a)
(i) Potential for r < a: V(r) = λ / 2π∈₀㏑ (b/a)
(ii) Potential for a < r < b: V(r) = λ / 2π∈₀㏑ (b/r)
(iii) Potential for r > b: V(r) = 0
Here we want to calculate the potential for r < a.
Before calculating the potential, we have to keep in mind that the electric field outside an infinite wire or an infinite cylinder uniformly charged is
E = λ / 2 π ∈₀* r
where, λ is the linear charge density
r is the distance from the wire/surface of the cylinder
By integration, we find an expression for the electric potential at a distance of r:
V(r) = ∫ E dr = λ / 2π∈₀ ㏑ (r)
Inside the cylinder, however, the electric field is zero, because the charge contained by the Gaussian surface is zero:
E = 0
So, the potential where the electric field is zero is constant:
V = constant
(iii) We start by evaluating the potential in the region r > b. Here, the net electric field is zero, because the Gaussian surface of radius r here contains a positive charge density +λ and an equal negative charge density -λ. Therefore, the net charge is zero, so the electric field is zero.
This means that the electric potential is constant so we can write:
ΔV = V(r) - V(b) = 0
V(r) = V(b)
However, we know that the potential b is zero, so
V(r) = V(b) = 0
(ii) The electric field in the region a < r < b instead it is given only by the positive charge +λ distributed over the surface of the inner cylinder of radius a, therefore it is
E = λ / 2π∈₀
And so the potential in this region is given by:
V(r) = ∫ E dr = λ / 2π∈₀ [ ㏑(b) - ㏑(r)] = λ / 2π∈₀ ㏑(b/r) ----(1)
(i) Finally, the electric field in the region r < a is zero, because the charge contained in this region is zero: E = 0
This means that the potential in this region remains constant and it is equal to the potential at the surface of the inner cylinder, so calculated at r = a
which can be calculated by substituting r = a in expression (1)
V(a) = λ / 2π∈₀ ㏑(b/a)
And so, for r < a
V(r) = λ / 2π∈₀ ㏑(b/a)
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How can you find the distance travelled or displacement of an object in a velocity-time graph?
Answer:
by calculating the total area under the displacement of the graph
Dakota moves a magnetic toy train toward a magnet that cannot move. What happens to the potential energy in the system of magnets during the movement?.
A 1000-kg car is moving at 27 m/s when it slams on the brakes and skids to a stop with a leftward acceleration
of 9 m/s/s.
The length of skidding marks will be of 46.49m
Explain what an acceleration is.Acceleration is the rate at which the direction and speed of motion change over time. It is said to have been accelerated when something changes its direction and moves faster or slower. Motion on a circle accelerates even when the speed is constant because the direction is constantly changing.
Acceleration is the term for the rate at which speed changes. Velocity is a vector quantity because it has both a magnitude and a direction component. Acceleration is also a vector quantity since it is simply the rate at which velocity changes.
Given m = 1000 kg
v = 27 m/s
µ = 0.80
we have a = µ g and v² - u² = 2as
then for s = u²/2gµ
s = 27²/2 X 9.8 X 0.8
s = 46.49 m
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Complete question is " A driver in a 1000 kg car traveling at 27 m/s slams on the brakes and skids to a stop. If the coefficient of friction between the tires and the horizontal road is 0.80, how long will the skid marks be?".
An object moving at 44 m/s is increasing in speed by 2 m/s². After 3 seconds, what
would its velocity be?
Answer:
50m/s
Explanation:
a =(V-U)/t
V=? , U = 44m/s, t= 3s, a = 2m/s²
so, using the equation,
2= (V -44)/3
V = 50m/s
consider the following circuit. after leaving the switch at the position a for a long time, move the switch from a to b. there will be current oscillations.
- What is the maximum current?
- Consider the following statements
A1. The current flow is counterclockwise
A2. The current is zero
A3. The current flow is clockwise
B1. The charge on the left plate of C is positive
B2. The charge on the left plate of C is zero
B3. The charge on the left plate of C is negative
Which pair of choices below best describesthe situation at t =5/8T, where T is the periodof oscillations in LC circuit? Let the timewhen the switch is moved from a to b be att = 0.
After leaving the provided switch at the given position for a longer time, then its moves given switch from a to b. At t = 0, the left part of the plate C has charge q = max and therefore, the current flowing through it is zero.
Oscillation is the repetitive or periodic variation, usually in time, of a few degree approximately a crucial value or extra one-of-a-kind states. Familiar examples for all oscillation encompass a swinging type of pendulum with alternating current. A wave is stated to oscillate, which means to transport to and fro in a regular, repeating way.
