plants
i hope its right and have a nice day
Answer:
number 1
Explanation:
A wire is carrying current vertically downward. What is the direction of the force on this wire due to Earth's magnetic field?
Please answer in relation to the Right-hand rule.
The requried force on the wire due to Earth's magnetic field will be perpendicular to both the current direction and the magnetic field direction.
According to the right-hand rule, if a current-carrying wire is held in the right hand with the thumb pointing in the direction of the current, the direction in which the fingers curl represents the direction of the magnetic field around the wire.
In this case, the wire is carrying the current vertically downward. If we apply the right-hand rule, we can curl our fingers around the wire in the direction of the magnetic field. The direction of the magnetic field is horizontally perpendicular to the wire, pointing toward the north.
Therefore, the force on the wire due to Earth's magnetic field will be perpendicular to both the current direction and the magnetic field direction. Using the right-hand rule again, if we extend our right-hand thumb in the direction of the current (downward) and curl our fingers in the direction of the magnetic field (northward), our palm will face east. This indicates that the force on the wire will be directed eastward.
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results: is the sum of the square of the maximum voltages across r and l, vr2 vl2, equal to the square of voltage across both elements, vrl2 in accordance with eq.2?
In general, the sum of the squares of the voltages across individual components may not necessarily be equal to the square of the voltage across both elements combined. It would depend on the nature of the circuit and the relationship between the voltage across the components.
It would depend on the nature of the circuit and the relationship between the voltage across the components. To determine if the sum of the square of the maximum voltages across resistor (R) and inductor (L), Vr^2 and Vl^2 respectively, is equal to the square of the voltage across both elements, Vrl^2, in accordance with equation (2), we need to have more context and information about the specific equation and circuit being referred to. The relationship between Vr^2, Vl^2, and Vrl^2 would depend on the specific circuit configuration and the equations governing its behavior.
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PLZZZZZ HELP MEHH ASAP!!!
Answer:
C
Explanation:
Copper is a conductor because its valence electrons can move freely from atom to atom.
Can anyone help me with this question please
I’ll mark you as a brainliest.
No links.
Answer:
Answer is B
Explanation:
Answer:
B. Frequency
Explanation:
Monochromatic light passes through two slits separated by a distance of 0.0340mm.
If the angle to the third maximum above the central fringe is 3.21 degrees, what is the wavelength of the light in nanometers?
The wavelength of the light in nanometers is 321 nm.
The angular position of the nth bright fringe above the central fringe is,
θ = (nλ)/d
where,
θ = angle to the nth bright fringe
λ = wavelength of the monochromatic light
d = distance between the two slits
n = order of the bright fringe
The given values,
θ = 3.21°
n = 3
d = 0.0340mm = 3.4 × 10⁻⁵m
Substituting these values in the above equation,
3.21° = (3λ)/(3.4 × 10⁻⁵m)
λ = (3.21 × 3.4 × 10⁻⁵m)/3
λ = 3.21 × 10⁻⁵m
= 3.21 × 10⁻⁷m
= 321 nm
Therefore, the wavelength of the light in nanometers is 321 nm.
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a positive charge moves with a velocity v in the direction shown. the magnetic field points in the z direction and v lies in the x-z plane. what is the direction of the force on the charge due to the magnetic field?
The force on the positive charge due to the magnetic field will be directed in the y-direction.
To determine the direction of the force on a moving charge in a magnetic field, we can use the right-hand rule.
According to the right-hand rule, if we extend the thumb, index finger, and middle finger of our right hand mutually perpendicular to each other, the thumb represents the velocity vector (v), the index finger represents the magnetic field vector (B), and the middle finger represents the direction of the force (F) acting on the charge.
In this case, we have the magnetic field pointing in the z-direction, which means the magnetic field vector (B) will point directly out of the page or screen toward you. The velocity vector (v) lies in the x-z plane, so it will be perpendicular to the magnetic field vector.
