If it has enough kinetic energy, a molecule
at the surface of the Earth can escape the
Earth’s gravitation.
The acceleration of gravity is 9.8 m/s^2
and the Boltzmanns’ constant is 1.38066 ×
10−23 J/K.
Using energy conservation, determine the
minimum kinetic energy needed to escape in
terms of the mass of the molecule m, the
free-fall acceleration at the surface g, and the
radius of the Earth R.

1. Kmin =1√2m g R
2. Kmin = m g R
3. Kmin = 2 m g R
4. Kmin =1/3m g R
5. Kmin =1/2m g R

Answers

Answer 1

Minimum kinetic energy needed to escape is calculated as:(5) Kmin = (1/2)m g R.

What is kinetic energy?

The form of energy that it possesses due to its motion is referred as kinetic energy.

As U = -GMm/R

G is gravitational constant, M is mass of the Earth, m is mass of molecule, and R is radius of the Earth.

Kinetic energy of the molecule is given by: K = (1/2)mv²

v is velocity of molecule.

At the surface of the Earth, velocity of the molecule needed to escape  Earth's gravitation is given by: v = √(2GM/R)

Kmin = (1/2)mv² = (1/2)m(2GM/R) = GMm/R

So, minimum kinetic energy needed to escape in terms of mass of molecule m, free-fall acceleration at surface g and radius of Earth R is calculated as: Kmin = GMm/R = (6.6743 × 10⁻¹¹ m³/kg/s²)(M/R)(m) = (9.81 m/s²)(R)(m)

Answer is (5) Kmin = (1/2)m g R.

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Related Questions

A high frequency sound wave corresponds to high _____.

Answers

A highly frequency sound wave corresponds to a high pitch sound

discuss impact of Newton's second law on roads​

Answers

Answer:

The second law: When a force is applied to a car, the change in motion is proportional to the force divided by the mass of the car. This law is expressed by the famous equation F = ma, where F is a force, m is the mass of the car, and a is the acceleration, or change in motion, of the car

why are illegal drugs dangerous

Answers

Answer:

Illegal drugs are dangerous because once someone starts doing drugs they go insane for more and their demand for my drugs can be so dangerous that they would even sometimes harm the people close to them and, In some cases people start to hate them selves and some even killed themselves.

5) the platter in a belt drive turntable is driven by a belt that wraps around a hub, of radius 3.00 cm, below the platter and around the shaft of the motor. if the platter rotates at 33.3 rpm and the motor rotates at 60 rpm, what is the required radius of the shaft?

Answers

The required radius of the shaft is 1.66 cm.

A radius of a circle or sphere is any of the road segments from its middle to its perimeter, and in greater current usage, it's also their duration. The name comes from the Latin radius, which means ray however also observed as a chariot wheel.

The radius of a circle is the gap from the middle of the circle to any factor on its circumference. it's also denoted via 'R' or 'r'.while the radius of a circle runs from its center to its facet, the diameter runs from aspect to aspect and cuts thru the middle. A circle's diameter basically splits the shape in half.

Calculation:-

w = v/r

W₁/w₂ = r₂/r₁

r₂ = (w₁/w₂) × r₁

   = (33.3/60) × 3

  = 1.66 cm

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a fully dressed person is at rest in the middle of a pond on perfectly frictionless ice and must get to shore. how can this be accomplished? explain in terms of momentum conservation.

Answers

Throwing the clothes with a force can exert an equal force on the person.

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

The person needs to remove his clothes and throw it to the opposite direction with a force, such that the cloth exerts an equal and opposite force to the person, thus he can move forward to the shore.

The momentum of the person will be cancelled by the equal and opposite momentum of the clothes. So, the momentum is conserved.

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A clock which has brass pendulum beats seconds correctly when the temperature of the room is 30° C. how many seconds will it gain or lose per day when the temperature of the room falls to 10° C?

