When a soccer ball is rolling along a grassy field, it does not continue moving forever. What force is acting upon it to change its state?.

The size of an atom is primarily determined by the size of its electron cloud, which is much larger than the size of its nucleus.

The diameter of an atom can be estimated using the Bohr model, which states that the electron orbits the nucleus at a distance proportional to the square of the principal quantum number. For a hydrogen atom, the most basic and simplest atom, the radius of the first orbital is approximately 0.0529 nanometers.

To convert this value to feet, we can use the conversion factor of 1 foot = 30.48 cm = 30.48 x 10^-2 m = 30.48 x 10^8 nm. Therefore, the diameter of a hydrogen atom in feet can be estimated as:

2 * 0.0529 nm * (30.48 x 10^8 nm/foot) = 3.29 x 10^-10 feet

Note that this is an estimate and the actual size of an atom may vary slightly depending on the atom's structure and the conditions in which it is observed. However, this estimate can give us a rough idea of the scale of an atom in comparison to a pencil eraser, which is much larger.

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The compression stroke of a four-cycle diesel engine, begins when the piston reaches TDC (top dead center) on the intake stroke and begins moving downward.

During the compression stroke, the air-fuel mixture is compressed by the piston, increasing its temperature and pressure. This high-pressure and high-temperature air-fuel mixture is then ignited by the spark plug or the high compression pressure in the case of a diesel engine, which drives the piston back up and completes the power stroke. The compression stroke is an essential part of the internal combustion process and helps to create the power needed to drive the vehicle. The engine's compression stroke is the phase during which the fuel/air combination is compressed prior to ignition. On the compression stroke, the intake valve closes and the piston begins to move. The piston ascends the cylinder during the compression stroke, compressing the fuel-air mixture.

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Jack's preferences are strictly monotonic and exhibit diminishing marginal utility.

Strictly convex preferences mean that Jack's preferences between two bundles of goods do not change as the proportion of goods in the bundle changes. In other words, Jack values diversity of goods and the more he has of one good, the less he values additional units of that good.

The fact that Jack finds the bundles (1,9) and (9,1) to be indifferent means that he values both of these bundles equally, or in other words, he has the same utility from both of these bundles. This implies that Jack's marginal utility of the two goods decreases as he consumes more of either of them.

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The least harmful form of ionizing radiation is considered to be low-energy X-rays. X-rays are a form of electromagnetic radiation with a higher frequency and energy than visible light.

They have sufficient energy to ionize atoms and molecules, but their low energy level means that they generally do not cause significant harm to living tissue. However, it is important to note that even low-energy X-rays can still be harmful if a person is exposed to a large dose of them. This is why it is important to limit exposure to ionizing radiation, including X-rays, by using protective measures such as lead shielding and keeping the exposure time as short as possible. In general, the harm from ionizing radiation is related to the energy of the radiation and the amount of exposure. Higher energy and higher dose levels are more harmful. So, it is always important to minimize exposure to ionizing radiation, regardless of the type.

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The statement that's true about the tire pressure (in pounds per square inch) of tires in different cars is the data are continuous because the data can take on any value in an interval (option D)

When we measure tire pressure in a car, we are working with a continuous variable. From 0 psi to a high value that would cause the tire to burst, the air pressure can range in value.

There are an infinite number of additional valid values for a continuous variable between any two values, which can be used to distinguish it from discrete variables. Contrary to popular belief, discrete variables have an integer number (0, 1, 2,...) of possible values between any two discrete values. These are regarded as countable values for a discrete variable because there are an infinite number of them.

The distinction between discrete and continuous data is that the former only accepts whole numbers as values, while the latter accepts any value along an interval. Because they can take any value on the interval, the tire pressures on various cars represent continuous data.