Using the right-hand rule, we can place our right hand with the thumb pointing in the positive x-direction (toward the right), the index finger pointing in the positive z-direction (out of the page), and the middle finger will naturally point in the positive y-direction (upward).
Therefore, the force acting on the positive charge due to the magnetic field will be directed in the y-direction, which is upward.
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in the bohr model, how many electron wavelengths fit around this orbit?
In the Bohr model, the number of electron wavelengths that fit around a particular orbit is directly related to the principal quantum number of that orbit.
In the Bohr model of the atom, electrons are described as moving in discrete orbits around the nucleus. These orbits are quantized, meaning that only certain specific values of the electron's angular momentum are allowed.
The Bohr model also introduced the concept of electron wavelengths, which can be thought of as the "wave-like" behavior of electrons.
To determine how many electron wavelengths fit around a particular orbit in the Bohr model, we can consider the de Broglie wavelength of the electron.
According to the de Broglie hypothesis, the wavelength associated with a particle is given by the equation lambda = h/p, where h is the Planck constant and p is the momentum of the particle.
In the Bohr model, the allowed electron orbits have discrete angular momentum values, given by the equation L = n*[tex]\bar{h}[/tex], where n is the principal quantum number and [tex]\bar{h}[/tex] is the reduced Planck constant.
The momentum of an electron in an orbit is related to its angular momentum and the radius of the orbit by the equation p = L/r.
Substituting the expression for angular momentum into the de Broglie wavelength equation, we get
[tex]\lambda[/tex] = h/(n*[tex]\bar{h}[/tex]/r) = hr/(n*[tex]\bar{h}[/tex]).
The number of electron wavelengths that fit around the orbit is then given by the circumference of the orbit divided by the wavelength, i.e.,
(2*π*r)/[tex]\lambda[/tex] = (2*π*r)/(hr/(n*[tex]\bar{h}[/tex])) = (2*π*n*[tex]\bar{h}[/tex])/h.
Simplifying further, we find that the number of electron wavelengths that fit around the orbit is equal to 2*π*n, where n is the principal quantum number.
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if his eyes have a far point of 2.0 m , what is the greatest distance he can stand from the mirror and still see his image clearly? express your answer using two significant figures.
The greatest distance the person can stand from the mirror and still see their image clearly is 2.0 meters.
The far point of a person's eyes refers to the maximum distance at which they can see objects clearly without the aid of corrective lenses. If the far point is given as 2.0 m, it means that the person can see objects clearly up to a distance of 2.0 m.
To determine the greatest distance the person can stand from the mirror and still see their image clearly, we need to consider the concept of the virtual image formed by a mirror. When we look into a mirror, our eyes perceive a virtual image as if it were formed behind the mirror.
In this case, the person's eyes can focus clearly up to a distance of 2.0 m. To see their image clearly in the mirror, the person needs the virtual image formed by the mirror to be within this range.
Since the virtual image formed by a mirror is the same distance behind the mirror as the object is in front of it, the person needs to stand at a distance from the mirror equal to the maximum distance they can focus clearly.
Therefore, the greatest distance the person can stand from the mirror and still see their image clearly is 2.0 meters.
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An airplane traveling 919 m above the ocean at 505 m/s is to drop a case of twinkies to the victims below. How much time before being directly overhead should the box be dropped? What is the horizontal distance between the plane and the victims when the box is dropped?
Answer:
a. 13.7 s b. 6913.5 m
Explanation:
a. How much time before being directly overhead should the box be dropped?
Since the box falls under gravity we use the equation
y = ut - 1/2gt² where y = height of plane above ocean = 919 m, u = initial vertical velocity of airplane = 0 m/s, g = acceleration due to gravity = -9.8 m/s² and t = time it takes the airplane to be directly overhead.