This fluctuation may be among extremes for all position, like force or quantity. Different sorts of waves have one-of-a-kind sorts of oscillations.
Longitudinal types of waves: here oscillation is parallel route of the wave.
The maximum charge stored in the capacitor is,
Q = CE ------(1)
i = 0
At t = t/4, the left part of the plate C has charge q = 0 and therefore, the current flowing through it is clockwise.
i = clockwise
At t = t/2, the left part of the plate C has charge q = -9max and therefore, the current flowing through it is zero.
i = 0
At t = 3t/4, the left part of the plate C has charge q = 0 and therefore, the current flowing through it is counter clockwise
i = counter clockwise
At t = 0, the left part of the plate C has charge q = max and therefore, the current flowing through it is zero.
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why were you cautioned not to mix the solution in one spot with the solution in another spot on your spot plate
Answer: Depending on the factors, combining two chemicals that aren't designed to interact might result in an explosion, an unintended chemical reaction, or a misleading result.
What is explosion ?
An explosion is a sudden increase in volume accompanied by a tremendous energy release that typically results in the production of high temperatures and the discharge of high-pressure gases. High explosive detonations produce supersonic explosions that move through shock waves.
Explosions often fall into one of three categories: chemical, mechanical, or nuclear. Every kind of explosion has the potential to be devastating and serious, wreaking unimaginable damage on the local populace, environment, and infrastructure.
What causes gamma ray bursts is one of the largest unsolved questions of all. These bursts, which happen around once every day, are the most powerful explosions known to science.
Thus, depending on the factors, combining two chemicals that aren't designed to interact might result in an explosion, an unintended chemical reaction.
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In a competition, a football player kicked a ball 250 meters into the air. While in flight, the ball traveled at
an average speed of 17.0 m/s. How long did the ball remain in the air?
With the assumption that 250 meters is horizontal range, the ball remain in the air for a period of 14.7 s
What is Range ?Range is the horizontal distance from the point of projection to the point where the projectile hits the projection plane again.
Given that In a competition, a football player kicked a ball 250 meters into the air. While in flight, the ball traveled at an average speed of 17.0 m/s.
The parameters are;
Range R = 250 mInitial speed u = 17 m/sPeriod T = ?R = uT
Substitute all the parameters into the formula
250 = 17T
T = 250/17
T = 14.7s
Therefore, the ball remained in the air for 14.7 s long.
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if the ring is off-center when it drops on the disk, how will that affect the results? think about the effect on the moment of inertia.
The disk will continue to spin if the ring strikes it off-center, but the moment of inertia will be affected.
The disk will be out of balance due to the ring's off-center placement, which will result in a lower moment of inertia than it would have if the ring were centered. The disk will therefore not spin as quickly or for as long as it would if the ring were in the middle.
This implies that the ring's rotational energy will not be dispersed uniformly, leading to an uneven, or skewed, rotation. The off-center ring's inability to accurately reflect the moment of inertia will result in an erroneous measurement of it.
What is moment of inertia?
The term "moment of inertia" refers to a physical quantity that quantifies a body's resistance to having its speed of rotation along an axis changed by the application of a torque (turning force).
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A light shines on a metal surface but no electrons are observed to be leaving. What would we need to do experimentally to eject electrons from the surface?.
what is the ppc cycle? what is the process?
Answer:
The PPC Cycle refers to Production Planning Control. It has 3 phases—preplanning, planning, controlling. The Pre-Planning Phase consists of product development, sales forecasting, factory or plant layout, equipment selection policy, and preplanning of production just prior to large scale production.
an ambulance is generating a siren sound at a frequency of 2,400 hz. the velocity of sound is 345.0 m/s. if the ambulance is traveling at a velocity of 24.00 m/s toward from the stationary observer, then what is the frequency of the siren perceived by the observer?
The frequency of the siren perceived by the observer is 2,566 Hz.
Calculation:
F = fo(Vsound +V)/(Vsound⁻V source) 2000*(345+24)/345 = 2,566 Hz.
Frequency describes the number of waves passing through a particular location at a particular time. So if the wave takes 1/2 second to travel, the frequency is 2 per second. If it takes 1/100th of an hour, the frequency is 100 per hour.
The term frequency refers to the number of waves passing through a fixed point in a unit of time. It also describes the number of cycles or vibrations an object undergoes in periodic motion in a unit of time. The frequency of a particular data is the frequency with which the data value occurs. Denote the frequency of the data values by f.
