The mass of the planet with the same radius as Earth is 3.05 × 10^24 kg.
What is mass?Mass is a measure of the amount of matter contained in an object. It can be measured using scales, balances or other measuring instruments. Mass is a fundamental property of all matter, and its measurement is the basis for many scientific and engineering calculations. Mass is not the same as weight, which is a measure of the force exerted by gravity on an object. Mass is often expressed in units such as kilograms or grams.
To calculate the mass of the planet, we must use Newton's Second Law of Motion, which states that the force (F) is equal to the mass (m) times the acceleration (a): F = ma. Since the astronaut's weight on the planet is twice what it is on Earth, the acceleration on the planet must be twice what it is on Earth. We can then use the equation F = mg (where m is the mass of the astronaut and g is the gravitational acceleration on Earth) to calculate the acceleration on the new planet.
We know that the gravitational acceleration on Earth is 9.81 m/s2, so the gravitational acceleration on the new planet is twice that, or 19.62 m/s2. We can now use Newton's Second Law of Motion to solve for the mass of the planet:
F = ma
mg = ma
m = (mg)/a
m = (60kg * 9.81m/s2)/(19.62m/s2)
m = 3.05 × 10^24 kg
Therefore, the mass of the planet with the same radius as Earth is 3.05 × 10^24 kg.
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choose the statement that accurately describes nuclear energy. exposure to benzene compounds can cause cancer among those who work with this energy source. waste from this energy source must be stored safely for hundreds of years. emissions from this energy source can create acid rain, which disrupts forest ecosystems. animal habitats are damaged and fragmented when pipes are laid to distribute this energy source
The statement that accurately describes nuclear energy is: "Waste from this energy source must be stored safely for hundreds of years."
What is nuclear energy?Nuclear energy is energy released from the nucleus of an atom. It is produced through the process of nuclear fission, which splits the nucleus of an atom into two lighter nuclei. The energy released during this process is used to generate electricity, power ships, and to provide heat and power for industrial processes.
Nuclear energy is a clean, efficient, and reliable source of power, but it also produces radioactive waste that must be safely stored away from the environment and living creatures. This radioactive waste is highly toxic and must be stored in a secure facility for hundreds of years until it is no longer dangerous.
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Experimental data indicate that in a region downstream of a given louvered supply vent the velocity of the emitted air is defined by v=0.18v0/x, where v and x are expressed in m/s and meters, respectively, and v0 is the initial discharge velocity of the air. For v0=3.6m/s, determine:
a) the acceleration of the air at x=2m,
b) the time required for the air to flow from x=1 to x=3m.
a) a = - 0.0524 m/s²
b) t = 6.17 s
Determine:
a) the acceleration of the air at x=2m,
b) the time required for the air to flow from x=1 to x=3m.
Given
τ = 0.18*τ₀ / x
τ₀ = 3.6 m/s
Determine:
a) The acceleration of the air at x= 2m.
Knowing
a = dτ / dt
Multiplying both the numerator and denominator by dx
a = (dτ / dx) (dx / dt)
Substituting τ for dx / dt
a = τ*(dτ / dx)
⇒ a = τ*(-0.18*τ₀ / x²) = (0.18*τ₀ / x)(-0.18*τ₀ / x²)
⇒ a = - 0.18²*τ₀² / x³ = - 0.18²*(3.6)² / x³
⇒ a = - 0.4199 / x³
If x = 2m
⇒ a = - 0.4199 / (2)³
⇒ a = - 0.0524 m/s²
b) The time required for the air to flow from x=1 to x= 3m.
If
τ = dx / dt = 0.18*τ₀ / x
⇒ dt = (x / 0.18*τ₀) dx
⇒ t = (1 / 0.18*τ₀) ∫x dx
⇒ t = (1 / 0.18*τ₀)*(1 / 2)*x²
then
t = (1 / (0.18*3.6))*(1 / 2)*((3)² - (1)²)
⇒ t = 6.17 s
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The following 5 sodium control values in unit (mEq/L) were obtained:140, 135, 138, 140, 142Calculate the coefficient of variation?
The coefficient of variation for the 5 sodium control values is 1.61%.
What is coefficient?Coefficient is a numerical value used to express the magnitude of a physical quantity in relation to another physical quantity. It is a constant value used to convert one set of units to another set of units, or to express the relationship between two physical quantities.
