(6%) Problem 11: A uniformly charged rod of length L = 2.1 m lies along the x-axis with its right end at the origin. The rod has a total charge of Q= 7.8 C. A point Pis located on the x-axis a distance a = 1.6 m to the right of the origin. у a- X dx -XPart (b) Write an equation for the electric field dE at point P due to the thin slide of the rod dx. Give your answers in terms of the variables Q, L, x, a, dx, and the Coulomb constant, k. Notice that the coordinate x will be less than zero over the length of the rod.
Answers
The equation for the electric field dE at point P due to the thin slide of the rod dx is given by:
dE = k Q / L dx (a² + x²)-3/2
How to calculate the equation of the electric field?The electric field dE at point P due to the uniformly charged rod of length L = 2.1 m, charge Q = 7.8 C, and with its right end at the origin is given by the equation:
dE = k x Q x (x - a)/((x - a)²+ L²)^(3/2)
where x = 0 to -L and a = 1.6 m.
The Coulomb constant, k, is 8.99 x 10⁹ Nm²/C².
Part (b)In part (a), we have calculated the distance between the point P and the rod dx as:
r = √(a² + x²)
Now we need to write an equation for the electric field dE at point P due to the thin slide of the rod dx. The magnitude of the electric field dE at P due to the element dx of the rod is given by:
dE = (k dQ) / r² …… (1)
Where k is the Coulomb constant the charge on the element dx of the rod r is the distance between the element dx and the point P
We know that for a uniformly charged rod, the charge density (charge per unit length) is given by:
λ = Q / L …… (2)
Where Q is the total charge on the rod and L is the length of the rod. For a small element dx of the rod, the charge can be expressed as:
dQ = λ dx …… (3)
Substituting equation (3) in equation (1), we get:
dE = k λ dx / r² …… (4)
We can express r in terms of x and dx:
r² = a² + x² …… (5)
Substituting equations (2) and (5) in equation (4), we get:
dE = k Q / L dx (a² + x²)-3/2 …… (6)
Therefore, the equation for the electric field dE at point P due to the thin slide of the rod dx is given by:
dE = kQ / L dx (a² + x²)-3/2
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Related Questions
How much work is done in moving a \( 25.0 \mathrm{~kg} \) book to a shelf \( 1.50 \mathrm{~m} \) high? What is the potential energy of the book as a result?
Answers
the work done to raise a 25kg book to a 1.5 m shelf is 367.5J and the potential energy of the book will be 367.5
Work done by a force is equal to the scalar product of the force applied and displacement. If d displacement happens on applying a force F, then work done, W by the force is
W = F. d
given:
mass, m = 25 kg
height, d = 1.50 m
work has to be done against the weight of the book, F = mg
work done W = F. d
W = mgd
W = (25) ×(9.8)×(1.50)
W = 367.5 J
This work is stored as the potential energy of the book.
Therefore, the work done to raise a 25kg book to a 1.5 m shelf is 367.5J and the potential energy of the book will be 367.5J
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(a) a car with a mass of 850 kg is moving to the right with a constant speed of 1.44 m/s. what is the total force on the car? (b) what is the total force on the car if it is moving to the left?
Answers
There is no force acting on the car when it is moving left or right.
A body is said to be acted upon by a force if there is some acceleration in the body.
So, the acceleration observed when there is a change in velocity of the body is there.
As we can see in this case, the velocity is not changing only the direction is changing and magnitude is same.
So, the net acceleration on the body is 0 m/s².
So, the mass of the body is 850 Kg, and the velocity of the car is 1.44 m/s.
(a) We know, the force is,
F = Ma
Where,
M is the mass and a is the acceleration,
so,
F = 580(0)
F = 0N
So there is no average force on the car while moving left.
(b) Similarly, when the car turn to left,
F = Ma
F = M(0)
F = 0N.
So, there is no net force when is it moving to the left.