So,
y = ut - 1/2gt²
y = 0 × t - 1/2gt²
y = 0 - 1/2gt²
y = - 1/2gt²
t² = -2y/g
t = √(-2y/g)
So, t = √(-2 × 919 m/-9.8 m/s²)
t = √(-1838 m/-9.8 m/s²)
t = √(187.551 m²/s²)
t = 13.69 s
t ≅ 13.7 s
So, the box should be dropped 13.69 s before being directly overhead.
b. What is the horizontal distance between the plane and the victims when the box is dropped?
The horizontal distance x between plane and victims, x = speed of plane × time it takes for box to drop = 505 m/s × 13.69 s = 6913.45 m ≅ 6913.5 m
Why can water dissolve some ionic compounds, like NH4Cl, as well as some nonionic compounds, like methanol?
Answer:
Water is polar molecule. ... The ionic compounds are dissolved as these ions attract the hydrogen( negative charge attraacts them) and oxygen (positive charge attracts them) whereas methanol is a polar molecule and forms hydrogen bond with water molecules and hence dissolves.
Explanation:
U can choose any scenario just answer please :)))
Answer:
A roller coaster:
The first law states that an object either remains at rest or continues to move at a constant velocity, unless it is acted upon by an external force.
Hope this helps!
Answer:
This
Explanation:
First Law: Newtons first law of motion explains what happens in a car crash because it basically states that the passenger will continue to travel at the same velocity until an unbalanced force acts on he or she. The force that will act upon he or she would be the window, so you should always wear a seat belt!
Second Law: In other words, it states that the force that is applied in the crash is proportional to mass of impacting cars. This means that the bigger the force of impacting cars, the bigger the force applied, which implies a greater destruction.
Third law: Newton's Laws Applied to Collisions. Newton's third law of motion is naturally applied to collisions between two objects. In a collision between two objects, both objects experience forces that are equal in magnitude and opposite in direction.
answer the following questions about the anions of second-row elements, which are commonly used in substitution and proton transfer reactions.
An atom acquires one or more electrons, which results in the formation of an ion with a negative charge known as an anion. Anions of elements in the second row are frequently utilised in chemical processes involving proton transfer and substitution.
Tetrahedral structures are seen by the oxyanions of second-row elements in their group oxidation states. Olivine minerals, also known as (Mg,Fe)₂SiO₄, contain tetrahedral SiO₄ units; nevertheless, the anion does not have a separate existence inside the mineral since the oxygen atoms in the solid state are surrounded tetrahedrally by cations.
Ate anions are extremely resistant to the loss of CH 3 because they have ionic connections between the core atom and the ligands, which are generated by elements that belong to the first three primary groups. Hypervalent anions, which are obtained from the other second-row elements, have predominantly covalent X-C bonding, which gives them (sometimes marginal) resistance to the effects of ligand loss. Hypervalent anions are obtained from the other second-row elements.
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If the skateboarder started at the top of the ramp at 6 m and had a mass of 30 kg, and made it to the bottom going 8 m/s, how much energy was lost to friction?
Answer:
i dont know
Explanation:
sorry
how to spot homogeneous and heterogeneous mixtures
a certain satellite travels in an approximately circular orbit of radius 2.1 × 106 m with a period of 7 h 38 min. calculate the mass of its planet from this information.
To calculate the mass of the planet, we can use the formula for the period of a satellite in circular orbit:
T = 2π√(r³/GM)
T is the period of the satellite (in seconds)
r is the radius of the orbit (in meters)
G is the gravitational constant (approximately 6.67430 × 10^(-11) m³/kg/s²)
M is the mass of the planet (in kilograms)
First, let's convert the period of the satellite into seconds. 7 hours and 38 minutes is equal to 7 × 60 × 60 seconds + 38 × 60 seconds, which gives us a total of 27,480 seconds.
Plugging the given values into the formula, we have:
27,480 = 2π√((2.1 × 10^6)³/(6.67430 × 10^(-11) × M))
To solve for M, we can rearrange the equation:
M = ((2.1 × 10^6)³ × 6.67430 × 10^(-11))/(2π)² × (27,480)²
M ≈ 6.042 × 10^24 kg
Therefore, the mass of the planet is approximately 6.042 × 10^24 kg.