The coefficient of variation (CV) is a measure of the variability of a set of values relative to its mean. To calculate the coefficient of variation, we need to calculate the standard deviation of the values.
Standard deviation = √((140-138.2)2 + (135-138.2)2 + (138-138.2)2 + (140-138.2)2 + (142-138.2)2 / 5)
Standard deviation = 2.22
Coefficient of variation = (Standard deviation/mean)*100
Coefficient of variation = (2.22/138.2)*100
Coefficient of variation = 1.61%
Therefore, the coefficient of variation for the 5 sodium control values is 1.61%.
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in a command economy, which group is most responsible for producing the goods for people in society need
In a command economy, the government is responsible for producing the goods that people need.
In a command economy, what does the government accomplish?
The production and distribution of goods and services are directed and regulated by the government in a command economy. The prices at which these goods and services are sold are set by the government, which also controls and manages the production and supply of these goods and services.
The government also decides what will be produced in terms of goods and services as well as how resources will be distributed. The majority of the resources and businesses are owned by the government, which also sets production targets and determines how they will be achieved.
The government also sets the wage rate and manages the flow of money, including the interest rate. Additionally, the government offers its citizens basic services like health care and education.
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A UFO going 17 m/s north suddenly experienced a constant acceleration for 77 s during which it’s displacement was 19,096 m north. Determine the final speed of the UFO and the magnitude of the UFOs acceleration
a) The final speed of the UFO is 0 m/s.
b) The acceleration of the UFO is 0.0076 m/s^2.
What is the speed?We know that the speed would have to do with the rate of change of the displacement of the object with time. We known that within the time in which the UFO has a constant acceleration then the final velocity of the UFO is 0 m/s.
We have that;
v^2 = u^2 - 2as
v = final velocity
a = acceleration
s = displacement
u = initial speed
The final speed of the UFO is 0 m/s
We then have;
u^2 = 2as
a = u^2/2s
a = (17)^2/2 * 19096
a = 0.0076 m/s^2
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what is summer caused by
Summer is caused by the tilt of the Earth's axis. The Earth's axis is tilted at an angle of about 23.5 degrees relative to its orbit around the sun. As the Earth orbits the sun, different parts of the Earth receive more or less direct sunlight depending on the tilt of the axis. When the northern hemisphere is tilted towards the sun, it is summer in the northern hemisphere and winter in the southern hemisphere. This is the opposite when the northern hemisphere is tilted away from the sun, it is winter in the northern hemisphere and summer in the southern hemisphere.
Answer: Direct sunlight striking Earth
Explanation: I read it on a book of space. : D
which of the following resources would most likely be mined from the plant remains buried in eastern montana during the cretaceous?
The most likely resource to be mined from the plant remains buried in eastern Montana during the Cretaceous would be fossil fuels.
What is Montana?Montana is a state in the western region of the United States. It is bordered by North Dakota to the east, South Dakota and Wyoming to the south, Idaho to the west, and the Canadian provinces of British Columbia, Alberta, and Saskatchewan to the north.
Fossil fuels are formed from the remains of plants and animals which have been buried and subjected to high temperatures and pressures over millions of years. The remains of plants buried in eastern Montana during the Cretaceous period would have been subjected to these conditions and thus may contain deposits of fossil fuels such as oil and natural gas.
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alculate the total lifting energy required to build this structure from the ground up. you should first use a riemann sum to estimate the total energy to within j joules, and then write and evaluate a definite integral that will calculate the desired energy. be sure to label each piece of the definite integral to show the weight-distance product being constructed, and to specify what each symbol in the integral formula means.
The most basic equation is GPE = m*g*h. GPE = gravitational potential energy in that location (joules j) m = kilogrammes of mass (kg) G stands for gravitational acceleration (m/s2). h = height change h.
What is energy?In physics, energy is the quantitative quality that is transferred to a body or to a physical system. It is recognised in the execution of work as well as in the form of heat and light (from the Ancient Greek: v, enérgeia, "activity"). Energy is a preserved resource; according to the rule of conservation of energy, energy can only be transformed from one form to another and cannot be created or destroyed. The joule is the SI's (International System of Units) unit of measurement for energy (J). A moving object's kinetic energy, a potential energy stored by an object (for instance because of its position in a field), the elastic energy contained in a solid object, chemical energy linked to chemical reactions, radiant energy carried by electromagnetic radiation, and internal energy contained within a thermodynamic system are examples of common forms of energy. Energy is constantly being consumed and expended by all living things.