Answers

Answer:A::C

Solution :

ΔT=

1

2

 

TαΔθ

rArr Δt=

ΔT

T1t

 

But T′≈T

∴Δt=

1

2

 

αΔθ(t)

=

1

2

 

×0.000012×20×24×3600

=10.37s

At higher temperture, length of pendulum clock will be more. So, time period will be more and it will lose the time.

Explanation:

Which of the following substances is the closest to a neutral pH? O A. milk

Answers

Answer:

The answer is water

Explanation:

it has a netural ph of 7.0

why is the only option milk?

The Ph for milk is about 6.5 to 6.7,  it varies becauses milks gets sour when it rots.

How do greenhouse gasses help warm the planet?

Answers

Answer:

Greenhouse gases include carbon dioxide, methane, nitrous oxide and other gases that accumulate in the atmosphere and create the heat-reflective layer that keeps the Earth at a livable temperature. These gases form the insulation that keeps the planet warm enough to support life.

A boy of 50 kg climbs a wall 2m high. Calculate the change in potential energy of the boy

Answers

Answer:

If this is the question : boy weighing 50kg climbs up a vertical height of 100m. Calculate the amount of work done by him. How much potential energy does he gain (g=9.8m/s2)

So the answer will be:

mass of boy = m = 50 kg   
height = h = 100m  

 since boy does not move anything with his force, work done by him is zero    work done on the boy = gain in potential energy   
 P.E=mgh    P.E=50×9.8×100   P.E=49KJ  so, potential energy gained by boy is 49 KJ 

Explanation:

How much work is done by a pump to slowly compress, isothermally, 3.40 L of nitrogen at 0 ∘C and 1.00 atm to 1.70 L at 0 ∘C?

Answers

The work done by the pump is -39.5 J.

The work done on a system during an isothermal compression can be calculated using the equation:

W = -nRT ln(V2/V1)

where n is the number of moles of gas, R is the gas constant (8.31 J/mol•K), T is the temperature in Kelvin, V1 is the initial volume, and V2 is the final volume.

Converting the temperature to Kelvin:

0 ∘C = 273.15 K

Using the ideal gas law:

n = PV/RT

P = 1.00 atm = 1.00 x 10^5 Pa

R = 8.31 J/mol•K

T = 273.15 K

Solving for n:

n = (PV) / RT

n = (1.00 x 10^5 Pa)(3.40 L) / (8.31 J/mol•K)(273.15 K)

n = 0.0167 moles

Substituting the values into the equation for work:

W = -nRT ln(V2/V1)

W = -(0.0167 moles)(8.31 J/mol•K)(273.15 K) ln(1.70 L/3.40 L)

W = -39.5 J

The work done by the pump is -39.5 J. This means that 39.5 J of energy is required to compress the gas isothermally from 3.40 L to 1.70 L.

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Prelab exercise 1. Why is it important for your measurements that the track is level?

Answers

It is very important for your measurements that the track is level because unlevel track change the acceleration of an object.

Why track's level is important?

A non-level track leads to bring change in the acceleration of an object which leads to different value of experiment.

So we can conclude that it is important for your measurements that the track is level because unlevel track change the acceleration of an object.

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The track must be level for your measurements because an unlevel track changes the acceleration of an object.

What is measurement?

It is defined as the numerical quantity that gives an idea about object length, width, and many more. It can be used to compare two objects.

The non-level track causes changes in an object's acceleration, resulting in various experiment values.

As a result, we can deduce that now the levelness of the track is critical for your measurements, as an uneven track changes an entity's acceleration.

Thus, the track must be level for your measurements because an unlevel track changes the acceleration of an object.

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which direction are the courts moving regarding the rights of the accused?

Answers

The direction of the courts in recent years has been towards expanding and strengthening the rights of the accused, while also ensuring that justice is served and the rights of victims are protected.

