Potential energy is the energy that an object possesses due to its position or configuration. So, the difference in potential energy is PE_top - PE_bottom = 24,500 J - 0 J = 24,500 J.
The gravitational potential energy (PE) of an object is the energy it possesses due to its position in a gravitational field. The formula for gravitational potential energy is PE = mgh, where m is the mass of the object, g is the acceleration due to gravity (9.8 m/s^2 on Earth), and h is the height above a reference point.
Given that the person weighs 500 N and climbed a ladder of 5 m, the difference in potential energy at the bottom and the top of the ladder is:
PE_bottom = m * g * h_bottom = (500 N) * (9.8 m/s^2) * (0 m) = 0 J
PE_top = m * g * h_top = (500 N) * (9.8 m/s^2) * (5 m) = 24,500 J
So the difference in potential energy is PE_top - PE_bottom = 24,500 J - 0 J = 24,500 J
This means that the person has an increase in potential energy of 24,500 J as a result of climbing the ladder, which is equal to the work done to lift the person to the top of the ladder.
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If the velocity of an object is zero at some point, then its acceleration must also be zero at that point.
A.) True or B.) False
It is a false statement that if the velocity of an object is zero at some point, then its acceleration must also be zero at that point.
What is Velocity?
The total displacement covered by any object per unit of time is known as velocity. It depends on the magnitude as well as the direction of the moving object.
When any object is thrown vertically upward at the highest point its velocity would be zero but its acceleration would be non zero which is equal to the acceleration due to gravity.
It is a false statement that if the velocity of an object is zero at some point, then its acceleration must also be zero at that point.
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A glacier advances at 3.7 × 10^−6 cm/s. How far will it move in 89000 s? Answer in units of cm.^
\(v = 3.7 \times {10}^{ - 6} \: \: \frac{cm}{s} \)
\(3.7 \times {10}^{ - 6} = \frac{x}{89000} \\ \)
Multiply sides by 89000
\(3.7 \times {10}^{ - 6} \times 89 \times {10}^{3} = x \)
\(37 \times {10}^{ - 1} \times 89 \times {10}^{ - 3} =x \)
\(37 \times 89 \times {10}^{ - 4} = x \)
\(x = 3293 \times {10}^{ - 4} \: \: cm \)
And we're done.....♥️♥️♥️♥️♥️
how fast is the cheetah running in m/s
With 4.3 m/s velocity, is the cheetah running.
velocity= distance/time
distance=27.6 m
time=6.3 s
velocity=27.6 m/6.3 s
velocity=4.3 m/s
A vector number known as velocity describes "the pace at which an item changes its location." Imagine a person moving quickly, taking one stride ahead, one step back, and then beginning from the same place each time. A vector quantity is velocity. As a result, velocity is aware of direction. One must consider direction while calculating an object's velocity. Saying that an item has a velocity of 55 miles per hour is insufficient. The direction must be included in order to adequately characterize the object's velocity. Simply said, the velocity vector's direction corresponds to the motion of an item.
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What is the distance between two spheres, each with a charge of 1. 05 X 10^-7 C when the force between them is 0. 40 N?
Answer:
Answer:please mark as brainliest
-Which phase of the Moon occurs when the Earth is located directly between the Moon and the Sun?
-New moon
-First quarter
-Full moon
-Last quarter
pls help
Answer: new moon
Explanation:
Calculate the Schwarzschild radius (in kilometers) for each of the following.1.) A 1 ×108MSun black hole in the center of a quasar. Express your answer using two significant figures.2.) A 6 MSun black hole that formed in the supernova of a massive star. Express your answer using two significant figures.3.) A mini-black hole with the mass of the Moon. Express your answer using two significant figures.4.) Estimate the Schwarzschild radius (in kilometers) for a mini-black hole formed when a superadvanced civilization decides to punish you (unfairly) by squeezing you until you become so small that you disappear inside your own event horizon. (Assume that your weight is 50 kg.) Express your answer using one significant figure.
Answer:
(I). The Schwarzschild radius is \(2.94\times10^{8}\ km\)
(II). The Schwarzschild radius is 17.7 km.