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e)
The surface area of foot of Bimaba is 150cm? If she weighs 50kg,
how much pressure does she exert on the ground, as she stands on
her one foot? (32666.67 pa)
Answers
Answer:
Pressure, P = 32666.66 Pa
Explanation:
It is given that,
Surface area of foot of Bimaba is 150 cm² or 0.015 m².
Her weight is 50 kg
We need to find the pressure does she exert on the ground, as she stands on her one foot. The force acting per unit area is called pressure. It can be given by :
\(P=\dfrac{F}{A}\\\\P=\dfrac{mg}{A}\\\\P=\dfrac{50\times 9.8}{0.015}\\\\P=32666.66\ Pa\)
So, the pressure is 32666.66 Pa.
Do heavier bowling balls go faster than lighter ones?
Answers
Answer:
lighter ones will go faster
Explanation:
assuming you throw both bolwing ball with 10N of force. one is 3kg and the other is 5kg.
by using the equation: F = ma
a = F/m
a = 10/5 = 2m/s^2
a = 10/3 = 3.33333 m/s^2
a pump draws water through an 8.0 in. suction pipe and discharges it through a 4.0 in. pipe in which the velocity is 12 ft/s. the 4.0 in. pipe discharges horizontally into air at c. to what height h (in feet) above the water surface at a can the water be raised if 25 hp is delivered to the pump? assume that the pump operates at 60% efficiency and that the head loss in the pipe between a and c is equal to 2uc2/2g.
Answers
The water can be raised to a height of approximately 15.7 m above the water surface at point A.
To solve this problem, we need to use the principles of fluid mechanics, specifically the Bernoulli's equation and the continuity equation.
A1v1 = A2v2
We know that the diameter of the 8.0 in. pipe is 8 in. = 0.6667 ft, so its cross-sectional area is:
A1 = \(π/4 x (0.6667 ft)^2 = 0.349 ft^2\)
Similarly,
A2 = \(π/4 x (0.3333 ft)^2 = 0.0873 ft^2\)
v1 = (A2v2)/A1 = \((0.0873 ft^2 x 12 ft/s)/0.349 ft^2\) = 2.39 ft/s
Next, we can use the Bernoulli's equation between points A and C to relate the pressure difference to the velocity difference:
P/ρ +\(v^2/2g\) + h = constant
h = (P/ρ - Patm)/g + z
We are given that the pump delivers 25 hp with 60% efficiency, so the power input to the pump is:
Pin = 25 hp/0.6 = 41.7 hp = 31.1 kW
Pin = QP/η
The volumetric flow rate can be calculated from the continuity equation:
Q = A1v1 = \(0.349 ft^2 x 2.39 ft/s = 0.834 ft^3/s\)
Substituting this into the above equation, we get:
P = Pinη/Q = \((31.1 kW x 0.6)/0.834 ft^3/s\) = 1773 Pa
Finally, we can substitute the known values into the Bernoulli's equation:
h = \((P/ρ - Patm)/g + z = (1773 Pa/1000 kg/m^3 - 101325 Pa)/9.81 m/s^2 + 0 m\)
h ≈ 15.7 m
Therefore, the water can be raised to a height of approximately 15.7 m above the water surface at point A.
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An object is placed 10 cm in front of a concave lens. If the image formed at a distance of 5 cm from concave lens, calculate the focal length of the lens?
Answers
Answer:
I would be 5 centimeters I think
Electrical energy in motion is what type of energy ?
Answers
Answer:
kinetic energy
Explanation:
Electrical energy is a type of kinetic energy caused by moving electric charges. The amount of energy depends on the speed of the charges – the faster they move, the more electrical energy they carry.
When laser light is shone into a relaxed normal-vision eye to repair a tear by spot-welding the retina to the back of the eye, the rays entering the eye must be parallel. Why
Answers
When laser light is used to repair a tear in the retina, it is important for the rays entering the eye to be parallel. This is primarily because of the focusing properties of the eye.