The question is incomplete, it should be:

State whether the data described below are discrete or continuous, and explain why. The tire pressures (in pounds per square inch) of tires on different cars Choose the correct answer below. A. The data are continuous because the data can only take on specific values. B. The data are discrete because the data can take on any value in an interval. C. The data are discrete because the data can only take on spacific values. D. The data are continuous because the data can take on any value in an interval.

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The value of a is calculated to be -1 from the equation of linear combination of vectors.

The given vectors are,

v = <−3 −1>, w = <−2 −3 >, u = <−3 −8 >

To find the value of a substitute the value of the vectors in the given equation,

u = av + bw

<-3, -8 > = a <-3, -1> + b <-2, -3>

The vector can be written as follows,

-3a -2b = -3 ----(1)

-a -3b = -8 ----(2)

Solving the equations, we have

-3a -2b = -3  

a + 3b = 8 ⇒ 3a +9b = 24

7 b = 21

b = 3 and a = -1

Thus, the value of a is determined to be -1.

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It is possible to receive a severe electrical shock from an ordinary outlet that would prevent a person from releasing the wire with dry hands, but it is not likely.

Our body depends on neurons to receive and transmit any signals. The sodium concentration in our body is disturbed by any external stimuli, and it instigates the neurons to send electric impulses in the brain.

Upon interpreting, the brain sends back signals to the muscles connected by neurons. When a person gets a severe shock, the signal gets disturbed, and a huge surge of electricity reaches the brain. This causes the brain to send reflex stimuli for the contraction of the muscle in the palm. Thus, the person will be unable to leave the wire even if he has dry hands.

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W = fd means that the work is equal to the force f times the distance d. The work is W = fd cosФ if the force is applied at an angle of Ф to the displacement.

Work is a unit of energy that is generated when a force is applied to the body and the body is moved. The Joule is the SI unit of work.

A displacement and the force that triggered it are necessary for a force to be considered to have accomplished work on an item.

The displacement of the body: At constant load and constant angle between force and displacement, work is directly proportional to the displacement.

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The work formula is used to calculate the amount of energy required to move an object a certain distance.

Energy is a fundamental concept in physics. It is defined as the capacity for doing work or the ability to produce change. Energy can be found in many forms, such as thermal, kinetic, chemical, electrical, gravitational, and nuclear. It can be converted from one form to another and can be transferred from one object to another. Energy is neither created nor destroyed, but can be changed from one form to another. This concept is known as the law of conservation of energy. In physics, energy is used to describe the ability to do work.

It is expressed as the multiplication of the magnitude of displacement (d) and the component of the force (F) acting on the object. The angle θ is the angle between the direction of the force and the direction of the displacement. The cosine of this angle (cosθ) is used to account for the fact that the force does not always act in the same direction as the displacement. The work formula can be expressed
as:  W = F × d × cosθ.

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A jet stream is a fast-flowing, narrow air current found in the upper levels of the Earth's atmosphere. It is formed due to differences in air temperature and pressure, and it can have a significant impact on the weather and climate.

Jet streams are formed as a result of the movement of air from warm to cold regions.

The Great Red Spot (GRS) on Jupiter is a long-lived, high-pressure storm that has been observed for over 300 years. Scientists believe that the stability and longevity of the GRS can be attributed to several factors, including:

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As the frequency of a wave decreases, the wavelength increases, and the energy decreases.

The wavelength and energy of a wave are inversely proportional, meaning that as one increases, the other decreases, and vice versa.

In the case of a wave, as the frequency decreases, the wavelength increases. This is ecause the speed of a wave is constant, and it is equal to the frequency multiplied by the wavelength (v = fλ). As the frequency decreases, the wavelength must increase in order to keep the product (v) constant.

At the same time, as the frequency decreases, the energy of the wave decreases as well. This is because the energy of a wave is proportional to the square of its frequency (E ∝ f^2). As the frequency decreases, the energy decreases in proportion to the square of the decrease in frequency.

Therefore, as the frequency of a wave decreases, the wavelength increases, and the energy decreases.

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You need a capacitance of 6.00 μF to store 60.0 μC of charge using  single 10.0-V battery.