Any stationary object that has mass (referred to as rest mass) also has an equivalent amount of energy (referred to as rest energy), and any additional energy (of any form) that the object acquires above that rest energy will increase the object's total mass just as it increases its total energy. This is known as mass-energy equivalence.
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A spring is stretched by 35 Cm and attached to a 500 g air-track glider, which is then released. The spring does 0.45 J of work on the glider as it returns to its equilibrium length. What is the value of the spring constant?
A 500 g air-track glider is fastened to a spring that has been 35 cm extended before being let off. In order for the glider to return to its equilibrium length, the spring must exert 0.45 J of force on it. 8 N/m is the spring constant.
Using the equation for the work a spring does, we can get the spring constant:
Work completed equals (1/2)*k*x2.
In this situation, the spring's displacement is 35 cm, and the work done is 0.45 J. K is the spring constant.
This allows us to determine k: k = (2 * work done) / x.
2 \s k = (2 * 0.45 J) / (35 cm)^2
Divide by 100 k to convert cm to m: (2 * 0.45 J) / (0.35 m).
2 \s k = 8 J/m^2
The spring constant is thus 8 N/m.
The spring stiffness is quantified by the spring constant, or k.
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The approximate shortest road miles distance from yosemite lodge to mirror lake is __ miles. (use your ruler or protractor to measure and calculate the approximate distance in miles. remember 1 inch equals 2,000 feet.)
a. 1 mile
b. 3 miles
c. 5 miles
d. 6 miles
The approximate shortest road miles distance from yosemite lodge to mirror lake is 3 miles.
What is meant by distance?
The midpoint between a celestial body's greatest and smallest separations from its primary.The metre is the SI unit for distance (m). Long distances can be measured in kilometres, whereas little distances can be gauged in millimetres (cm) (km).For instance, you might measure the distance in centimetres between the bottom and top of a piece of paper and the kilometres between your home and school.The International System of Units defines a metre as the distance unit. It's interesting to note that many other derived units or quantities, such as volume, area, acceleration, and speed, may be constructed using this as the basic unit and a few formulae.To learn more about distance refer to
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Joan decided to go for a walk, st arting from her house. The diagram below shows the m easurement between places on t he route where he walks. what wil I be his Position when he is at c ar?*
(GIVING BRAINLIST TO THE CORRECT ANSWER)
Based on the information provided, his position when he is at a car will be -13 west.
What is the distance between Joan's house and the car?The distance can be found by adding smaller distances as shown below:
Distance from the house to the wheelbarrow: 11 meters
Distance from the wheelbarrow to the car: 2 meters
11 meters + 2 meters = 13 meters
This means the magnitude is 13 meters.
What is the direction?Based on the map, the direction is west, and considering this goes to the left this would be negative, making his position -13 west.
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Two charges +1x10-6 and -4x10-°C are separated by a distance of 2m. Determine the position of the null point.
A null point is a location in a field where the value of the field is 0 as a result of two or more opposite quantities entirely canceling one another.
Where is a null point located, and how can you find it?A null point is a location in a field where the value of the field is 0 as a result of two or more opposite quantities entirely canceling one another. The field of two positive point charges at point C in the figure is plainly seen to be canceling out and being equal to zero. C is a null point hence.
The null point, sometimes referred to as the null zone or region, is the location when the nystagmus eye movements abruptly calm down and vision becomes clearer. When looking straight ahead at anything or someone, a person with nystagmus may seem to tilt their focus to the right or left, up or down.
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An object floats in water with 5/8 of its volume submerged. The ratio of the density of the obkect to that of water is:
(a) 8/5
(b) 1/2
(c) 3/8
(d) 5/8
(e) 2/1
An object floats in water with 5/8 of its volume submerged. The ratio of the density of the obkect to that of water is 5/8.
What is meant by density ?