From the given information about the satellite's radius (2.1 × 10^6 m) and period (7 hours 38 minutes), we calculated the mass of the planet to be approximately 6.042 × 10^24 kg using the formula for the period of a satellite in circular orbit.
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An Otto cycle with compression ratio of 10. The air is at 100 kPa, 27 °C, and 500 cm³ prior to the compression stroke. Temperature at the end of isentropic expansion is 1000 K. Determine the followings:
a) Highest temperature and pressure in the cycle b) amount of heat transferred, c) thermal efficiency, and d) mean effective pressure. Use constant specific heat approach - k-1.4, cp= 1.005 kJ/kg.K cv=0.718 kJ/kg.K, R = 0.287 kJ/kg.K
An Otto cycle is used in gasoline engines to convert the thermal energy of burning gasoline into mechanical work. It consists of four stages: compression, heat addition, expansion, and exhaust. The compression ratio is defined as the ratio of the volume of the combustion chamber at the beginning of the compression stroke to the volume of the combustion chamber at the end of the expansion stroke.
Compression ratio, r = V1/V2 Here, V1 = Initial volume of air before compression stroke = 500 cm³V2 = Volume of air after the compression stroke. As the compression ratio is given as 10, the volume of air after the compression stroke, V2 = V1/10 = 500/10 = 50 cm³.
Temperature and pressure can be calculated using the following equations.
PV¹⁴ = Constant (P₁V₁¹⁴) T₁/V₁ = T₂/V₂ (isentropic process)
a) The highest temperature can be found at the end of the combustion stroke.
Here, V3 = V2T3/T2 = V4T4/T3T1V1¹⁴ = V2V3¹⁴ Pmax = T3V3/V2 = T4V4/V3 = P4
b) Amount of heat transferred, Qn = Cn (T4 - T1) Where Cn is the specific heat at constant volume.
Qn = Cn (T4 - T1) = cv (T4 - T1)
c) Thermal efficiency,
η = (Wnet)/Qn = (Qn - Qout)/Qn = 1 - (Qout/Qn) = 1 - (cv (T3 - T2))/(cv (T4 - T1))
d) Mean effective pressure, MEP = (Pmax - Pmin)/2 = (P4V3/V4 - P2V1/V2)/2
The formula for the constant specific heat approach - k-1.4, cp= 1.005 kJ/kg.K cv=0.718 kJ/kg.K, R = 0.287 kJ/kg.K is given below.
Cn = cp/(k-1) = 1.005/(1.4 - 1) = 1.005/0.4 = 2.5125 kJ/kg.Kcv = R/(k-1) = 0.287/(1.4 - 1) = 0.287/0.4 = 0.7175 kJ/kg.K
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Through which of the following ways does the Sun primarily transfer its heat energy to the Earth?
A.
conduction
B.
radiation
C.
convection
D.
reflection
Answer:
B. Radiation
Explanation:
Transfer of heat energy through space by electromagnetic radiation
steam is compressed from 4 mpa and 300 c to 9 mpa isentropically. the final temperature of the steam is group of answer choices
The initial pressure of steam (P1) = 4 MPa, the Initial temperature of steam (T1) = 300°C = 573.15 K, Final pressure of steam (P2) = 9 MPaProcess: The given process is Isentropic Process Formula: For isentropic process, P1V1^γ = P2V2^γWhere γ = Cp / Cv = 1.3 (For Steam)And, V1 / T1^γ-1 = V2 / T2^γ-1,
Where V = Specific volume of steam solution: Specific volume of steam (V1) at initial state is given by, V1 = V2 = v (From the principle of the isentropic process).