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What is the acceleration of a 50 kg object pushed with a force of 200N?
Answer:
40 m/s
Explanation:
F = ma (force = mass * acceleration)
a = F/m
a = 200 N / 50 kg
a = 40 m/s
when did the photons in the cosmic microwave background first travel freely through the universe?
if a system does 57.0 kj of work on its surroundings and releases 105 kj of heat, what is the change in the internal energy of the system, in kj?
The changes in the internal energy of the system -164 KJ.
Solution:
change in internal energy = q + w
= -105 KJ(+ 57 kg)
= -164 KJ.
The change in internal energy of the system is the sum of heat transferred and work done. The heat flux is equal to the change in internal energy of the system plus the PV work done. The change in internal energy of the system is the sum of heat transferred and work done.
The heat flux equals the change in internal energy of the system plus the PV work. An isolated system cannot exchange heat or interact with its surroundings, so its internal energy change is equal to zero. But in a cyclical process, the total change in the internal energy of the system is zero.
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Which way is rain formed in the tropics where the air is warmer?
A) Condensed ice crystals collect other ice crystals until they fall from the clouds and
then melt into rain when they hit a layer of warm air.
B) Condensed water droplets collect other water droplets to form the collector drop
until they fall from the clouds as rain.
Condensed water droplets collect other water droplets to form the collector drop until they fall from the clouds as rain. In this way rain is formed in the tropics where the air is warmer.
What does the process of rain formation?A significant volume of water evaporates and is released into the atmosphere when water bodies are heated during the day. Evaporation is the term for this. Water vapour is carried upward by the hot air as it rises. The air cools and expands as it rises. Condensation is the term for this occurrence. Clouds are created as a result of water vapour condensation. With the assistance of the wind, these clouds are transported away, and when they become heavy, they drop to the ground as rain.
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The bob of a simple pendulum is swinging between points X and Y.
It takes 8.6 s to swing from X to Y and back to X ten times.
What is the period of the pendulum?
A 0.43s
B 0.86s
C 4.3s
D 86s
If the bob of a straightforward pendulum swings between points X and Y, then its period is 0.86 seconds.
What does a pendulum do and why does it swing?a system made composed of a string that hangs from an overhead support as well as an object at the string's bottom. Gravity and the string's combined force cause the object to swing back and forth. Bob the Pendulum any item that is dangling from the pendulum string.
Why is the pendulum significant?Because a pendulum travels back to towards the mean position due to the influence of gravitational force, it is used to gauge the gravitational effect. A pendulum can be used to identify the moment because its time period is constant. A clock's hands are kept moving by a pendulum inside.
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the theory that dark matter is not real and is just a a problem with our theory of gravity has been falsified by
The findings of Fritz Zwicky and Jan Oort suggest the motion of neighboring stars in our galaxy and galaxies in the Coma cluster do not follow Newton's law of gravity.
Exists dark matter in reality?In fact, the gravitational pull that dark matter appears to have on visible stuff is the only way that researchers have been able to deduce its existence. Dark matter, which makes up about 27% of the cosmos, appears to outnumber visible matter by a factor of nearly six to one.
Do dark matter and gravity interact?Given the rates at which astronomers observe the galaxies revolving, the prevailing view among cosmologists holds that dark matter permeates nearly every galaxy and provides the extra gravity that prevents stars from swirling out into space.
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Once a tropical storm forms over the ocean, which conditions must exist in its path for it most likely to develop into a hurricane?
O warm ocean temperatures, moderate winds, and moist atmospheric layers
O cold ocean temperatures, weak winds, and dry atmospheric layers
O warm land temperatures, strong winds, and moist atmospheric layers
O cold land temperatures, moderate winds, and dry atmospheric layers
Answer:
O warm ocean temperatures, moderate winds, and moist atmospheric layers
On a recent adventure trip, Anita Break went rock-climbing. Anita was able to steadily lift her 80.0-
kg body 20.0 meters in 100 seconds. Determine Anita's power rating during this portion of the
climb.
Anita's power rating during this portion of the climb is 15680 J.
What is the rock-climbing?Rock climbing is an activity in which people climb up, down, or over natural or man-made rock cliffs. The objective is to reach the top of the terminus of a path without falling. It is under the physical Education.
Given that,
mass (m) = 80.0 kg
time = 100 sec
height = 20.0 m
Now, Anita needs to apply a force that is equal to her weight in order to elevate her body a distance of 20.0 m.