The measure of how densely a material is packed together is called density. As the mass per unit volume, it has that definition.Symbol for density: D or Formula for Density: Where is the density, m is the object's mass, and V is its volume, the equation is: = m/V.How much matter is confined within a volume is determined by density. For an identical size object, a dense object weighs more than a less dense one.A substance that is less dense than water will float on it; a substance that is denser will sink.Density equals mass per unit volume, or D = M / V, is the density equation.To learn more about density refer to
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you observe that a negatively charged plastic pen repels a charged piece of magic tape. you then observe that the same piece of tape is repelled when brought near a small metal sphere. you are wearing rubber soled shoes, and you touch the metal sphere with your hand. after you touch the metal sphere, you observe that the tape is attracted to the metal sphere. which of the following statements could be true. list all that apply, sep
The correct statements are options given below:
(The complete question is attached below)
According to the statement there is a force of repulsion between the two objects. Remember that two objects must have the same charge so that they repel each other.In this way if the tape is repelled by a plastic pen that is negatively charged, this allows us to appreciate that the tape is also negatively charged. Now if the tape repels the sphere, therefore the sphere is also negatively charged.Under these considerations the correct answers would be
2. Sodium ions from the salt water on your hand moved onto the sphere
4. The excess negative charge from the sphere spread out all over your body
6. Electrons from the sphere moved into the salt water on your skin, where they reacted with sodium ions
7. After you touched it, the metal sphere was very nearly neutral.
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what happens inside when an air-filled, sealed can, is heated?responsesthe collisions of air molecules against the wall of the can do not change.the collisions of air molecules against the wall of the can do not change.the collisions of air molecules against the wall of the can are weaker and less frequent.the collisions of air molecules against the wall of the can are weaker and less frequent.the collisions of air molecules against the wall of the can are stronger and more frequent.
When an air-filled, sealed can is heated, the temperature of the air inside the can increases.
What is temperature?Temperature is the measure of the average kinetic energy of the particles in a substance. Temperature is measured using a thermometer and is usually expressed in degrees Celsius (°C), Fahrenheit (°F), Kelvin (K), or Rankine (R).
This causes the air molecules to move faster, resulting in more frequent and stronger collisions against the wall of the can. As the temperature of the air inside the can continues to increase, the air molecules move faster and the collisions against the wall of the can become stronger and more frequent.
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which of the following are true of the transfer of thermal energy in the oceans? select the three correct answers.
Near the equator, energy is more readily emitted than absorbed. Near the poles, energy is mostly absorbed rather than radiated. In depth ocean currents, energy is transported from the equator to the poles.
What does a scientific energy exactly mean?Energy is described as the capacity to apply a force sufficient to move an object, or the capacity to "accomplish work." Despite the vagueness of the definition, the concept is actually quite straightforward: electricity simply denotes the force that drives objects. Potential energy falls into two distinct kinds.
basic description of energyThe ability to work is the most fundamental definition of energy. Energy is what moves and transforms things. It is many in shape and is found everywhere. Food preparation demands energy.
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"_____is the process by which rocks break down in place to produce soils and sediments. group of answer choices:
a. weathering b. metamorphism c. lithification
d. subduction"
Weathering is the process by which rocks break down in place to produce soils and sediments.
The breakdown or dissolving of rocks and minerals on the earth's surface is known as weathering. Carrier of weathering include water, ice, acids, plants, animals and variations in temperature.
Erosion is the movement of soil, rock, or dissolved material from one region of the earth's crust to another, where it is deposited. Weathering, which is a static process, is distinct from erosion.
Rocks break down by the process called weathering. The effect of weathering and erosion cannot be resisted by any rock on Earth due to its softness.
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Name a structure that is on the ventral side of the heart, located more laterally within the axial region
The structure that is on the ventral side of the heart, located more laterally within the axial region is axillary lymph nodes.
What is axillary lymph nodes?The axillary lymph nodes are lymph nodes located in the human armpit. They drain lymph vessels from the lateral quadrants of the breast, superficial lymph vessels from the thin walls of the chest and abdomen above the level of the navel, and upper limb vessels.
They are classified into several groups based on their location in the armpit. These lymph nodes are clinically significant in breast cancer, and metastasis from the breast to the axillary lymph nodes is taken into account in disease staging.
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a drug is infused into a patient's bloodstream at a constant rate of r grams per second. simultaneously, the drug is removed at a rate proportional to the amount x(t) of the drug present at time t. determine a differential equation for the amount x(t). (use k > 0 for the constant of proportionality and x for x(t).)
