6.6743 x 10¹¹ N(m^2/kg²))(30 N)

m₂ = 1.35 x 10⁻⁶ kg

Therefore, the mass of Ball B is approximately 1.35 x 10⁻⁶kg.

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Answer:

To determine the force exerted on your hand, we can use the impulse-momentum theorem which states that the change in momentum of an object equals the impulse exerted on it. The impulse is the product of the force and the time of contact. Therefore, we have:

Initial momentum = m * v = 0 (since your hand is initially at rest)

Final momentum = m * vf (where vf is the final velocity of the ball after being caught)

Change in momentum = Final momentum - Initial momentum = m * vf

Impulse = F * t (where F is the force exerted on your hand)

By the impulse-momentum theorem, we have:

m * vf = F * t

Solving for F, we get:

F = m * vf / t

Given, m = 0.168 kg, v = 16 m/s, and t = 0.025 s

Final velocity, vf = 0 m/s (since the ball comes to rest after being caught)

Substituting the values, we get:

F = 0.168 kg * 0 m/s / 0.025 s

F = 0 N

Therefore, the force exerted on your hand when catching a 0.168 kg ball moving at 16 m/s in 0.025 s is 0 N.

Explanation:

A mercury barometer gives the local atmospheric pressure as 750 mmHg, then the absolute pressure of carbon dioxide is 89.87 kPa.

A vacuum gage indicates that the pressure of carbon dioxide in a closed tank is −10 kPa. A mercury barometer gives the local atmospheric pressure as 750 mmHg.

To determine the absolute pressure of carbon dioxide, we need to add the atmospheric pressure to the pressure indicated by the vacuum gauge.

Converting the atmospheric pressure from mmHg to kPa

750 mmHg x (101.3 kPa / 760 mmHg) = 99.87 kPa

Absolute pressure of carbon dioxide

-10 kPa + 99.87 kPa = 89.87 kPa

Therefore, the absolute pressure of carbon dioxide is 89.87 kPa.

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The ratio of their rotational kinetic energies is 4/5 or 0.8.

Let's denote the mass and radius of the cylinder and sphere as "m" and "r", respectively. At the top of the incline, both objects have only potential energy, which is then converted to kinetic energy. At the bottom of the incline, both objects have both translational and rotational kinetic energy.

For a uniform solid cylinder, the rotational inertia is[tex]1/2 * m * r^2[/tex]. For a uniform sphere, the rotational inertia is[tex]2/5 * m * r^2[/tex]. Therefore, the ratio of their rotational kinetic energies is:

(rotational kinetic energy of sphere) / (rotational kinetic energy of cylinder)

[tex]= (2/5 * m * r^2 * (v/r)^2) / (1/2 * m * r^2 * (v/r)^2)[/tex]

= (4/5)

Therefore,  rotational kinetic energy of  sphere is 80% of  rotational kinetic energy of the cylinder at  bottom of the incline.

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--The complete Question is, A uniform solid cylinder and a uniform sphere with the same mass and radius are released from rest at the top of an incline. They both roll without slipping down the incline and reach the bottom with the same translational speed. What is the ratio of their rotational kinetic energies at the bottom of the incline?--

Answer: Fitness assessments are designed to screen for risk of heart disease.

Explanation:

Fitness assessments are medical examinations that are designed to measure a person's physical fitness and identify any health risks they may have. These assessments may include tests of strength, endurance, flexibility, and cardiovascular fitness. One of the primary objectives of a fitness assessment is to screen for the risk of heart disease, which is a major health concern that can be prevented or treated through exercise and other lifestyle changes. While fitness assessments may identify specific injuries or medical conditions, their primary focus is on evaluating a person's overall health and fitness.

The net electric force on charge q2 is 28.7 N.

The net electric force on charge q2 is calculated by applying Coulomb's law of electrostatic force.