The amount of charge that can be stored at a given voltage by an electrical component is called a capacitor. The unit of capacitance is Farad (F) and 1F capacitor charged to 1V will hold one Coulomb of charge.

Capacitance, C, can be calculated as :

C = Q / V = 60.0 μC / 10.0 V = 6.00 μF

So, you need a capacitance of 6.00 μF to store 60.0 μC of charge using a single 10.0-V battery.

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The solar calendar is based on the earth's orbit around the sun, with a year being 365 or 366 days long, depending on whether it's a leap year. The lunar calendar is based on the phases of the moon, with a month being 29.5 or 29.53 days long.

The solar calendar has a fixed year length, while the lunar calendar has 12 or 13 lunar months in a year, which is about 11 days shorter than a solar year. The difference between the two calendars leads to the occurrence of lunar holidays like the Islamic and Jewish calendars, which drift through the solar calendar year. The solar calendar is used in most countries around the world, while the lunar calendar is still used in some countries, especially those with religious traditions linked to the phases of the moon.

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Based on the recoil distance of the two balls, the ball that has greater density is Ball A.

The relationship between a substance's mass and the amount of space it occupies is known as its density (volume).

The density of a substance is determined by the mass, size, and arrangement of its atoms. Density (D) is defined as the product of a substance's mass and volume.

Comparing the densities of the balls show that the ball with the lesser density will recoil farther than the ball with the greater density because it has less momentum.

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200 degrees Celsius is equivalent to 392 degrees Fahrenheit (200°C 9/5) and 32. There are several standard temperature scales, including Celsius.

Bread is baked for 25 to 28 min at room temperature of 160 to 180 degrees Celsius. For around 40 to 45 minutes, the thimble cake is energy at 150 to 160 degrees Celsius. For 15 to 25 minutes, bake cookies at 170 to 190 degrees Celsius. Cream puffs bake for 25 to 30 minutes at 190 to 200 degrees Celsius. an appropriate way to.

According to Al Jazeera, Death Valley in California recorded the highest temperature ever, which was 134 ℃, or 56.7 degrees C, in 1913. By The highest temperatures ever recorded in this area are: Europe: 128 F (Tunisia, 1931) Asia.

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Weber's Law is a principle in psychology that states that the difference threshold, or just noticeable difference (JND), between two stimuli is proportional to the magnitude of the stimuli. In other words, the greater the weight, the more weight is needed to be added for the change to be noticeable.

Applying this to Samson's weightlifting, we can calculate the JND by using the formula JND = k * stimulus, where k is a constant of proportionality known as Weber's fraction. In this case, the stimulus would be 240 pounds, the weight that Samson typically lifts.

A commonly used value for Weber's fraction in weightlifting is 0.2, meaning that the JND is 20% of the stimulus. So, for Samson, the JND would be 240 * 0.2 = 48 pounds. This means that for Samson to notice an increase in weight beyond 240 pounds, the weight would need to be increased by at least 48 pounds.

Therefore, if Samson wants to sense an increase in weight, he would need to lift a minimum of 240 + 48 = 288 pounds. However, it is important to keep in mind that the Weber's fraction may vary between individuals, and it may also depend on the specific task and the individual's level of experience and sensitivity.

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The elastic constant for the spring is 205,7 N/m. The result is obtained by using the formula in Hooke's law.

The Hooke's Law states that the restoring force of a spring equals the spring constant times the change in length. It can be expressed as

F = - kΔx

Where

Note: the minus sign is used to indicate that F is in the opposite direction to the displacement of a free end.

A certain spring has

Find the elastic constant!

Using the equation apply in Hooke's law, the elastic constant is

F = kΔx

72 = k(0.35)

k = 72/0.35

k = 205,7 N/m

Hence, the magnitude of the spring elastic constant is 205,7 N/m.

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The maximum shear stress at 18 degrees and the primary stress, respectively, are both 36.05 mpa.