(III). The Schwarzschild radius is \(1.1\times10^{-7}\ km\)
(IV). The Schwarzschild radius is \(7.4\times10^{-29}\ km\)
Explanation:
Given that,
Mass of black hole \(m= 1\times10^{8} M_{sun}\)
(I). We need to calculate the Schwarzschild radius
Using formula of radius
\(R_{g}=\dfrac{2MG}{c^2}\)
Where, G = gravitational constant
M = mass
c = speed of light
Put the value into the formula
\(R_{g}=\dfrac{2\times6.67\times10^{-11}\times1\times10^{8}\times1.989\times10^{30}}{(3\times10^{8})^2}\)
\(R_{g}=2.94\times10^{8}\ km\)
(II). Mass of block hole \(m= 6 M_{sun}\)
We need to calculate the Schwarzschild radius
Using formula of radius
\(R_{g}=\dfrac{2MG}{c^2}\)
Put the value into the formula
\(R_{g}=\dfrac{2\times6.67\times10^{-11}\times6\times1.989\times10^{30}}{(3\times10^{8})^2}\)
\(R_{g}=17.7\ km\)
(III). Mass of block hole m= mass of moon
We need to calculate the Schwarzschild radius
Using formula of radius
\(R_{g}=\dfrac{2MG}{c^2}\)
Put the value into the formula
\(R_{g}=\dfrac{2\times6.67\times10^{-11}\times7.35\times10^{22}}{(3\times10^{8})^2}\)
\(R_{g}=1.1\times10^{-7}\ km\)
(IV). Mass = 50 kg
We need to calculate the Schwarzschild radius
Using formula of radius
\(R_{g}=\dfrac{2MG}{c^2}\)
Put the value into the formula
\(R_{g}=\dfrac{2\times6.67\times10^{-11}\times50}{(3\times10^{8})^2}\)
\(R_{g}=7.4\times10^{-29}\ km\)
Hence, (I). The Schwarzschild radius is \(2.94\times10^{8}\ km\)
(II). The Schwarzschild radius is 17.7 km.
(III). The Schwarzschild radius is \(1.1\times10^{-7}\ km\)
(IV). The Schwarzschild radius is \(7.4\times10^{-29}\ km\)
The energy conservation allows to find the Schwarschild radius for several bodies of different masses are:
1) Black hole quasar is: r = 2.9 10⁸ km
2) Blsck hole supernove is: r = 17.7 km
3) Mini black hole is: r = 1.1 10⁻⁷ km
4) Human body is: r= 7 10⁻²⁹ km
The schwarschild radius is defined as the distance from a black hole center at radius which the escape velocity is equal to the light speed, in some cases it is also called the event horizon.
Let's use Newton's second law where force is the universal law of attraction and acceleration is centripetal.
F = ma
F = \(G \frac{Mm}{r^2}\)
Where F is the force, M the mass of the black hole, m the handle of the body, r the radius and v the speed of the body.
The energy of the gravitational field is
F = \(- \frac{dU}{dr }\)
U = \(-G \frac{Mm}{r}\)
Let's use conservation of energy
Em₀ = K + U = ½ m v² - \(G \frac{Mm}{r}\)
In infinity the energy
Em_f = 0
energy is conserved
Em₀ = Em_f
½ m v² - \(G \frac{Mm }{r}\) = 0
r = \(\frac{2GM}{v^2}\)
From the definition of the Schwarschild radius this speed is equal to the light speed
v = c
r = \(\frac{2GM}{c^2 }\)
They ask to calculate the radius for several cases of different mass, claculate the constant value
V = \(\frac{2 \ 6.67 \ 10^{-11} }{(3 \ 10^8) ^2 }\)
V = 1.482 10⁻²⁷
1) A black hole of mass M = 1 10⁸ \(M_{sum}\)
The tabulated mass of the sun is \(M_{sum}\) = 1.989 10³⁰ kg
Let's substitute
r = 1.482 10⁻²⁷ 1 10⁸ 1.989 10³⁰
r = 2.94 10⁸ km
With two significant figures
r = 2.9 10⁸ km
2) A black hole of mass M = 6 \(M_{sum}\)
r = 1.482 10⁻²⁷ 6 1.989 10-30
r = 17.7 km
3) a mini black hole with the mass of the moon
Tabulated mass of the moon M = 7.35 10²² kg
r = 1.482 10⁻²⁷ 7.35 10²²
r = 1.1 10⁻⁷ km
4) A person of M = 50 kg
r = 1.482 10⁻²⁷ 50
r= 7 10-29 km
In conclusion using the conservation of energy we can find the Schwarschild radius for several bodies of different masses are:
1) Black hole quasar is: r = 2.9 10⁸ km
2) Blsck hole supernove is: r = 17.7 km
3) Mini black hole is: r = 1.1 10⁻⁷ km
4) Human body is: r= 7 10⁻²⁹ km
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a rock is an example of a solid because
Answer:
The key is that solids hold their shape and they don't flow like a liquid. A rock will always look like a rock unless something happens to it.