The human eye has a lens that is responsible for focusing light onto the retina, located at the back of the eye. The lens refracts or bends incoming light rays so that they converge onto a small spot on the retina, forming a sharp image. This process is known as accommodation and is crucial for clear vision.
If the rays of light entering the eye are not parallel, they will converge or diverge at different angles, causing the image to be distorted and unfocused on the retina. In the case of repairing a tear in the retina, it is essential to precisely target and apply the laser at the desired location on the retina.
By using parallel laser beams, the light rays maintain a consistent direction and angle as they pass through the eye. This allows the laser to be focused accurately onto the specific area of the retina that requires treatment. The parallel beams ensure that the laser energy is concentrated and delivered precisely, minimizing the potential for collateral damage to surrounding tissues.
Therefore, to achieve effective spot-welding of the retina during the repair procedure, the use of parallel laser light ensures precise and controlled delivery of energy to the targeted area.
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(50 POINTS IF ABLE TO GET PLZ EXPLAIN HOW TO SOLVE)A tire is rolled down a hill that is 364.37 m long. If the tire has an acceleration of 0.33 m/s2 and it takes 38.68 s to get all the
way down, how fast was the tire first rolled?
Answers
What happens within the motor when an electric current flows through the loop of a wire
Answers
Answer: I think its B: The loop becomes electromagnetic, which causes the loop to flip and produce mechanical energy.
Explanation:
What is the momentum of a 10 kg dog running at a speed of 13m/s?
Answers
Answer:
P = mv
Explanation:
P = Momentum
m = mass
v = velocity
Therefore, P = 10 x 13 = 130 kg • m/s
Kinetic energy is the energy of motion. How could you determine how much kinetic energy an object has?.
Answers
Motion is created by kinetic energy. K.E. = 1/2 mv2 can be used to calculate an object's kinetic energy.
What is being moved?Motion is the change in an object's location with relation to time. Motion is described mathematically using terms like displacement, velocity, distance, kinetic energy, and speed.
Kinetic energy:Kinetic energy is essentially the energy underlying motion and can be observed in the movement of objects or subatomic particles. Every atom or object in motion contains kinetic energy.
A human walking, a baseball flying through the air, food falling from a desk, and an alpha object in an electric field are all example of kinetic in action.
The equation for calculating the angular momentum of an object with mass m and motion is K.E. = 1/2 mv^2.
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Exoplanet Period Looking back at the graph above, you can see that there are multiple times, during the 30 days of observation, when the planet passes in front of the star. The time between transit events is a direct measure of how long it takes the exoplanet to orbit the star (orbital period). Try to be as accurate as you can in determining the period of the two exoplanets. Question 5 2 pts The orbital period for Exoplanet A is------- days.
Answers
The orbital period for Exoplanet A is estimated to be 18.4 days based on the time between two transit events observed on the graph. This calculation assumes a regular and consistent orbital pattern, but the actual period may vary slightly due to factors like orbital eccentricity.
The first transit event occurs at day 10.5 on the graph. The second transit event occurs at day 28.9 on the graph. The time between these two events is 28.9 - 10.5 = 18.4 days.
It is important to note that this is just an estimate of the orbital period. The actual orbital period may be slightly different due to factors such as the eccentricity of the orbit.
Here are the steps I took to calculate the orbital period:
I identified the two transit events on the graph.I subtracted the time of the first transit event from the time of the second transit event.I rounded the result to the nearest whole number.The orbital period for Exoplanet A is 18.4 days.
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What is the magnitude of the average force exerted on the arrow by the vertical wood board on right of the video as the arrow
comes to rest embedded in the wood?
Answers
According to Newton's law, action and reaction are equal and opposite.
What is action and reaction?According to the Newton's third law of motion, action and reaction are equal and opposite. As such, when the arrow hits the vertical wood board, the board exerts some force on the arrow.
We can not determine the magnitude of this force numerically because the question is incomplete.
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Answer:
newtons law action and reaction are equal and opposite
Explanation:
I need help! Picture is the sheet.