Now, from the steam table, At 4 MPa (P1) and 573.15 K (T1), V1 = 0.1006 m³/kgAt 9 MPa (P2), V2 = V1 × (P1 / P2)^(1/γ)= 0.1006 × (4 / 9)^(1/1.3)= 0.080 m³/kg.
Let's use the formula for calculating the final temperature of the steamV1 / T1^γ-1 = V2 / T2^γ-1⇒ T2 = (V2 / V1)^(1/γ-1) × T1= (0.08 / 0.1006)^(1/1.3-1) × 573.15≈ 764.5 K≈ 491.5°C.
Therefore, the final temperature of the steam is 491.5°C (rounded off to one decimal place).
Hence, option D is correct.
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PLSSS HELPP
If humans are evolving, who is having the biggest effect on humanities gene pool? Rich vs poor? Educated vs uneducated? Certain countries over others? Etc.? And how will this affect our evolution in the future?
Answer:
Well, if you look up countries with the highest birth rates, also those countries poverty rates and what class the majority of the people are in then you should have a better understanding. Also, education is not passed through genes it is learned through expirience and being taught. Also being rich vs being poor probably doesn't have that big of an effect either. It is the living conditions.
Explanation:
The forces shaping the short-term future of man, perhaps to the turn of this century, are apparent, and the events are in train. The shape of the world in the year 2000 and man's place therein will be determined by the manner in which organized humanity confronts several major challenges. If sufficiently successful, and mankind escapes the dark abysses of its own making, then truly will the future belong to man, the only product of biological evolution capable of controlling its own further destiny.
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Transform plate tectonic boundaries slide/move past each other, rubbing along the edges cause what types of damage?
Question 3 options:
tornadoes, flooding, destruction
hurricanes, flooding, wave surge
earthquakes, tsunami, landslides
blizzards, freezing conditions, snow drifts
Transform plate tectonic boundaries slide/move past each other, rubbing along the edges causing earthquakes, tsunami, landslides
What is earthquake?An earthquake is the shaking of the surface of the Earth resulting from a sudden release of energy in the Earth's lithosphere that creates seismic waves.
The answer is c is because when tectonic plates are rubbing against each other that’s how an earthquake is formed.
another reason the answer is C is because when the tectonic plates are moving together it can cause the land to slide.
the last reason the answer is C is because when the tectonic plates in the ocean move it can cause a tsunami.
Hence transform plate tectonic boundaries slide/move past each other, rubbing along the edges causing earthquakes, tsunami, landslides
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hi:):):):):):):):):):):):):):):):):):):):):):):):)
Answer:
hi. :)))))))))))))))))))))
What is the full meaning of ROYGBIV?
Answer:
Red, orange, yellow, green, blue, indigo and violet.
Explanation:
Hope I helped! cute copy and paste ☏ ♡ ☆⋆◦★◦⋆°*•°
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° :. ° . ☆ . . • . ● .° °★ Not sure how to copy and paste? Just right click your mouse and choose copy in options, to release repeat the process and just paste it. No mouse? Select the text with your computer pad and use ctrl c to release, ctrl v. On mobile? Press on your screen and select the text, use the option copy and paste wherever you would like!
⭐ Hii ⭐
➡️ Abbreviation for shades of colors often described as creating rainbows: red, orange, yellow, green, blue, indigo, and violet. Its beginning is sometimes called VIBGYOR in reverse order.
Byy...
If one asteroid has an orbital radius of 2AU and another an orbital radius of 4 AU, the orbital period of the farther asteroid will be ____ the orbital period of the closer one.
1- impossible to tell
2- more than twice
3- twice
4- less than twice
The orbital period of the farther asteroid will be less than twice the orbital period of the closer one.
The orbital period of an object around the Sun depends on its distance from the Sun. According to Kepler's third law of planetary motion, the square of the orbital period is directly proportional to the cube of the semi-major axis (orbital radius) of the object. Since the two asteroids have different orbital radii, their orbital periods will differ.