Solids can hold their shape because their molecules are tightly packed together.
Explanation:
Yes; it is a solid
Could gold be made from other elements?
Answer:
Yeah, you can make gold from other elements.
Explanation:
To make gold out of other elements you need to have a nuclear reaction.
I hope it helps! Have a great day!
Muffin ^^
Answer:
Yes.
Explanation:
Gold can be made from other elements but it is too expensive so it’s not really worth it.
I hope it helps! Have a great day!
bren~
a series rlc circuit has an impedance of 120 ω and a resistance of 64 ω. what average power is delivered to this circuit when vrms = 90 volts?
The average power delivered to the circuit is 126.56 watts.
In a series RLC circuit, the impedance is given by Z = √(R^2 + (XL - XC)^2), where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance. We know that the impedance Z is 120 ω and the resistance R is 64 ω. So, we can use these values to find the values of XL and XC.
XL = Z^2 - R^2 = √(120^2 - 64^2) = 105.17 ω
XC = √(Z^2 - R^2) = √(120^2 - 64^2) = 105.17 ω
Now, we can use the formula for average power in a series RLC circuit, which is P = Vrms^2/R, where Vrms is the rms voltage. Here, Vrms is given as 90 volts.
P = Vrms^2/R = 90^2/64 = 126.56 watts.
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can you please help me?
Answer:
Iron, You're Welcome :)
Answer:
iron
Explanation:
All living organisms are mainly composed of what elements? * 1 point A. Carbon, Phosphorus, Nitrogen, Oxygen, Potassium B. Calcium, Phosphorus, Nitrogen, Oxygen, Vibranium C. Oxygen, Carbon, Hydrogen, Nitrogen, Phosphorus D. Sodium, Carbon, Nitrogen, Hydrogen, Helium
All living organisms are mainly composed of the elements: Oxygen, Carbon, Hydrogen, Nitrogen, Phosphorus.
The correct answer choice is option c.
What are living organisms?Living organisms are those things that has life. They include plants and animals. Living organisms be it plants or animals are composed of important elements such as carbon, oxygen and others.
However, there are certain characteristic features which living organisms possess. Some of these characteristics of living things are as follows:
Movement: The ability of living organisms to move from one place to another or to move Its body parts. There are two major types of movement known in living organisms. These are: Active movementPassive movementOther characteristics of living organisms are:
RespirationNutritionIrritabilityGrowthExcretionReproduction AdaptationCompetitionIn conclusion, we can now confirm from above the explanation given above that living things are made up of certain elements.
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Which of the following might be the material list for an experiment?
A data tables and graphs
B.meters, liters, and kilograms
C plastic containers, soil, water, thermometers, and plants
D temperature, light, and time
Answer:
C
Explanation:
If the total angular momentum of a system of particles is zero, are all the particles at
rest? Explain.
Answer: No.
Explanation:
Firstly, I want to make the argument that objects moving in a straight line can have angular momentum (you'll see why later).
Suppose we have a particle located at \(\vec{r}=-y\hat{j}\), where r describes the position vector for any particle located at any point directly below the origin. Now suppose its momentum is described by \(\vec{p}=p\hat{j}\), where p is a positive scalar quantity (in other words, the particle has a momentum that drives its motion upward). Angular momentum is a vector quantity and is described by \(\vec{L} = \vec{r} \times \vec{p}\). Since both vectors point in the \(\hat{j}\) direction, their cross products will give us 0 (you should convince yourself of this property if you don't believe it). Now suppose we shift this object some distance d to the right, such that its new position vector is described by \(\vec{r}=d\hat{i}-y\hat{j}\). The \(\hat{j}\) components still cancel, but \(\hat{i} \times \hat{j} = \hat{k}\), so our cross product for angular momentum yields \(\vec{L}=\vec{r} \times \vec{p}=d\hat{i} \times p\hat{j}=dp\hat{k}\). So despite having the same motion (momentum), the particle has an angular momentum. This tells us two important characteristics about angular momentum:
Particles moving in a straight line can have non-zero angular momentum.Angular momentum depends on the choice of origin (notice how we shifted the object a distance d to the right, which you can say means we shifted the origin a distance d to the left)Please see attachment for an image reference if you cannot picture/diagram this (ignore the gravitational force drawn on the particle).