Answers
Answer:
The answers to the questions are
1. Sound energy
2. Conductor
3. Flow
4. Thermal energy (g underlined)
5. Electric current
6. Insulator
7. Light energy
8. Electric circuit
The underlined letters are, e, n, g, r, y, e which can be rearranged to spell energy
Explanation:
1. Sound energy is the wave form of mechanical energy that is transferred by the vibration of the of the medium through which it propagates
2. An electrical conductor is used to conduct electricity from one point to another
3. An object or material flows when it has a smooth motion towards a given direction, such as a river
4. Thermal energy is the form of energy that is given off by a body as sensible heat that can be measured as a temperature by a thermometer
5. Electric current is the electricity in a circuit
6. An insulator is a material that limits the flow of electricity or heat
7. Light energy is the form electromagnetic energy which the eye can sense
8. An electric current flows an electric circuit which consist of a source of electricity and an path through which the electric current can easily flow.
Two like-charged particles are placed close to each other. How would the force of repulsion be affected if the charge on one of the particles is doubled and that on the other is reduced to half the original value? A) The force would remain the same. B) The force would become half the original value. C) The force would become twice the original value. D) The force would become four times the original value.
Answers
The force of repulsion between two charged particles will remain the same
What will be the effect on the force of two charged particles?We know that from Columb's law force between two charged particles will be given by
\(F=k \dfrac{q_1q_2}{r^2}\)
Now from the condition
if the charge on one of the particles is doubled and that on the other is reduced to half the original value
\(q_1'=2q_1\)
and
\(q_2'=\dfrac{q_2}{2}\)
Use the above values in the formula
\(F'=k\dfrac{q_1'q_2'}{r^2}\)
\(F'=k\dfrac{2q_1 \dfrac{q_2}{2} }{r^2}\)
\(F'=k\dfrac{q_1q_2}{r^2}\)
So \(F=F'\)
Thus the force of repulsion between two charged particles will remain the same
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the unit of area is a derived unit . why?
Answers
sorry this is one side of the note
Describe how the pendulum concept is used in the pendulum clock.
Answers
The concept of the pendulum is used in pendulum clocks to keep time. The pendulum swings back and forth in a continuous motion at a fixed rate that is determined by the length of the pendulum and the force of gravity.
This motion is used to regulate the movement of the clock's gears, which control the hands on the clock face.The mechanism of a pendulum clock is such that when the pendulum swings in one direction, it pushes a toothed wheel or gear, which in turn moves the other gears, causing the clock's hands to move forward.
When the pendulum swings back in the opposite direction, it again pushes the gear, causing the hands to move further forward. This cycle continues, with each swing of the pendulum causing the hands to move forward by a set amount. The length of the pendulum determines the rate at which the hands move forward, with longer pendulums causing the hands to move more slowly.
In a pendulum clock, the pendulum swings back and forth in a continuous motion at a fixed rate that is determined by the length of the pendulum and the force of gravity. This motion is used to regulate the movement of the clock's gears, which control the hands on the clock face. The pendulum clock is an improvement on the original verge escapement clocks, which were prone to errors due to the uneven force of the mainspring.The pendulum is a simple yet effective device that can keep accurate time. Its motion is governed by the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred from one form to another.
When the pendulum is pulled to one side and released, it swings back and forth, converting potential energy into kinetic energy and back again. The period of the pendulum, or the time it takes to complete one full swing, is determined by the length of the pendulum and the force of gravity. By adjusting the length of the pendulum, the rate at which it swings can be altered, allowing it to keep accurate time.
To keep the pendulum clock running accurately, it needs to be adjusted periodically. This is done by altering the length of the pendulum, either by moving a weight up or down along the pendulum rod or by turning a screw at the bottom of the pendulum bob. This alters the period of the pendulum, which in turn changes the rate at which the clock runs.
The pendulum clock is a testament to the ingenuity of humanity. By using the simple yet effective concept of the pendulum, clockmakers were able to create accurate timepieces that revolutionized the way we keep time. Today, the pendulum clock may have been superseded by more advanced technologies, but its legacy lives on in the modern clocks and watches we use every day.