However, the relationship between orbital radius and orbital period is not linear but follows a power law. In this case, the ratio of the orbital periods can be calculated by taking the cube root of the ratio of the orbital radii. By applying this formula, we find that the ratio of the orbital periods is approximately 1.5874. Therefore, the orbital period of the farther asteroid will be less than twice the orbital period of the closer one, making option 4 the correct answer.
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If a 120-W lightbulb emits 3.5 % of the input energy as visible light (average wavelength 550 nm) uniformly in all directions.
PART A: How many photons per second of visible light will strike the pupil (4.0 mm diameter) of the eye of an observer 2.2 m away?
PART B: How many photons per second of visible light will strike the pupil (4.0 mm diameter) of the eye of an observer 1.5 km away?
part a: N= 4.39 x 10^10 photons/second. part b: N = 8.25 photons/second are the answers.
The energy of a photon of wavelength 550 nm can be calculated as follows:
h*c/λ = 6.626 x 10^-34 x 3 x 10^8 / (550 x 10^-9)
wavelength = 3.6 x 10^-19 J.
In one second, a 120-W lightbulb emits energy as visible light in the following amount:
120 x 0.035 = 4.2 W.
As a result, the number of photons emitted per second can be computed as follows:
N = Power/Energy of a photon
N = 4.2/3.6 x 10^-19
N = 1.17 x 10^16 photons/second
PART A: The area of a 4.0-mm diameter pupil is given by the following formula:
A = πr^2
A = π(2.0 mm)^2
A= 3.14 x 4.0 x 10^-6 m^2
The distance from the bulb to the pupil is 2.2 m.
The bulb radiates in all directions, therefore the power per unit area is given by:
P = Power/4πr^2
P = 4.2/(4π(2.2)^2)
P = 0.04 W/m^2
The number of photons striking the pupil per second is determined by the following formula:
N = P*A/E
N = (0.04)(3.14 x 4.0 x 10^-6)/3.6 x 10^-19
N = 4.39 x 10^10 photons/second
PART B: The bulb is now 1.5 km distant from the pupil.
The power per unit area at this distance is:
P = Power/(4πr^2)
P = 4.2/(4π(1500)^2)
P = 2.98 x 10^-10 W/m^2.
Using the equation for the number of photons striking the pupil per second,
N = P*A/E
N = (2.98 x 10^-10)(3.14 x 4.0 x 10^-6)/3.6 x 10^-19
N = 8.25 photons/second
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select three parts of a circular saw
spindle
trigger
base
handle
key
chuck
Answer:
handle, trigger, spindle
Michelle is going to vacation in a location on the globe that is currently experiencing summer and daylight. According the model below, which location could Michelle be visiting? Location A - Axis Sun Location C Location B Equator Location D A) Location A B) Location B ) Location ( D) Location D
a plane monochromatic electromagnetic wave with wavelength λ = 2.8 cm, propagates through a vacuum. its magnetic field is described by
uploaded image
where Bx = 3.1 X 10-6 T, By = 3.4 X 10-6 T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively. .
1) What is f, the frequency of this wave?
2) What is I, the intensity of this wave?
3) What is Sz, the z-component of the Poynting vector at (x = 0, y = 0, z = 0) at t = 0?
4) What is Ex, the x-component of the electric field at (x = 0, y = 0, z = 0) at t = 0?
Sz, the z-component of the Poynting vector at (x = 0, y = 0, z = 0) at t = 0 is 0.
A monochromatic electromagnetic wave with wavelength λ = 2.8 cm, is propagating through a vacuum and its magnetic field is described by B = 8.4 sin(2π(1.0 × 10^9)t - 2π(1.0 × 10^4)x) µT.
The Poynting vector can be used to explain this in more detail. The Poynting vector can be calculated using the formula [rmS = rmE times B over rm2mu], where is the permeability of the medium through which the wave is propagating and E is the electric field.
The equation for the electric field is E = cB, where c is the vacuum speed of light.
The above formula can be used to determine S = 0 for the Poynting vector for the given wave.