Now, lets take a system of particles. Suppose we have two particles on the x-axis with mass m, a distance d from the origin on either side, and velocities such that one particle moves to the right and the other moves to the left. For a system, angular momentum is defined as the following:
\(\vec{L}=\sum_i \vec{r_i} \times \vec{p_i}=\sum_i m_i(\vec{r_i} \times \vec{v_i})\)
Note: mass is a scalar quantity, so the cross product is not defined for it.
For this system, we can write out the angular momentum as the following:
\(\vec{L}=m(d\hat{i} \times v\hat{i}) + m(-d\hat{i} \times -v\hat{i})\)
However, we established above that the cross product of two identical vectors yields a result of 0. So we get that the angular momentum is 0, and yet both particles move, just that one moves to the right while the other moves to the left. In other words, the total angular momentum of the system is zero while the particles are not at rest.
If this is confusing, think about it in a more mathematical way. Angular momentum is a vector quantity, and thus follows the rules of vector algebra. In other words,
\(\vec{L}=\vec{L_1}}+\vec{L_2}}+\vec{L_3}}+...+\vec{L_n}}\)
This is known as superposition. Suppose we constructed a system of two particles where their cross products didn't evaluate to 0. We can still use the principle of superposition to create a scenario where the angular momentum is 0.
Suppose we have a system of 2 particles where \(\vec{L_1} = -\vec{L_2}\). The total angular momentum would be defined as
\(\vec{L}=\vec{L_1}+\vec{L_2}=\vec{L_1}-\vec{L_1}=0\).
Now it doesn't matter if the particles move in a straight line, a circular path, or any other type of motion. If their individual angular momentums are equal in magnitude and opposite in direction, the angular momentum of the system is zero without the particles needing to be necessarily at rest.
Please help me Calculate the total energy stored in the capacitor
La fórmula: P = W/t ó W = P x t. donde:
P = potencia
W = trabajo
t = tiempo
Otra fórmula de potencia es: P= I x V
Proceso de carga de un capacitor - condensador
Una fórmula muy importante que también hay que tener en cuenta es: V = q/C que indica que el voltaje es proporcional a la carga que hay en un condensador.
De la fórmula de potencia P= I x V y considerando que la corriente es constante (corriente continua), entonces la potencia es proporcional al voltaje. Si el voltaje aumenta en forma lineal, la potencia aumentará igual. Ver el siguiente diagrama.
Como la potencia varía en función del tiempo, no se puede aplicar la fórmula W = P x t, para calcular la energía transferida. Pero observando el gráfico, se ve que esta energía se puede determinar midiendo el área bajo la curva de la figura.
Energía Almacenada en un Condensador - Capacitor
El área bajo la curva es igual a la mitad de la potencia en el momento “t”, multiplicada por “t”.
Entonces: W = (P x t) / 2. Pero se sabe que P = V x I. Si se reemplaza esta última fórmula en la anterior se obtiene: W = (V x I x t) / 2, y como I x t = CV = Q, entonces para saber cuanta energía (W) hay en un condensador usamos una de las siguientes fórmulas:
W = (CV2/2) julios
W = (QV/2) julios
W = (Q2/2C) julios
, donde:
W = Trabajo (Energía) en julios
C = Capacidad en faradios
V = voltaje en voltios en los extremos del condensador
Q = carga del condensador
Answer with the given explanations below: First the given formula that looks like this is: or where:
P = power
W = work
t = time
Next with another given power formula that looks like this is:
This is the charging process of a capacitor - capacitor #1.
Then it's a very important given formula that it must also be taken into account is: which it was indicated that the voltage is proportional to the charge on a capacitor.