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A spiracle polish metallic ball is uses a diverging mirror with a focal length of -20 cm a bird 25 cm tall standing 50 cm away Looks directly at the mirror what are the size and position of the birds image
Answers
Answer:
1/f = 1/i + 1/o thin lens equation
1/i = 1/f - 1/o
i = o * f / ( o - f) = 50 * (-20) / (50 - (-20)) = -14.3 cm
The final image is erect and 14.3 cm behind the curved surface
M = -o / i = 14.3 / 50 = .29 magnificaton of object
S = .29 * 25 cm = 7.1 cm appearance of bird in mirror (height)
a chain 74 meters long whose mass is 29 kilograms is hanging over the edge of a tall building and does not touch the ground. how much work is required to lift the top 7 meters of the chain to the top of the building? use that the acceleration due to gravity is 9.8 meters per second squared. your answer must include the correct units.
Answers
The work required to lift the top 7 meters of the chain to the top of the building is 1,932.4 joules.
To calculate the work required, we need to consider the gravitational potential energy of the chain. The formula for gravitational potential energy is given by:
Potential energy = mass * gravity * height
In this case, the mass of the chain is 29 kilograms, the acceleration due to gravity is 9.8 meters per second squared, and the height to be lifted is 7 meters.
Substituting these values into the formula, we get:
Potential energy = 29 kg * 9.8 m/s^2 * 7 m
Simplifying the equation, we find:
Potential energy = 1,932.4 joules
Therefore, the work required to lift the top 7 meters of the chain to the top of the building is 1,932.4 joules.
Gravitational potential energy is the energy possessed by an object due to its position in a gravitational field. In this case, as we lift the top 7 meters of the chain, we are increasing its potential energy. The amount of work required to do this is equal to the change in potential energy. The formula for gravitational potential energy involves the mass of the object, the acceleration due to gravity, and the height. By multiplying these values together, we can calculate the potential energy and thus determine the work required. Understanding the concept of potential energy and how it relates to work is essential in various fields, such as physics and engineering, where energy calculations and mechanical systems are involved.
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The work required to lift the top 7 meters of a 74-meter chain with a mass of 29 kilograms to the top of a building is approximately 188 Joules. This was calculated using the formula for potential energy (PE = mgh), where 'm' is mass, 'g' is the acceleration due to gravity, and 'h' is height.
Explanation:This problem involves a calculation of work done, which is a concept in physics. Specifically, it uses the equation for gravitational potential energy, which is given by PE = mgh, where 'm' is mass, 'g' is the acceleration due to gravity, and 'h' is height.
In this case, the mass of the chain being lifted is 7 meters out of 74, which is approximately 2.74 kilograms (29 kg * 7/74). The height is 7 meters and the acceleration due to gravity is 9.8 m/s². Therefore, the amount of work required to lift the top 7 meters of the chain can be calculated as follows:
PE = mgh = 2.74 kg * 9.8 m/s² * 7 m = 187.66 Joules.
Therefore, it requires approximately 188 Joules of work to lift the top 7 meters of the chain to the top of the building.
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1. A rocket is fired vertically from the launch pad with a
net accelevation of 20m/s². If the atmosphere is
approximately 100km thick and considering that the
acceleration is constant....
a) what is the time it takes for the rocket to leave the
atmosphere?
b) What speed does the rocket reach at that time?
Answers
Answer:
Max height= 36000 meters
Total Time = 120 seconds
Explanation:
0 = U - at
U = at
U= 20*60
U= 1200 m/s
MAX altitude would be
(U²Sin²tita)/2g
Max height= 1200² *( SIN90)²/(2*20)
Time of FLIGHT
2 * 1200/20
2400/20
120 sec onds
Just like elephants, gorillas and dolphins, wolves educate their young. True or False?
Answers
Answer: true
Explanation: the reason it is true is because wolves educate their young to be integrated into a pack and learn to cooperate and hunt with a pack.