One important development has been the increased recognition of the importance of the right to counsel. The Supreme courts has clarified that this right applies not only at trial, but also interrogations and other critical stages of criminal proceedings. The Court has also recognized that the right to counsel encompasses the right to effective assistance of counsel, meaning that the defendant's lawyer must be competent and provide a proper defense.Another area of focus has been the use of evidence obtained through unconstitutional means. The Supreme Court has ruled that such evidence cannot be used in court, even if it was obtained in good faith. This protects the accused from having their rights violated and ensures that only reliable and trustworthy evidence is used in criminal proceedings.Finally, the courts have also been moving towards greater protection for the rights of individuals who have been wrongfully convicted. This includes expanding the right to post-conviction DNA testing, as well as the right to compensation for individuals who have been wrongfully imprisoned.

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Why are temperatures in the thermosphere not strictly comparable to those experienced near earth's surface?

Answers

Temperatures in the thermosphere are not strictly comparable to those experienced near Earth's surface because the gases of the thermosphere are moving at very high speeds, and the temperature is very high.

The thermosphere lies among the exosphere and the mesosphere. “Thermo” way warmness and the temperature in this layer can reach as much as 4,500 tiers Fahrenheit. in case you have been to hang around inside the thermosphere, though, you'll be very cold because there are not sufficient fuel molecules to transfer the warmth to you.

The thermosphere is the outer layer of the Earth's surroundings, extending from about 53 miles to greater than 370 miles above the surface. The temperature increases rapidly in this layer due to the absorption of huge quantities of incoming excessive electricity sun radiation by using atoms of nitrogen and oxygen.

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A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.

Answers

Answer: 8.1m/s^2

Explanation:

For this question, in order to solve it, we have to use the second equation of motion which will be:

s = ut + 1/2at^2

where,

u = initial velocity

v = final velocity

t = time

a = acceleration

Since u = 0, then

a = 2s/t^2

a = 2 × 110/5.21^2

a = 220/27.1441

a = 8.1m/s^2

What is the estimated effective nuclear charge, zeff, experienced by an electron in a 3p orbital of a chlorine atom?.

Answers

estimated effective nuclear charge experienced by a 3 p electron of chlorine is 6.1.

What is nuclear charge ?

In atomic physics, the net nuclear charge is the actual amount of positive (nuclear) charge experienced by electrons in a multi-electron atom. The term "effective" is used because the shielding effect of negatively charged electrons prevents higher energy electrons from experiencing the full nuclear charge of the nucleus due to inner layer repulsive effects. The net nuclear charge experienced by an electron is also called the nuclear charge. The strength of the nuclear charge can be determined by the oxidation number of the atom. Most of the physical and chemical properties of elements can be described in terms of their electronic configurations. . It is known that the magnitude of the ionization potential depends on the following factors:

atomic size;

nuclear charge;

Inner shell shielding effect u

The extent to which the outermost electrons penetrate the charge cloud created by the inner electrons.

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Children on the autism spectrum are at risk for nutritional deficiencies because?

Answers

Explanation: Research highlights the individuals with ASDS are nutritionally vulnerable because they exhibit a selective or pick eating pattern and sensory sensitivity that predisposes them to restricted intakes.

I hope this helps!

For this discussion post, you will use data about planetary orbits from a planetary fact sheet published on a NASA website to calculate both the angular and linear velocity of one planet from our sola

Answers

The angular velocity of a planet can be calculated by dividing 2π radians by the time it takes for the planet to complete one orbit around the Sun. The linear velocity of a planet can be calculated by multiplying the planet's angular velocity by its average distance from the Sun.

Angular velocity refers to the rate at which an object moves around a central point. In the case of a planet orbiting the Sun, the central point is the Sun itself. To calculate the angular velocity of a planet, we divide the angle traveled by the planet in one orbit by the time it takes to complete that orbit. Since a full circle is 2π radians, the angular velocity can be calculated by dividing 2π by the orbital period of the planet.