Thus, force is equal to:
F = (80 kg) × (9.8 N/kg)
F = 784 N.
So the work she does to lift her body in 20.0 m is:
W = (784 N) ×(20.0 m) × cosine(0°)
W = 15680 J.
So, Anita's power rating during this portion of the climb is 15680 J.
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Find the value of the decay constant of a radioactive substance having a half-life of
0.02 seconds.
34.65 is the value of the decay constant of a radioactive substance having a half-life of 0.02sec.
Half-Life: It is the amount of time it takes for half of a Radioactive particular sample to react particular quantity requires to reduce its initial value to half. That means the time taken by the radioactive substance or isotopes to decay half.
Half-Life Formula :t₁/₂ = 0.693/λ
Where as t1/2 is Half-Life of a radioactive substance
λ= decay constant
We have t1/2 = 0.02sec substitute in the formula
0.02=0.693/λ ⇒λ= [tex]\frac{0.693}{0.02}[/tex]
λ= 34.65
The decay constant of a radioactive substance having a half life-life of 0.02 is 34.65.
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Write the derived unit of following physical quantities. (a) (Area) (b) (Pressure)
Answer:
The SI unit of Area is meter square (represent as m2)
The SI unit of pressure is one newton per square metre ( represent as N/m2).
a crate of grapes lifted 10 meters gains 200 j of potential energy. if the same crate is instead lifted 20 meters, its gain in potential energy is
A same crate gains twice as much potential energy when it is raised 20 meters alternatively.
What is potential energy, exactly?Potential energy is a form of energy that is dependent on the relationship between different system components. When a springy is stretched or stretched, its potential energy increases. If a steel ball is pushed above the ground as opposed to descending to the ground, it has more energy stored.
What kind of potential energy is that?An object has the capacity to store energy because of its position. As an example, a destruction machine's large ball is conserving energy by being held in a high position. This positional force that has been saved is known as electric potential.
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you are riding on the edge of a spinning playground merry-go-round. if you pull yourself to the center of the merry-go-round, what will happen to its rotation?
If you pull yourself to the center of the merry-go-round, the rotation of the merry go round will decrease.
What is the centripetal acceleration of a merry go round?This is the radial acceleration experienced by a person moving in a circular path as the merry-go-round rotates about its mean position.
a = v²/r
where;
v is the linear speed of the merry go roundr is the radius of the merry go rounda is the centripetal acceleration of the merry go roundFrom the formula given above, as the radius of the merry go round increases, the centripetal acceleration of the merry go round decreases.
v = ωr
where;
v is the tangential speed or linear speed of the merry go roundr is the radius of the circular path from the edgeThus, when the radius of the circular path decreases, the speed of the merry go round will decrease as well.
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how does the size of the habitable zone around a star of spectral class g compare to the size of the habitable zone around a spectral class m star?
The size of the habitable zone around a star of spectral class g is larger to the size of the habitable zone around a spectral class m star.
What is a habitable zone?The range of orbits around a star within which a planetary surface may sustain liquid water given sufficient atmospheric pressure is known as the habitable zone, sometimes known as the circumstellar habitable zone (CHZ) or simply the habitable zone.The CHZ's boundaries are determined by Earth's location within the Solar System and the quantity of solar radiation it receives.Given the significance of liquid water to Earth's biosphere, the nature of the CHZ and the things contained inside it may be crucial in defining the range and distribution of planets capable of supporting Earth-like extra terrestrial life and intelligence.Due to the possibility that there are more planetary-mass moons in the CHZ than planets, the region is also of great interest to the newly growing topic of the habitability of natural satellites.To learn more about habitable zone, refer:
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A network of transformers and transmission cables transfers electrical power from
power stations to consumers.
What is this network called?
A transmission Grid is called a network of transformers and transmission cables that transfer electrical power from power stations to consumers
Electrical transmission is the process of providing highly efficiently generated electricity to a district or over larger and longer distances. The main point of the grid is to give people access to electricity 24 hours without interruption and without any trouble in populated areas. Transformers play a crucial role in this. Transformer help in increasing the voltage of the grid to make it more powerful and effective. It helps in the feasible transmission of the grid.
The electrical transmission system is combined with power plants in cities, distribution systems for easier access to electricity, and sub-stations for backup and other purposes which is to form what is known as the electrical grid. The grid meets people's electricity requirements and is what gets the electrical power from its generation to its end use. Since power plants are most often located outside of densely populated areas, the transmission system must be fairly large scale.
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A network of transformers and transmission cables transfers electrical power from power stations to consumers is called as a transmission grid.