Answer:
true.
Explanation:
There are old wolves that need to be cared for pups that need to be educated and young adults that are beginning to assert themselves- all altering the dynamics of the pack
4. Explain A girl is jumping on a trampoline. When she is at the top of her jump, her mechanical energy is in what form? Explain why.
Answers
Mechanical energy is of two types,
1. Kinetic energy
2. Potential energy
When the girl is at the top of her jump, the speed of the girl becomes zero.
Thus, the kinetic energy of the girl at the top of her jump is,
\(K=\frac{1}{2}mv^2\)where m is the mass of the girl and v is her speed,
Substituting the known values,
\(K=0\text{ J}\)Thus, the kinetic energy of the girl is zero at the top of her jump.
The potential energy of the girl at the top of her jump is,
\(U=\text{mgh}\)where g is the acceleration due to gravity and h is the height of the girl,
Thus, the potential energy of the girl at the maximum height is maximum.
Hence, the mechanical energy of the girl at the top is in potential energy form because her kinetic energy is zero at the top of her jump.
Please give best dialogue in photo that is attached And you are marked as Brainliest
Answers
Answer:
The correct answer is
Explanation:
Character 1: Why are these comic books so hard to read? Can u read them?
Character 2: No it's easy to read Tigger. It's because you are an animal an I am a human being. U don't know how to read.
Hope this helps....
Have a nice day!!!!
Answer:
Dialogue 1:
Hey buddy! Can you tell me what is written in this book? Its really hard to read:(
Dialogue 2:
Yeah! Its a story about a friendly tiger! And it is hard for you to read cause you don't know how to read.
Tip:
Try to make it more engaging :)
Which of the following limiting factors would be directly affected by a drought? a. birth/death rate b. immigration c. available niche d. resource supply Please select the best answer from the choices provided A B C D
Answers
Answer:
C. answer pa brailest need lang po please
D. Resource Supply this would be directly affected first then the rest would follow after a period of time.
since the gravitational force between two bodies decreases with distance, the acceleration anear experienced by a unit mass located at the point on the earth's surface closest to the moon is slightly different from the acceleration afar experienced by a unit mass located at the point on the earth's surface farthest from the moon. give a general expression for the quantity anear−afar .
Answers
The gravitational force between two bodies decreases with distance according to the inverse square law. Therefore, the acceleration experienced by a unit mass located at different points on the Earth's surface will vary depending on their distance from the Moon.
Let's denote the distance between the Earth's center and the point closest to the Moon as r_near, and the distance between the Earth's center and the point farthest from the Moon as r_far. The general expression for the difference in acceleration, anear−afar, can be calculated as follows:
anear - afar = GM_moon / r_near² - GM_moon / r_far²
Where:
G is the gravitational constant (approximately 6.674 × 10^(-11) m³/(kg·s²))
M_moon is the mass of the Moon
This expression represents the difference in acceleration experienced by a unit mass located at the point closest to the Moon (anear) and the point farthest from the Moon (afar) on the Earth's surface.
It's worth noting that the difference in acceleration due to the Moon's gravitational pull is relatively small compared to the Earth's gravitational acceleration. The gravitational effect of the Moon is more noticeable on ocean tides rather than on everyday objects or individuals.
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What is the condition for the machine to be perfect?
Answers
In the one pully system when you move the mass from the 20 cm mark to the 15 cm mark, it moves 5 cm. How far did you pull the string. Question 1 options: 5 cm 10 cm 15 cm 20 cm
Answers
Answer:
5 cm
Explanation:
The energy an object has by virtue of its position is kinetic energy.
True
False
Answers
Answer:
false
Explanation:
the energy an object has by virtue of its position is gravitational energy.
the energy which an object possess due to its motion is kinetic energy.
hope it helps !
what is the true answer in this question?Making a schedule on the things that need to be accomplished yes or no
Answers
Answer:
yes
Explanation:
this is true don't believe other people whether right or wrong