On the other hand, linear velocity refers to the speed at which an object moves in a straight line. In the context of a planet's orbit, the linear velocity can be derived from the angular velocity. By multiplying the angular velocity of the planet by its average distance from the Sun, we can determine the linear velocity of the planet in its orbit.

By calculating both the angular and linear velocities of a planet, we can gain insights into its motion and speed within the solar system. These calculations allow us to better understand the dynamics of planetary orbits and the forces that govern them.

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What happens in both hemispheres when Earth is at position c

What happens in both hemispheres when Earth is at position c

Answers

When the Earth is at point C, Equinox happens.

In Equinox, the Sun is directly above the equitor making day and night equal in both hemispheres.

Which direction does heat flow from?

hot to cold
cold to hot
hot to hot
cold to cold

Answers

Answer:

A.) Hot to cold.

Explanation:

I took the quiz on Edge, 2022.

(See the attachment below.)

Hope this helped! <3

Which direction does heat flow from?hot to coldcold to hothot to hotcold to cold

Based on scientific information, the direction that heat generally flow from is: A. hot to cold.

What is heat?

Heat is also known as thermal energy and it refers to a form of energy that is only transferred from an object to another due to a difference in temperature.

During the process of heat conduction, heat would only be transferred between objects that are having different levels of temperature and objects that are directly in contact with one another.

In conclusion, heat is generally transferred from a hot object to a cold object as a result of their varying temperature.

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true/false: cold fronts are not associated with group of answer choices a trough of low pressure. showery type of precipitation temperature change a ridge of high pressure

Answers

Cold fronts are not associated with group of answer choices a trough of low pressure. showery type of precipitation temperature change a ridge of high pressure. the following statement is false.

Cold fronts are indeed associated with a trough of low pressure, a showery type of precipitation, and a temperature change. However, they are not associated with a ridge of high pressure. Cold fronts typically occur when a cold air mass advances and replaces a warmer air mass. The boundary between these two air masses is represented by a frontal system, with the cold front marking the leading edge of the colder air. Along a cold front, the advancing cold air acts as a wedge, lifting the warm air ahead of it. This lifting motion creates a trough of low pressure along the front, leading to unstable atmospheric conditions and the formation of showery precipitation, such as rain or thunderstorms.

The temperature change is also characteristic of a cold front, as the colder air replaces the warmer air, resulting in a noticeable drop in temperature. A ridge of high pressure, on the other hand, is associated with stable weather conditions and is typically found behind a cold front. It is characterized by sinking air, clear skies, and generally fair weather.

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PLEASE HELP!!! (15 points)

The only group of elements that DO NOT form ions and are found as monatomic atoms in nature are the:

halogens

noble gases

alkali metals

alkaline earth metals

Answers

Answer:

noble gases is those group of elements that DO NOT form ions and are found as monatomic atoms in nature .

The only group of elements that DO NOT form ions and are found as monatomic atoms in nature are the: noble gases.

What are noble gases?

The noble gases are a group of chemical elements with comparable qualities; under normal conditions, they are all odourless, colourless, monatomic gases with very minimal chemical reactivity. Historically, they were also known as inert gases and aerogens. Helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radioactive radon are the six naturally occurring noble gases (Rn).

Oganesson (Og) is a highly radioactive element created synthetically. Although the IUPAC has included oganesson since "group 18" and "noble gas" have been used interchangeably, oganesson may not be appreciably chemically noble and is projected to deviate from the norm and be reactive due to relativistic effects. Its chemistry has not yet been studied due to the single known isotope's relatively brief 0.7 ms half-life.

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(b) Figure 3 shows a wheelbarrow and stones with a total mass of 43 kg. The wheelbarrow is in equilibrium with two of the three forces acting on it shown in Figure 3. A applied 0.6 m 0.93 force (F) wheelbarrow 1.5 m → Figure 3 (i) Identify the nature and point of action of the third force acting on the wheelbarrow. Write down an equation showing the relationship between the THREE forces.​

Answers

An equation showing the relationship between the THREE forces is R -W +F= 0

What is moment of force?