In the following below, from the given power formula that looks like this is: and we are considering that the current is the constant (direct current), and then the power is proportional to the voltage. If the voltage increases linearly, the power will increase the same. See the following diagram. (I'm sorry, Yhungbabe, I don't have the diagram to show you in order to refer to the total energy stored in the capacitor because I havenèt learned the energy stored in the capacitor)
Anyway, since the power varies as a function of the time, the given formula that looks like this is: cannot be applied to calculate the energy transferred. But looking at the graph, it seems that this energy can also be determined by measuring the area under the curve of the figure.
This is The Energy Stored in a Capacitor - Capacitor #2.
The area under the curve is equal to the half of the power at time "t", being multiplied by "t".
Then with the given formula below that looks like this is:
But it's known that If this is the last given formula is being replaced in the previous one, we obtain the new given formula that looks like this is: and as another new given formula that looks like this is: there's so to find out how much energy (W) that there's in a capacitor that we use in one of the new given formulas that looks like in the listed below are:
joules
joules
joules
Now finally where:
W = Work (In The Energy) in Joules
C = Capacity in the farads
V = voltage in the volts at the ends of the capacitor
Q = a capacitor charge
I apologize for the late answer and the replies, so anyway, I use the online language translator in order to translate Spanish to English for you in order to understand my work given below, so, I hope my answer with the given explanation below here is very helpful to your own question about how to calculate the total energy stored in the capacitor with the image has been provided, please mark me as Brainliest and have a great rest of the day! :D
Sincerely,
Jason Ta,
The Ambitious of The Brainly And The Role of The TDSB And WHCI Student of The High School.
the work is done, but what two assumptions can be made?
Answer:
Oh for number this is the one?
Are we exceeding the carrying capacity of the entire planet?
Answer:
almost, we would need around 12 billion people to do that i believe
Explanation:
Answer:
no
Explanation:
The electric resistance of the element in a platinum resistance thermometer at 100°C, 0°C and room temperature are 75. 000, 63. 000 and 64. 992 ohms respectively. Use these data to determine the room temperature
The room temperature is approximately 0.95°C.
Rt = Ro[1 + A(Tt - To) + B(Tt - To)2]
75,000 = Ro[1 + A(100 - To) + B(100 - To)2]
64,992 = Ro[1 + A(25 - To) + B(25 - To)2]
Dividing the two equations, we can eliminate the unknown constant Ro and obtain an expression for the ratio of A/B:
75,000 / 64,992 = [1 + A(100 - To) + B(100 - To)2] / [1 + A(25 - To) + B(25 - To)2]
Simplifying and rearranging, we get:
A/B = [1 + (100 - To)(64,992/75,000) - (25 - To)] / [(100 - To)2 - (25 - To)2(64,992/75,000)]
Using the given resistance values, we can evaluate the ratio of A/B to be approximately 0.00386.
63,000 = Ro[1 + 0.00386(0 - To) + B(0 - To)2]
Simplifying and solving for To, we get:
To ≈ 0.95°C
Resistance is a property of materials that opposes the flow of electrical current. It is a measure of the degree to which an object resists the passage of electrons through it. Resistance is caused by collisions between the electrons and the atoms that make up the material. These collisions cause the electrons to lose energy and slow down, reducing the flow of current.
The unit of resistance is the ohm (Ω), and it is defined as the ratio of voltage to current. Materials with high resistance have a low conductivity, while materials with low resistance have a high conductivity. This property is important in designing electronic circuits, where different components need to have different levels of resistance to perform specific functions. Resistors, for example, are components that are designed specifically to provide a certain level of resistance to a circuit.
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Nuclear energy PLEASE HELP
Answer:
Nuclear to radiant to thermal
Explanation:
The Sun works on nuclear fusion, hence the nuclear energy, to radiant the type of energy given off the sun that is absorbed by the solar panel, to thermal, thermal energy is spread through the release of heat from the solar panel
All Sections
A student pushes a 40 Kg cart with a force of 300 Newtons. What is its
acceleration?