The constant of proportionality (k) is used to represent the rate at which the drug is removed.
What is proportionality?Proportionality is a mathematical concept that describes the relationship between two variables in which the ratio of their values is always constant. This ratio is known as a proportion and is expressed as a fraction.
The differential equation for the amount x(t) is given by:
dx/dt = r - kx
This equation states that the rate of change of x (dx/dt) is equal to the rate of infusion (r) minus the rate of removal (kx).
The rate of removal is proportional to the amount of the drug present at time t (x).
Therefore, the constant of proportionality (k) is used to represent the rate at which the drug is removed.
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When jumping, a flea rapidly extends its legs, reaching a takeoff speed of 1.0 m/s
over a distance of 0.50 mm
.
The maximum height reached by the flea is 1.23 m.
What is time of motion of the flea?
The time of motion of the flea is calculated by applying the following formula.
t = d / v
where;
d is the horizontal distance reached by the fleav is the horizontal speedt = ( 0.5 m ) / ( 1 m/s )
t = 0.5 s
The maximum height reached by the flea is calculated as follows;
h = ¹/₂gt²
where;
g is acceleration due to gravityt is the time of motion of the fleah = ¹/₂ x 9.8 x ( 0.5 )²
h = 1.23 m
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The complete question is below:
When jumping, a flea rapidly extends its legs, reaching a takeoff speed of 1.0 m/s over a distance of 0.50 m, what is the maximum height reached by the flea?
fill in the blank. when conducting an ero operation with a c-5 aircraft, vehicles and personnel exiting via the forward or aft ramp will proceed on a direct line with the fuselage at least___feet before turning, or at least____feet before stopping.
Vehicles and people leaving a C-5 aircraft via the forward or aft ramp must go at least 50 feet in front of the fuselage before turning or 100 feet before coming to a complete stop while executing an ERO operation.
ERO (emergency ramp offload) operations are carried out when the aircraft has to rapidly and safely dump goods and crew. Depending on the kind of aircraft, the location, and other variables, the particular standards and procedures for ERO operations may change. However, in general, it is important to make sure that any vehicles and people leaving the plane keep a safe distance from it and don't obstruct other activities. ERO activities target those who pose a threat to public safety, including gang members and noncitizens with criminal records, as well as those who have otherwise broken the country's immigration rules.
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use the time dependent schrodinger equation and the turnover rule to prove that where h is the hamiltonian operator
the Hamiltonian operator A quantum system's total energy is described by the operator h, and its temporal development is periodic.
The wave function of a quantum system, represented by the wave function psi, is said to change over time in accordance with the Hamiltonian operator, represented by H, according to the time-dependent Schrödinger equation (TDSE). The equation i/t = H provides the TDSE.
According to the turnover rule, a quantum system's time-evolution has a periodic nature, with a period equal to the reciprocal of the difference in energy eigenvalues between its beginning and final states. The following equation provides the turnover rule:
T = 2π/|Ef - Ei|
By replacing the TDSE into the turnover rule and simplifying, we can demonstrate using the TDSE and the turnover rule that where h is the Hamiltonian operator.
T= 2π/|Hf - Hi|
I / t = H I / t (f / t - I / t) = H f f - Hi I / t (e f - ei) = H f f - Hi
T= 2π/|Hf - Hi|
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in the figure, a particle is to be released at rest at point a and then is to be accelerated directly through point b by an electric field. the potential difference between points a and b is 100 v. which point should be at higher electric potential if the particle is (a) an electron, (b) a proton, and (c) an alpha particle (a nucleus of two protons and two neutrons)? (d) rank the kinetic energies of the particles at point b, greatest first.
The point that should be at higher potential if the particle is an electron is B. The point that should be at higher potential if the particle is an electron is A.
What is meant by electron ?