F(net) = F(12) + F(23)

The force on q2 due to charge 1 is calculated as;

F(12) = -(9 x 10⁹ x 8 x 10⁻⁶ x 3.5 x 10⁻⁶ )/(0.1²)

F(12) = 25.2 N

The force on q2 due to charge 3 is calculated as;

F(23) = (9 x 10⁹ x 2.5 x 10⁻⁶ x 3.5 x 10⁻⁶ )/(0.15²)

F(23) = 3.5 N

The net force on q2 is calculated as;

F(net) = 25.2 N + 3.5 N = 28.7 N

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The diagram to show behavior of magnetic poles is given.

Magnetic poles can be either north or south. Opposite magnetic poles (i.e., north and south) attract each other, while like magnetic poles (i.e., north and north, or south and south) repel each other. This behavior is due to the alignment of the magnetic fields around the poles.

The strongest part of a magnet's magnetic field is at the poles, while the weakest part is at the sides. Magnetic field lines flow out of the north pole and into the south pole, forming a loop around the magnet. The closer the field lines are to each other, the stronger the magnetic field is in that region.

Overall, this behavior of magnetic poles is a result of the interaction of magnetic fields, and is essential to many technological applications of magnets, such as in electric motors and generators.

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The initial volume of the liquid is 31.4 cm³. The volume coefficient of thermal expansion of the liquid is 0.002 per degree Celsius. A temperature increase of 109.5°C is needed for the liquid to rise to a height of 49cm.

The initial volume of the liquid can be found using the formula for the volume of a cylinder:

V = πr²h

where r is the radius (half the diameter), h is the height, and π is approximately 3.14. Plugging in the given values, we get:

V = π(0.5 cm)²(40 cm)

V = 31.4 cm³

The volume coefficient of thermal expansion (β) is defined as the fractional change in volume per degree Celsius change in temperature. It can be calculated using the formula:

β = ΔV/(VΔT)

where ΔV is the change in volume, V is the initial volume, and ΔT is the change in temperature. We can rearrange this formula to solve for ΔV:

ΔV = βVΔT

We know that ΔT = -10°C (a decrease of 10°C) and that the height decreased from 40cm to 37cm, or by 3cm. The change in volume can be found using the formula for the volume of a cylinder again, with the new height of 37cm:

ΔV = π(0.5 cm)²(40 cm - 37 cm)

ΔV = 0.59 cm³

Plugging in all the values, we get:

0.59 cm³ = β(31.4 cm³)(-10°C)

β = 0.002

To find the change in temperature needed for the liquid to rise to a height of 49cm, we can use the same formula as before, but solve for ΔT:

ΔT = ΔV/(βV)

We know that ΔV is the difference between the initial volume and the volume at the new height, which is:

ΔV = π(0.5 cm)²(49 cm - 40 cm)

ΔV = 6.86 cm³

Plugging in all the values, we get:

ΔT = 6.86 cm³/(0.002)(31.4 cm³)

ΔT = 109.5°C

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The charge required for the fixed point charge is approximately [tex]4.8032 * 10^{-10} C[/tex].

The electrostatic force between the fixed point charge and the electron is equal in magnitude to the gravitational force between the electron and the Earth, so we can set these two forces equal to each other and solve for the charge of the fixed point charge.

Electrostatic force between two point charges is given by Coulomb's law:

[tex]F = k * q1 * q2 / r^2[/tex]

The gravitational force between two masses is given by Newton's law of gravitation:

[tex]F = G * m1 * m2 / r^2[/tex]

Setting these two forces equal to each other and solving for q2, we get:

[tex]k * q1 * q2 / r^2 = G * m_e * m\_earth / r^2[/tex]

Solving for q2, we get:

[tex]q2 = G * m_e * m\_earth / k[/tex]

Substituting the given values, we get:

[tex]q2 = (6.67430 * 10^{-11} N * m^2 / kg^2) *\\ (9.10938356 *10^{-31} kg) *\\ (5.9722 *10^{24} kg) / (8.98755 * 10^9 N * m^2 / C^2)[/tex]

[tex]q2 = 4.8032 * 10^{-10} C[/tex]

Therefore, the charge required for the fixed point charge is approximately [tex]4.8032 * 10^{-10}[/tex]C.

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