The equal and opposite force acting at a point from the axis of rotation is called the moment of force.

M = F x r

Given is a wheelbarrow and stones with a total mass of 43 kg. The wheelbarrow is in equilibrium with two of the three forces acting on it

Taking moment about the wheel, we get

-43x 9.81 x 0.6 + F x 1.5 =0

F = 43 x 0.6/1.5

F = 168.732 N (upward force)

Summation of forces in y direction is zero.

R -W +F= 0

Where, R is the normal force, W is the Weight force and F is the applied force.

Thus, this is the equation representing all the three forces acting on wheelbarrow.

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A 1-kilogram stone is being dropped from a bridge 100 meters above a gorge.

What is the weight of the stone?
A. 1 newtons B. 10 newtons
C. 100 newtons D. 1,000 newtons

Answers

Answer:

C. 100 NEWTONS

Explanation:

just my brain being ly = brainly is the name so my brian is being ly

The weight of the stone is 10N.

To find the weight of the stone, we need to know about the gravitational force on any object due to earth.

What is gravitational force?Gravitational force is a attractive force that arises between any two objects. The objects, on the earth surface or near the earth surface, experience the gravitational force of earth. This gravitational force is Known as the weight of the object. How can we calculate the gravitational force or the weight of an object, when it's near the earth surface?

When an object is near the earth surface, its weight is mass × gravitational acceleration (g).

So, the weight of the stone= 1kg × 10 m/s²

                            = 10 N

Thus, we can conclude that the weight of the stone 100 m above a gorge is 10N.

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Why are thire only large impact craters on Venus?
A. There are only large impact craters on Venus because only large meteors and asteroids survive their fall through the planet's thick and corrosive atmosphere.
B. There are only large impact craters on Venus because geological activity erodes impact craters over time.
C. There are only large impact craters on Venus because most smaller asteroids and meteors have been cleared out of the inner solar system over the last few billion years.
D. There are only large impact craters on Venus because the weather on the planet erodes impact craters over time.
E. There are actually impact craters of all sizes on the surface of Venus.

Answers

Venus has large impact craters due to the absence of erosive forces and the survival of only the largest meteors and asteroids through its thick atmosphere.

Option (A) is correct.

Venus, known as the sister planet of Earth, is characterized by its thick, corrosive atmosphere and extreme temperatures. Its surface lacks water and volcanic activity, and is instead marked by numerous large impact craters. This is due to the absence of erosive forces, like water, which would have gradually eroded the craters over billions of years. The craters formed on Venus as a result of asteroid and comet impacts over the past 4.6 billion years. However, the impact process on Venus differs from that on Earth. Venus' thick atmosphere burns up most smaller meteorites and asteroids upon entry, allowing only the largest ones to survive their descent. Consequently, only the large impact craters remain visible on the planet's surface today. Therefore, option (A) is correct. In summary, Venus bears only large impact craters as a consequence of the survival of substantial meteors and asteroids through its thick and corrosive atmosphere.

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What is the process where some of the unsaturated fatty acids become saturated to prolong their shelf life?

Answers

The process of saturating unsaturated fatty acids is called hydrogenation. This involves adding hydrogen atoms to the unsaturated bonds of the fatty acids.

Hydrogenation increases the melting point and shelf life of the fatty acids and changes their texture from liquid to semi-solid or solid. This process is often used in the production of margarine, shortenings, and cooking oils. It also helps to reduce the amount of trans fat, which is associated with negative health effects.



The hydrogenation process is done by bubbling hydrogen gas through the fat or oil while it is heated, often with a catalyst. This breaks the double bonds of the unsaturated fatty acids and allows them to accept hydrogen. As the hydrogen atoms are added, the fatty acids become more saturated and the melting point increases. The hydrogenation process also changes the taste and smell of the fat or oil, as well as its color and texture.