A negatively charged subatomic particle known as an electron can either be free or attached to an atom (not bound).One of the three main types of particles inside an atom, along with protons and neutrons, is an electron that is linked to the atom. The nucleus of an atom is made up of electrons, protons, and neutrons together.The negatively charged particles known as electrons revolve around the outside of the nucleus. For scientists, it can be challenging to monitor them because of how quickly they spin. The tiniest particles in an atom, you can put 2000 of them into a proton, they are drawn to the positive charge of the protons.To learn more about electron refer to
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puck b has five times the mass of puck a . starting from rest, both pucks are pulled the same distance across frictionless ice by strings with the same tension. part a compare the final kinetic energies of pucks a and b . compare the final kinetic energies of pucks and . ka
Pack B has twice the mass of pack A, and thus twice the kinetic energy, but has the same final velocity as pack A.
a. The ultimate kinetic energy of an object is given by the formula KE = 1/2 × m × v². where m is the object's mass and v is its velocity. Since both pucks are pulled at the same distance by a string of the same tension, the final kinetic energy of both pucks will be the same. However, pack B has twice the mass of pack A, so the final kinetic energy is twice that of pack A. The final velocity of the
b. Object is given by the equation v = √(2 × KE / m). Both packs have the same final kinetic energy, but pack B has twice the mass of pack A, so the final velocity is √(2 × KE / mB) = √(2 × KE / (2 × mA)) = √(KE / mA ), which is the square root of the terminal velocity of pack A.
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The question is -
Puck B has twice the mass of puck A. Starting from rest, both pucks are pulled the same distance across frictionless ice by strings with the same tension a. Compare the final kinetic energies of pucks A and B. b. Compare the final speeds of pucks A and B.
Two 0.90 g spheres are charged equally and placed 1.9 cm apart: When released they begin to accelerate at 130 m/s? Part A What is the magnitude of the charge on each sphere? Express your answer to two significant figures and include the appropriate units Value Units HA
The magnitude of the charge is 0.82 * 10-7 C, that can be calculated using the formula for the same.
Electric charge is available in types, which we pick to name high-quality charge and bad charge. This is the importance of the pressure which every fee exerts on the opposite fee (recollect Newton's third law).
Let the charge on each of them be "Q"
Now, electrostatic force of attraction on each of them = (1/4πε)(Q2/0.022)
Also, this force is being acted on each of the spheres, hence,
(1/4πε)(Q2/0.022) = M*a
9 * 109 * Q2 * 104 / 4 = 10-3 * 150
Q = 0.82 * 10-7 C
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Using the formula for the charge, it can be determined that the charge has a magnitude of 0.92 x [tex]10^{-7}[/tex] C.
There are many kinds of electric charge, which we will refer to as good charge and poor charge. This highlights the significance of the pressure one fee puts on the opposite fee remember Newton's third law.
Let "Q" be the charge on each of them.
Currently, the electrostatic force of attraction between each of them is equal to (1/4)(Q2/0.022).
Additionally, each of the spheres is being affected by this force, so
(1/4πε)(Q2/0.022) = M*a
9 x 109 x Q2 x 104 / 4 = [tex]10^{-3}[/tex] x130
Q = 0.92 x [tex]10^{-7}[/tex] C
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Please i need an answer to this question, "Trace the historical development of Ghana from 1957 till present day". Help me
The first nation south of the Sahara to achieve independence was Ghana, formerly the Gold Coast, on March 6, 1957.
What took place in Ghana in 1957?
On March 6, 1957, Kwame Nkrumah told the Ghanaian people that they were free and that "our beloved country, Ghana, is free forever." He also emphasized that "the African People are capable of administering their own affairs." Sub-Saharan Africa's first nation to attain independence from European colonial domination was Ghana.
Up until 1960, Ghana was a constitutional monarchy and parliamentary democracy. Following a national vote, Ghana was then proclaimed a republic. Following the Soviet example, the Second Development Plan (1959–1964) switched away from increasing state services and toward increasing productivity in the important sectors. In 1959–1964, expansion of secondary schools, as well as of vocational and higher education, became a top goal.
If Ghana was to play its leadership role in the liberation of Africa from colonial and neo-colonial rule, government spending on road building projects, mass education of adults and children, health services, and the construction of the Akosombo Dam were all crucial. Increases in the price and output of cocoa, gold, and oil during the past 30 years have contributed to Ghana's transformation: real GDP growth has quadrupled, extreme poverty has decreased by half, and in 2011, Ghana was upgraded to a lower middle-income country status.
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when we placed the bottle in the cold water, what happened to the air inside the bottle? make sure density is included in your answer.