The Mohr method is a very useful tool for finding primary stress, maximum shear stress, principle plane, or angle of the action. It is a technique that plots a circle using a graphical way in order to gather the necessary information.

Shear stress= 30

Tensile stress= 40

Compressive Stress= -40

Mohr circle using data is:

Figure

And the principal stress will be 36.05 mpa and maximum shear stress would be 36.05 mpa at 18 degrees.

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Answer:

The four types of thermal energy we have...

Explanation:

Evaporation

By heating a substance to a temperature where the vapour pressure is appreciable and atoms or molecules are lost from the surface in a vacuum, a substance is said to have undergone thermal evaporation.

Conduction

The transfer of thermal energy within a substance or between materials in contact is known as thermal conduction.

Convection

Convection is the process through which matter moves inside fluids to transfer thermal energy.

Radiation

The electromagnetic radiation that a body produces when its temperature is higher than absolute zero is known as thermal radiation.

Have a lovely day :)

We have four forms of thermal energy:

Evaporation

Conduction

Convection

Radiation

The four types of thermal energy are:

Evaporation: Thermal evaporation occurs when a material is heated to a temperature where the vapour pressure is perceptible and atoms or molecules are lost off the surface in a vacuum.

Conduction: Heat conduction is the flow of thermal energy within a substance or between materials in contact.

Convection: Convection is the movement of materials inside fluids to transmit thermal energy.

Radiation: The electromagnetic radiation that a body produces when its temperature is higher than absolute zero is known as thermal radiation.

Here,

The four types of thermal energy we have...

Evaporation

Conduction

Convection

Radiation

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The speed of the southbound boat is 6 mph.

Acceleration or a rapid rate of motion are most frequently described as speed. When something accelerates too quickly, it may veer off course, similar to a child riding a bike down a steep hill in an uncontrollable manner.

Let speed of southbound boat be X mph

So speed of eastbound boat =X+2 mph

After 5 hrs, south boat has travelled 5X miles & east boat has travelled 5× (X+2) = 5X+10 miles

(5X)^2 + (5X+10)^2 = 50^2

25X^2 + 25X^2 + 100 + 100X = 2500

Or 50X^2 + 100X-2400 = 0

Or X^2+2X-48=0

(X-6)(X+8)=0

we get X=6 mph

Thus, the speed of the southbound boat is 6 mph.

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The same capacitors, if connected in parallel across the same line, the energy stored is 36 J. The individual capacitances is 3.0μF.

What is capacitor?

A capacitor is a two-terminal electrical part with the capacity to store energy in the form of an electric charge. It uses two electrical cables that are separated from one another. The void between the conductors can be filled with vacuum or a dielectric, an insulating material.

What is energy?

The definition of energy is "capacity to do work, which is ability to apply force causing displacement of an object." Energy is just the force that moves objects, despite this definition's seeming complexity.

Let the capacitance of two capacitors be C1and C 2

​Line voltage V=4000 volts

Parallel connection :

Equivalent capacitance of series connection Cp =C1+C2

Energy stored Ep= 1/2 cpv²

∴ 36=1/2(C 1+C2 )(4000)²

C1+C2=4.5μF

We get C2=4.5μF−C1

Series connection :

Equivalent capacitance of series connection Cs= C₁C₂/C₁+C₂= C₁C₂/4.5 μF

C1C2 =4.5μF

Or C1(4.5−C1 )=4.5

Solving we get C1=1.5μF

C2=4.5−1.5=3.0μF

Therefore, the same capacitors, if connected in parallel across the same line, the energy stored is 36 J. The individual capacitances is 3.0μF.

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​

​

A beam has a square cross-section, a x a, where a is the linear dimension, and is subject to a pure bending moment, The minimum design factor such that the beam is guaranteed not to fail is (1.1 x M) / (1.12 x σ x (1.05 x a)^2 / 6).