Answer:
7.5 m/s2
Explanation:
F = ma
300 = 40 kg (a)
divide both sides by 40 to single out the variable a (acceleration)
300/40 = 7.5 m/s2
A toy airplane is flying at a speed of 3 m/s with an acceleration of 1.1 m/s squared how fast is it flying after five seconds
Answer:
\(8.5\frac{m}{s}\)
Explanation:
Use Kinematics:
\(v = v_0 + at\)
\(v = 3 + 1.1 * 5\)
\(v = 8.5 \frac{m}{s}\)
How much power is used by 4 A appliance that is plugged into a 120 V circuit for 4 minutes
Answer:
Power, P = 480 W
Explanation:
It is required to find the power used by 4 A appliance that is plugged into a 120 V circuit for 4 minutes. Power used by an appliance is given by the formula as follows :
\(P=VI\)
Plugging all the values we get :
\(P=120\times 4\\\\P=480\ W\)
So, the power used by the appliance is 480 W.
what is thermal conductivity?
Explanation:
Thermal conductivity is a measure that refers to the rate at which heat is transferred by conduction through a unit cross-section area of a material.
or in simpler terms how well a substance conducts heat.
its formula is seen in the attachment. hope this helps.
The trapping of heat in the lower atmosphere (the troposphere), referred to as the greenhouse effect, is a natural process that helps regulate the temperature of our planet, allowing for life on Earth to exist and flourish. Nitrogen and oxygen molecules make up 99% of Earth's atmosphere, with water and carbon dioxide accounting for less than 0.5%. This natural greenhouse effect is the result of heat absorption by H2O and CO2 molecules in the lower atmosphere, and re-radiation of this trapped heat back to Earth's surface. Without the natural greenhouse effect, Earth's temperature would be 0°F instead of its present 57°F. The question for some is whether human activities are causing an increase of the greenhouse effect, and thus global climate change. Scientific data collected in the past 50 years indicates that the concentration of greenhouse gases in the atmosphere has been increasing.
Im not sure what your question is? Are you asking if humans have contributed to global warming?
Write the word conduction, convection or radiation in the blanks in front of the numbers.6. _____________________ Heat from the sun warming a swimming pool.7. _____________________ Changing a light bulb while it’s still hot.8. _____________________ Heat from the hood of a car when you touch it the hood.9. _____________________ Feeling the heat from a stove burner without touching the stove.10. ____________________ Boiling water moving in a circular motion.
Conduction: heat transfers by direct contact
Convection : heat transfers within fluid
Radiation: heat transfers due to electromagnetic waves
Conduction: 7 , 8 ,
Convection : 10
Radiation : 6,9
What is the approximate wavelength of a light whose second-order dark band forms a diffraction angle of 15. 0° when it passes through a diffraction grating that has 250. 0 lines per mm?.
The approximate wavelength of the light that forms a diffraction angle of 15.0° through a diffraction grating that has 250.0 lines per mm is 4.60 × 10⁻⁷ m.
formula for the angular position of the nth-order dark band in a diffraction grating is given by:
Where;λ is the wavelength of lightd is the grating separationn is the order of the diffractionθ_n is the angle at which the nth order appears
We are given;d = 1/ 250.0 = 4.0 × 10⁻³ mθ = 15.0° = 15 × (π/180) = 0.262 radiansn = 2
Substitute all values into the formula\(;$$d (\sin θ_n) = nλ$$$$(4.0 × 10⁻³)(\sin 0.262) = (2)λ$$$$\lambda = \frac{(4.0 × 10⁻³)(\sin 0.262)}{2}$$$$λ = 4.60 × 10⁻⁷ m$$\)
Therefore, the approximate wavelength of the light that forms a diffraction angle of 15.0° through a diffraction grating that has 250.0 lines per mm is 4.60 × 10⁻⁷ m.
Summary The wavelength of light that forms a diffraction angle of 15.0° through a diffraction grating that has 250.0 lines per mm is 4.60 × 10⁻⁷ m.
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A disk with radius R has uniform surface charge density σ.
Part A
By regarding the disk as a series of thin concentric rings, calculate the electric potential V at a point on the disk's axis a distance x from the center of the disk. Assume that the potential is zero at infinity. (Hint: Use the result that potential at a point on the ring axis at a distance x from the center of the ring is V=14πϵ0Qx2+a2√ where Q is the charge of the ring. )
Express your answer in terms of the given quantities and appropriate constants.
Part B
Calculate −∂V/∂x.