What is a transmission grid?Electric power transmission is the bulk movement of electrical energy or power from a generating site, such as a big power plant, to an electrical substation or other places. The interconnected lines which facilitate this movement of electrical energy form a transmission network or transmission grid.
A transmission grid is a network of power stations, transmission lines, and the substations. Energy is generally transmitted within a grid through the three-phase AC. Single-phase AC is used only for distribution to end users however, it is not usable for the large polyphase induction motors. The two-phase transmission was used but it either required a four wires system or three wires with unequal currents. Higher order phase systems require more than three wires, but they cannot deliver little or no benefit.
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a student pushes a 51.5 kilogram bookshelf across a smooth floor with a net force of 67 n. what is the approximate acceleration of the bookshelf?
Acceleration of the bookshelf is 1.30 m/[tex]s^{2}[/tex] when mass is 51.5 kg and force is 67 N.
To find the acceleration, we use newton's second law of motion. According to newton's second law of motion,
" The acceleration of an object is directly proportional to the net force acting on the object while being inversely proportional to its mass." Newton's second law of motion gives the measurement of force.
Acceleration is the result of force on an object.
The formula for finding acceleration from this law is.
Acceleration = Force/ Mass
a = F/m
So, a = 67/51.5 m/[tex]s^{2}[/tex]
= 1.30 m/[tex]s^{2}[/tex]
Acceleration in this case is 1.30 m/[tex]s^{2}[/tex]
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the amount of air drag on an 0.8n flying squirrel dropping vertically at terminal velocity is
The velocity of a vehicle is typically expressed relative to ground.
What is velocity?Velocity is the speed of something that is given direction.
velocity is the measurement to a body's "pace of change of the displacement in relation to time" whenever the main body is traveling through along a straight route.
It is common knowledge of that the word "linear" refers to be something that is totally straight; therefore, when the body moves in a straight path, it is said to be linear velocity .
Alternatively, velocity is the distance traveled by a body traveling in a specified to the direction during of a predetermined period of time. Thus, the fundamental idea of linear velocity is the provided by the union of these two quantities.
Because it always has the direction of velocity is a vector.
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A 70.0 kg astronaut is training for accelerations that he will experience upon reentry. He is placed in a centrifuge (r = 10.0 m) and spun at a constant angular velocity of 16.3 rpm. Answer the following:
What is the angular velocity of the centrifuge in rad/s ?
What is the linear velocity of the astronaut at the outer edge of the centrifuge?
What is the centripetal acceleration of the astronaut at the end of the centrifuge?
How many g’s does the astronaut experience?
What is the centripetal force and net torque experienced by the astronaut? Give magnitudes and directions.
The astronaut faces 1.71 rad/s angular velocity, 17.1 m/s linear velocity, 29.2 centripetal acceleration, 3 g's are experienced, and 2044 N of centripetal force. The torque experienced is zero
What is rotational motion?
An object is said to be in rotational motion when it is travelling in a circular route around a fixed axis. Centrifugal force is a radially outward force that the item experiences as a result of this motion.
The image given below explains the conversion. The torque is zero since there is no tangential force.
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An Amazon delivery driver, Shaggy, pushes a loaded dolly with a total mass of 30 kilograms onto a truck. Initially, the dolly accelerates at 0.2 meter/second^2. What force did Fred apply to the dolly?
The force applied to the dolly was 6N.
What is acceleration?Acceleration is the rate of change in velocity. It involves a change in speed and direction. When acceleration involves a change in speed only: Positive acceleration it occurs when an object speeds up. Negative acceleration it occurs when an object slows down.
Acceleration is a change of velocity over a period of time, expressed by the equation below.
F = ma
where f = force applied
m = mass of the body
a = acceleration of the body
F = ma
F = 30 x 0.2
F = 6N
In conclusion, the dolly received a force of 6N from Fred.
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Hello please .
How far would a person run in seconds at an average speed of 7ms-1
At an average speed of 7m/s, the distance covered in one second is 7 meters.
What is the distance covered in one second?Speed is simply referred to as distance traveled per unit time.
It is expressed mathematically as;
Speed = Distance ÷ time.
Given the data in the question;
Speed = 7m/sElapsed time = 1 secondDistance traveled = ?Plug the given values into the above formula and solve for distance traveled.
Speed = Distance ÷ time
Distance = Speed × Time
Distance = 7m/s × 1.0s
Distance = 7ms/s
Distance = 7m
Therefore, in a second, the person covers 7 meters.
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