The minimum design factor can be found by combining the uncertainties in the bending moment dimension, the cross-sectional area, and the material strength into a single factor that represents the safety margin against failure.

Let's call the design factor "n".

= n

= M / (σ.b.d^2 / 6)

here M is bending moment,

σ is material strength,

b is width of the cross-section,

d is height of the cross-section.

For a square cross-section, b = d = a.

The uncertainties in M, a, and σ can be taken into account by using the worst-case scenarios. In this case, the uncertainty in M is ±10%,

The minimum value for M is 0.9 x M

The maximum value for M is 1.1 x M.

The uncertainty in a is ±5%,

The minimum value for a is 0.95 x a

The maximum value for a is 1.05 x a.

The uncertainty in σ is ±12%,

The minimum value for σ is 0.88 x σ

The maximum value for σ is 1.12 x σ.

To find the minimum value for n, we'll use the minimum values for M, a, and σ:

= n

= (0.9 x M) / (0.88.σ.(0.95.a)^2 / 6)

To find the maximum value for n, we'll use the maximum values for M, a, and σ:

= n

= (1.1 x M) / (1.12 x σ x (1.05 x a)^2 / 6)

The minimum value for n is the larger of these two values, as it represents the worst-case scenario. If the minimum value for n is greater than 1, then the beam is guaranteed not to fail. If the minimum value for n is less than 1, then the beam is not guaranteed not to fail and must be redesigned to have a higher n value.

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The energy of the car at the bottom of the hill, given that it has a velocity of 10 m/s is 40000 J

We know that kinetic energy is the energy of moving objects and it is defined according to the following formula:

KE = ½mv²

Where

With the above formula, we can obtain the energy of the car at the bottom. Details below:

KE = ½mv²

KE = ½ × 800 × 10²

KE = 400 × 100

KE = 40000 J

Thus, the energy at the bottom is 40000 J

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Coefficient of volume expansion be for this metal is 7.66×10⁻⁵ K⁻¹

From the question,

γ = (v₂-v₁)/[v₁(t₂-t₁)]....................... Equation 1

Where γ = coefficient of volume expansion, v₁ = initial volume, v₂ = Final volume, t₁ = initial temperature, t₂ = Final Temperature.

Given: v₁ = 26.1 cm³, v₂ = 26.2 cm³, t₁ = 25 °C, t₂ = 75 °C.

Substitute these values into equation 1

γ = (26.2-26.1)/[26.1(75-25)]

γ = 0.1/(26.1×50)

γ = 0.1/1305

γ = 7.66×10⁻⁵ K⁻¹

In general, all substances expand when heated, except for water at temperatures between 0oC and 4oC, their volume decreases. Expansion of the substance generally occurs in all directions, towards the length, towards the width and towards the thickness. However, in certain discussions we may only look at expansion in one particular direction, for example in the direction of length, so we only discuss length expansion.

For liquids, because the shape is not certain, we only discuss the volume expansion. As for solids, which have a fixed shape, then in the expansion of solids we can discuss the expansion of length, area expansion and volume expansion.

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The statement that best describes what happened to the wave is D. the wave was transmitted through the object

A wave is a dynamic disturbance of one or more quantities that propagates through time. Quantities may oscillate repeatedly around an equilibrium value at a certain frequency if waves are periodic.

Hence, because it is stated that the wave was traveling through air and met an object and passes through it with no change in speed, energy, or direction, this means it was transmitted through the object

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A wave traveling through air meets an object and passes through it with no

change in speed, energy, or direction. Which statement best describes what

has happened to the wave?

O A. The wave was absorbed by the object.

O B. The object's surface reflected the wave.

O C. The object caused the wave to refract.

O D. The wave was transmitted through the object.

As the frequency of vibration of the wave generator increases, the wavelength of the waves will decrease.