Express your answer in terms of the given quantities and appropriate constants
Part A: The electric potential V at a point on the disk's axis a distance x from the center of the disk is given by:
V = σ/2ε₀ × \((R^{2}/(x^{2} +R^{2} )^{1/2})\)
Part B: After calculating for −∂V/∂x we get:
-∂V/∂x = σR²x/2ε₀\((x^{2}+R^{2})^{3/2}\)
Part A:
The disc can be split into a number of thin, concentric rings in order to compute the electric potential V at a point on its axis that is located x distance from the disk's centre.
Each ring's potential is determined by:
\(V_{ring}\) = 1/4πε₀ × (\(Q_{ring}\) / \((x^{2} +R^{2} )^{1/2}\))
where
\(Q_{ring}\) is the charge of the ring and
ε₀ is the permittivity of free space.
Since
the disk has uniform surface charge density σ, the charge on each ring is given by:
\(Q_{ring}\) = σ × 2πr × dr
where
r is the radius of the ring and
dr is its thickness.
By substituting \(Q_{ring}\) into the expression for \(V_{ring}\), we get:
\(V_{ring}\) = 1/4πε₀ × (σ × 2πr × dr / \((x^{2} +R^{2} )^{1/2}\))
By integrating across all the rings, it is possible to get the total potential V at any point along the axis of the disc:
V = ∫V_ring
V = ∫(1/4πε₀ × (σ x 2πr × dr / \((x^{2} +R^{2} )^{1/2}\))
V = σ/2ε₀ × ∫(r / \((x^{2} +R^{2} )^{1/2}\)) dr from 0 to R
By evaluating the integral and simplifying, we get:
V = σ/2ε₀ × [\((R^{2}/(x^{2} +R^{2} )^{1/2})\) - \((0/(x^2+0^2)^{1/2})\)]
V = σ/2ε₀ × \((R^{2}/(x^{2} +R^{2} )^{1/2})\)
Therefore, the electric potential V at a point on the disk's axis a distance x from the center of the disk is given by:
V = σ/2ε₀ × \((R^{2}/(x^{2} +R^{2} )^{1/2})\)
Part B:
To find the value of −∂V/∂x,
The derivative of the equation for V with regard to x must be taken:
∂V/∂x = -σR²x/2ε₀\((x^{2}+R^{2})^{3/2}\)
Hence, the expression for −∂V/∂x is:
-∂V/∂x = σR²x/2ε₀\((x^{2}+R^{2})^{3/2}\)
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Diagram shows the heating
curve for 0.5 kg heated by a
100 W immersion heater. What
is the specific heat capacity of
the liquid?
Answer: 35
Explanation:
Given the following :
M = 0.5 kg
Power of heater = 100W
From the graph ;
Time (t) = 7seconds
Change in temperature(Dt) = t2 - t1
Where t2 = 70°C, t1 = 30°C
Dt = (70 - 30)°C = 40°C
Recall Q = iVt
IV = power
Q = mcDt
c = specific heat capacity of liquid
mcDt = ivt
mcDt = power × t
0.5 × c × 40°C = 100 × 7
20°C × c = 700 J
c = 700 J/ 20°C
c = 35 J / kg°C
How can you calculate the reaction rate of your friend with a ruler? Design an experiment to calculate the reaction rate of your partner.
what is the condition for the first dark fringe through a single slit of width w?
The condition for the first dark fringe through a single slit of width w is when the path difference between the rays passing through the top and bottom edges of the slit is half a wavelength, which causes destructive interference and results in a dark band on the screen.
This can be expressed mathematically as sin θ = λ/w, where θ is the angle between the direction of the incoming light and the direction of the diffracted light, λ is the wavelength of the light, and w is the width of the slit.
The condition for the first dark fringe in a single-slit diffraction pattern occurs when the path difference between adjacent rays is equal to half the wavelength (λ/2). This can be represented by the equation:
sin(θ) = λ/(2w)
where θ is the angle of the first dark fringe, λ is the wavelength of the light, and w is the width of the slit.
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if a body starts from rest and attains a velocity of 20 metre per second in 8 seconds find the acceleration produced in the body
Answer:
2.5 m/s^2
Explanation:
the equation to find acceleration is \(\frac{v - v_{0} }{t}\) where \(v_{0}\) is the initial velocity, v is the current velocity, and t is the total time
so plug in your values: \(\frac{20 - 0}{8}\)
that turns into 20 ÷ 8
this equals 2.5 m/s^2