The air volume is lowered. The quantity of air remains constant, but its volume and pressure decrease as the temperature rises. There is no vacuum formed; the pressure within the container is just lower than the pressure outside.
What is pressure?Pressure is defined as the force applied perpendicular to an object's surface per unit area across which that force is dispersed. Gauge pressure is the pressure in relation to the surrounding atmosphere. Pressure is expressed using a variety of units. Pressure is the force exerted on a surface per unit area. When a force F is applied to area A, pressure P=F/A. Pressure is the force acting on a unit area of a surface. It works perpendicular to the surface under pressure. Pressure = force multiplied by the area on which it operates. The thrust (perpendicular force on a surface) acting per unit area of a body is described as pressure.
Here,
The air volume has been reduced. The volume and pressure of air drop as the temperature rises, but the amount of air remains constant. There is no vacuum created; the pressure within the container is just lower than the pressure outside.
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Alison is playing in front of her house. She skips forward 700 steps, skips back 900 steps and forward again 50
steps. If she has been skipping for 10 minutes, Find the speed at which Alison moves and her velocity. Draw
Alison's motion
The speed at which Alison moves is 2.75 steps per second.
The velocity of Alison is determined as 0.25 steps backward.
What is the speed of Alison?
The speed of Alison is the ratio of total distance travelled by Alison to total time of motion.
v = ( 700 + 900 + 50 ) / ( 10 min x 60 s )
v = 2.75 steps per second
The velocity of Alison is the ratio of the total displacement of Alison to total time of motion and it is calculated as follows;
v = ( 700 - 900 + 50 ) / ( 10 x 60 s )
v = ( - 150 steps ) / ( 600 s )
v = 0.25 steps / second backward
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Give an example where a combination of three nonzero vectors in R4 is the zero vector. Then write your example in the form Ax = 0. What are the shapes of A and x and 0 ?
An example where a combination of three nonzero vectors in R4 is the zero vectorv1 = [1, 2, 3, 4] : v2 = [2, 4, 6, 8] ; v3 = [-1, -2, -3, -4] A = [[1, 2, -1], [2, 4, -1], [3, 6, -1], [4, 8, -0.5]]; x = [a, b, c]^T ; 0 = [0, 0, 0, 0]
What is meant by vectors?Vectors are the combination of magnitude and direction, and they are drawn as arrows.
An example of a combination of three nonzero vectors in R4 being the zero vector is when the three vectors are linearly dependent. For example, let's consider the following three vectors in R4:
v1 = [1, 2, 3, 4]
v2 = [2, 4, 6, 8]
v3 = [-1, -2, -3, -4]
These three vectors are linearly dependent, because v3 can be written as a linear combination of v1 and v2:
v3 = -1 * v1 + -0.5 * v2
Their combination is the zero vector:
v1 + v2 + v3 = [1, 2, 3, 4] + [2, 4, 6, 8] + [-1, -2, -3, -4] = [2, 8, 12, 16] + [-1, -2, -3, -4] = [1, 6, 9, 12] + [-1, -2, -3, -4] = [0, 4, 6, 8] + [-1, -2, -3, -4] = [-1, 2, 3, 4] + [-1, -2, -3, -4]=[-2, 0, 0, 0]=[0, 0, 0, 0]
We can express this in form Ax = 0 where A is a matrix and x is a column vector.
A = [[1, 2, -1], [2, 4, -1], [3, 6, -1], [4, 8, -0.5]]
x = [a, b, c]^T
0 = [0, 0, 0, 0]
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On a highway curve with radius 36 m, the maximum force of static friction (centripetal force) that can act on a 1,223-kg car going around the curve is 7,927 N. What speed limit should be posted for the curve so that cars can negotiate it safely?
m/s
If on a highway curve with radius 36 m, the maximum force of static friction. The speed limit that should be posted for the curve so that cars can negotiate it safely is 15.28 m/s.
How to find the speed limit?Radius =36 m
Maximum force of static friction = 7,927 N
Magnitude of the force is F = m v2/r
So,
Limit speed is:
v = (Fr/m)^1/2
v= (7,927N × 36 m/ 1223 kg)^1/2
v= 15.275 m/s
v= 15.28 m/s (Approximately)
Therefore we can conclude that the speed limit is 15.28 m/s.
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