Waves are unsettling influences that movement through a medium, like water or air, and move energy without the exchange of mass. The recurrence of a wave alludes to the quantity of complete wave cycles that happen in a unit of time, normally estimated in Hertz (Hz). At the point when the recurrence of a wave generator expands, the frequency of the subsequent waves diminishes. This is on the grounds that the frequency is the distance between two successive pinnacles (or box) of a wave. In the event that the recurrence builds, there are more tops in a given unit of time, and that implies the distance between them should diminish. Subsequently, the frequency of the waves diminishes.

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Without more information, it is impossible to estimate the light output of the stage, which has six gels covering the spotlight.

However, without knowing more about the exponential relationship and the characteristics of the gels, it is impossible to precisely calculate the intensity of the light on stage with six gels over the spotlight. The statement that the temperature decays exponentially with the thickness of material covering it may imply that the intensity of light is proportional to the exponential of the thickness of material. It would be important to know more about how the exponential decrease of temperature and the thickness of the material relate in order to calculate the intensity. Additionally, the gels' characteristics, such as their optical characteristics, may also be important in

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1- The amount of heat added at constant pressure: The amount of heat added at constant pressure can be calculated by using the formula qp = cv(T2 - T1).

Constant pressure is a type of pressure that remains the same even when external forces are applied to it. It is also known as unchanging pressure or steady pressure. Constant pressure is usually measured with a barometer, which is a device used to measure atmospheric pressure. Constant pressure is most commonly seen in the form of air pressure, which is the pressure of the air around us. It is important to note that although the pressure remains constant, the temperature and density of the air can change. Constant pressure is essential for a variety of applications, such as in aircraft, where the air pressure in the cabin must remain constant for the comfort of the passengers.

In this case, qp = 0.719 kJ/kg.K (2200 - 273) = 1418.7 kJ/kg. 2- The amount of heat added at constant volume: The amount of heat added at constant volume can be calculated by using the formula qv = cp(T2 - T1). In this case, qv = 1.007 kJ/kg.K (2200 - 273) = 1810.7 kJ/kg. 3- The net work done by the cycle: The net work done by the cycle can be calculated by using the formula Wnet = qp - qv. In this case, Wnet = 1418.7 - 1810.7 = -392 kJ/kg. 4- The thermal efficiency of the cycle: The thermal efficiency of the cycle can be calculated by using the formula nth = (Wnet/qp) x 100. In this case, nth = (-392/1418.7) x 100 = -27.6%. 5- The mean effective pressure: The mean effective pressure can be calculated by using the formula m = (2/1-r) x (P2/P1). In this case, m = (2/1-18) x (2200/100) = 733.3 kPa.

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Answer:To solve this problem, we will use the following constants:

g

=

9.8

m

/

s

2

is the acceleration due to gravity

m

=

1.67

×

10

−

27

k

g

is the mass of a proton

q

=

1.602

×

10

−

19

C

is the charge of a proton

Let us first calculate the weight of a proton. To do so, we use:

F

=

m

g

We substitute:

F

=

(

1.67

×

10

−

27

k

g

)

(

9.8

m

/

s

2

)

We will get:

F

=

1.6366

×

10

−

26

N

As per the problem, the electrostatic force between the protons must be equal to the weight we derived. To calculate the electrostatic force, we use Coulomb's law:

F

=

k

q

1

q

2

r

2

Since we are dealing with two protons, we set:

q

1

=

q

2

=

q

We simplify:

F

=

k

q

2

r

2

We isolate the distance r:

r

=

√

k

q

2

F

We substitute:

r

=

√

(

9

×

10

9

N

m

2

/

C

2

)

(

1.602

×

10

−

19

C

)

2

1.6366

×

10

−

26

N

We get:

r

=

0.12

m

Explanation:

The protons must be placed at a distance of 7.42×10¹⁷ m apart so that the electrostatic force between them is equal to the weight of one proton.