The Poynting vector has a z-component of 0 at (x = 0, y = 0, z = 0) and t = 0.
The energy motion thickness of an electromagnetic field can be shown utilizing the Poynting vector, named after John Henry Poynting.
According to the definition, the Poynting vector is the result of the vector product of the electric and magnetic fields: 2.22) S → = E → × H →
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the transfer of thermal energy between particles of matter that are in contact with each other is called thermal _________.
Answer:
Hello There!!
Explanation:
The answer is=>Conduction.
hope this helps,have a great day!!
~Pinky~
[tex]\huge{\textbf{\textsf{{\color{pink}{An}}{\red{sw}}{\orange{er}} {\color{yellow}{:}}}}}[/tex]
Conduction.
thanksHope it helps.A scientist proposed a hypothesis that burning coal at higher altitudes would release less pollution. The data the scientist collected did not support the hypothesis. In what way is the hypothesis still valuable?
Answer: i really don't know bu i recomened you watch josie b asmr she is the best
Explanation:
A tetherball is attached to a pole with a 2.0-m rope. It iscircling at 0.20 rev/s. As the rope wraps around the pole itshortens. How long is the rope when the ball is moving at5.0m/s.
The length of the rope when the ball is moving at 5.0 m/s is approximately 0.925 meters. The calculation was based on the conservation of angular momentum .
To determine the length of the rope when the ball is moving at 5.0 m/s, we can use the conservation of angular momentum. The angular momentum of the system remains constant as the rope wraps around the pole.
The formula for angular momentum is given by:
L = Iω
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
In this case, the moment of inertia remains constant as the mass of the ball and the pole do not change. Therefore, we have:
L1 = L2
The initial angular momentum, L1, is given by:
L1 = I1ω1
The final angular momentum, L2, is given by:
L2 = I2ω2
The moment of inertia is proportional to the square of the radius of the circular motion. Since the rope shortens, the radius decreases as well.
The initial radius, r1, is given by:
r1 = 2.0 m
The final radius, r2, is unknown.
The initial angular velocity, ω1, is given by:
ω1 = 0.20 rev/s * 2π rad/rev
= 1.26 rad/s
The final angular velocity, ω2, is given by:
ω2 = v/r2
where v is the linear velocity of the ball. In this case, v = 5.0 m/s.
Thus, we can rearrange the equation to solve for r2:
r2 = v/ω2
Substituting the known values, we get:
r2 = 5.0 m/s / ω2
Now, we can substitute the equation for the angular momentum to solve for r2:
I1ω1 = I2ω2
r1^2 * ω1 = r2^2 * ω2
Solving for r2, we have:
r2^2 = (r1^2 * ω1) / ω2
Plugging in the known values:
r2^2 = (2.0 m)^2 * 1.26 rad/s / (5.0 m/s / ω2)
r2^2 = 5.04 m^2 rad/s / (5.0 m/s / ω2)
r2^2 = 5.04 m^2 rad/s * (ω2 / 5.0 m/s)
r2^2 = 5.04 m^2 rad/s * (ω2 / 5.0 m/s)
r2^2 = 5.04 m^2 rad/s * ω2 / 5.0 m/s
Simplifying the units:
r2^2 = 5.04 m^3 rad / s^2
r2 = √(5.04) m
r2 ≈ 2.244 m
Therefore, the length of the rope when the ball is moving at 5.0 m/s is approximately 0.925 meters (2.244 m - 2.0 m).
The length of the rope when the ball is moving at 5.0 m/s is approximately 0.925 meters. The calculation was based on the conservation of angular momentum, where the initial angular momentum of the system equals the final angular momentum. By considering the initial radius, initial angular velocity, final radius, and linear velocity of the ball, we derived the equation and solved for the final radius. The result was approximately 2.244 meters, and by subtracting the initial rope length (2.0 meters), we found that the shortened length of the rope is approximately 0.925 meters.
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