Hydrogenation is not the only process used to increase the shelf life of fatty acids. Other methods include partial hydrogenation, interesterification, and fractionation. Each of these processes has its own advantages and disadvantages, and the choice of which to use depends on the application.

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The part of the Electromagnetic (Light) Spectrum used to see through the dust
clouds in Space is?
A. Infrared light
B. Visible light
C. Radio waves

Answers

Answer:

A or C

Explanation:

The answer is A. Not C. C is what you use to remotely control something

What does storm signal number 1 mean?

Answers

Storm signal number 1 is a form of weather caution issued via the Philippine Atmospheric, Geophysical, and Astronomical Services Administration (PAGASA) to alert the public to the opportunity of a tropical cyclone entering the USA.

When a storm sign number 1 is raised, it method that a tropical cyclone, along with a tropical despair or tropical hurricane, is expected to affect a particular region within the next 36 hours.

The winds related to the cyclone aren't yet strong sufficient to cause widespread harm, but they may be sufficient to disrupt transportation and different outside sports.

Throughout storm sign number 1, the general public is cautioned to be vigilant and take precautions, which include securing loose items and staying indoors if feasible.

Fishermen are recommended to keep away from going out to sea, and small vessels are cautioned to take refuge. PAGASA issues hurricane signal warnings up to a wide variety of five, with better numbers indicating more intense climate situations.

The warnings are a crucial tool for helping the general public to put together for and stay safe throughout tropical cyclones, which could reason extensive damage and loss of life within the Philippines.

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.
A .63 kg ball is moving at 4.3m/s. What is the momentum of the ball?

Answers

Answer:

Given Mas (m) =63kg

velocity (v) =4.3m/s

momentum (p) =?

p=mv

63kgx4.3m/s

270.9kg.m/s

the momentum =270.9kg.m /s

If a ball of mass 0.63 kilograms is moving at 4.3 meters/seconds, then the momentum of the ball would be 2.709-kilogram meters/second.

What is momentum?

It can be defined as the product of the mass and the speed of the particle, it represents the combined effect of mass and the speed of any particle.

Momentum = mass of the object × velocity of the object

As given in the problem we have to calculate the momentum of the ball if it has a mass of 0.63 kilograms and moving with a speed of  4.3 meters/seconds,

The momentum of the ball = 0.63× 4.3

                                             

                                             =2.709 kilogram meters/second

Thus, the momentum of the ball comes out to be 2.709-kilogram meters/second.

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22. Calculate the displacement in meters a cyclist would travel in 5.00 h at an average
of 12.0 km/h to the south west

Answers


Explanation:
To whichever direction, if the cyclist did not change the direction, the displacement is
By formula :d=v×t
given, v=12km/h and, t=5h
=>
x=12km/h×5h=60km=60×1000m=60000m

A 0.311 kg tennis racket moving 30.3 m/s east makes an elastic collision with a 0.0570 kg ball moving 19.2 m/s east. Find the velocity of the tennis racket after the collision.

A 0.311 kg tennis racket moving 30.3 m/s east makes an elastic collision with a 0.0570 kg ball moving

Answers

The velocity of the tennis racket after the collision 14.966 m/s.

Step-by-step explanation:
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies remains the same.
let the following:
m₁ = mass of tennis racket = 0.311 kg
m₂ = mass of the ball = 0.057 kg
u₁ = velocity of tennis racket before collision = 30.3 m/s
u₂ = velocity of the ball before collision = -19.2 m/s
v₁ = velocity of tennis racket after collision
v₂ = velocity of the ball after collision
Right (+) , Left (-)
v₁ = [ u₁ * (m₁ - m₂) + u₂ * 2m₂ ]/ (m₁ + m₂)
= ( 30.3 * (0.311 - 0.057) - 19.2 * 2 * 0.057 ) / ( 0.311 + 0.057)
= 14.966 m/s.
So, the velocity of the tennis racket after the collision 14.966 m/s.
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