Mass of the proton, = 1.67×10⁻²⁷ kg

Weight of the proton, W = 1.67×10⁻²⁷×9.81 = 1.64×10⁻²⁶ N = F

Charge on one proton, q = 1

Let the distance between proton, = d

Constant of permittivity of vacuum, ε₀ = 8.8 × 10⁻¹² C²/N-m²

Electrostatic force between two proton, F = q²/(4πε₀d²)

1.64×10⁻²⁶ = 1²/(4π × 8.8 × 10⁻¹² × d²)

d² = 5.514 × 10³⁵

d = √(5.514 × 10³⁵)

d = 7.42×10¹⁷ m

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The final momentum - initial momentum is the change in momentum.

Momentum is defined as mass multiplied by velocity.

m1 = initial momentum, m2 = final momentum, m = momentum change

Also, we need the magnitude of the change in momentum here, so please disregard the sign of momentum.

(A) m1 = 10*3 = 30 kg-m/s

m2 = 10 *0 = 0 kg-m/s

m = m2-m1= | -30 | = 30 kg-m/s

(B) m1 = 10 kg-m/s

m2 = 10 * (-1)  = -10 kg-m/s

m = -10 -10 = | -20 | = 20 kg-m/s

(C) m1= 40 kg-m/s

m2 = -20 kg-m/s

m = | -60 | = 60 kg-m/s

(D) m1= 30 kg-m/s

m2= -30 kg-m/s

m = | -60 | = 60 kg-m/s

(E) m1= 40 kg-m/s

m2 = 0 kg-m/s

m = | -40 | = 40 kg-m/s

(F) m1 = 20 kg-m/s

m2 = -20 kg-m/s

m =| -40 | = 40 kg-m/s

(G) m1 = 20 kg-m/s

m2 = 0

m = | -20 |= 20 kg-m/s

(H) m1 = 20 kg-m/s

m2 = -40 kg-m/s

m= | -60 | = 60 kg-m/s

Greatkg-m/sest to least ranking :

C = D = H> E = F > A > B = G

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Distance between the particles when t = 4s:To find the distance between A and B, we need to find their positions as a function of time.

The position of particle A can be found using the equation:

[tex]x A = (1/2)at^2 + v0t + x0,[/tex]

where[tex]v0 = 0 m/s[/tex] (since both particles start from rest), [tex]x0 = 0 m[/tex], and[tex]a = 6 m/s^2.[/tex]

So,[tex]x A = (1/2)(6 m/s^2)(4 s)^2 = 48 m[/tex]

The position of particle B can be found using the equation:

[tex]x B = (1/2)at^2 + v0t + x0,[/tex]

where [tex]v0 = 0 m/s[/tex] (since both particles start from rest), [tex]x0 = 0 m[/tex], and [tex]a = (12t^2 - 8) m/s^2.[/tex]

So, [tex]x B = (1/2)((12)(4^2) - 8) (4s)^2 = 64 m[/tex]

The distance between the two particles at t = 4 s is [tex]|x A - x B| = |48 m - 64 m| = 16 m.[/tex]

Total distance traveled by each particle in t = 4s:

The total distance traveled by particle A in 4 seconds can be found using the equation:

[tex]d A = (1/2)at^2 + v0t + x0[/tex],

where[tex]v0 = 0 m/s[/tex] (since both particles start from rest), [tex]x0 = 0 m[/tex], and[tex]a = 6 m/s^2.[/tex]

So,[tex]d A = (1/2)(6 m/s^2)(4 s)^2 = 48 m[/tex]

The total distance traveled by particle B in 4 seconds can be found using the equation:

[tex]dB = (1/2)at^2 + v0t + x0[/tex],

where [tex]v0 = 0 m/s[/tex](since both particles start from rest), [tex]x0 = 0 m[/tex], and [tex]a = (12t^2 - 8) m/s^2.[/tex]

So, [tex]dB = (1/2)((12)(4^2) - 8) (4s)^2 = 64 m[/tex]

In 4 seconds, particle A travels a total of 48 m and particle B travels a total of 64 m.

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