The charge within a small volume dv is dq=ρdv. the integral of ρdv over a cylinder of length l is the total charge q=λl within the cylinder. use this fact to to determine the constant ρ0 in terms of λ and r. hint: let dv be a cylindrical shell of length l, radius r, and thickness dr. what is the volume of such a shell?
Answers
[tex]dV=2L\pi r dr[/tex]
Now we can rewrite the given integral:
[tex]\lambda L=\int\rho dV=L\rho\int2\pi r dr \\ \lambda L =L\rho \pi r^2\\ \rho=\frac{\lambda}{\pi r^2}[/tex]
I have attached the picture explaining how we got the formula for the volume.
On the picture, I marked the rectangle. You can of this rectangle as the base, and the height would be the circumference of the cylinder.
Answer:
Given
dq=density*dv
q=lamda*I
Taking double integration
density=lamda/2*pi*r^2
Related Questions
A circular loop of wire with a radius of 4.0 cm is in a uniform magnetic field of magnitude 0.069 t. the plane of the loop is perpendicular to the direction of the magnetic field. in a time interval of 0.46 s, the magnetic field changes to the opposite direction with a magnitude of 0.044 t. what is the magnitude of the average emf induced in the loop?
Answers
[tex]\epsilon = \frac{\Delta \Phi_B}{\Delta t} [/tex]
where [tex]\Delta \Phi_B[/tex] is the variation of magnetic flux through the area enclosed by the loop, and [tex]\Delta t[/tex] is the time interval.
The magnetic flux is given by
[tex]\Phi _B = BA\cos \alpha[/tex]
where B is the intensity of the magnetic field, A is the area enclosed by the loop and [tex]\alpha[/tex] is the angle between the perpendicular to the area and the magnetic field. In our problem, this angle is zero because the loop is perpendicular to the magnetic field, so the cosine is 1. The area of the loop is fixed, and it is
[tex]A=\pi r^2[/tex]
where [tex]r=4.0 cm=0.04 m[/tex] is the radius of the loop. The only element which is variable in the formula is B, which changes from 0.069 T to -0.044 T (opposite direction). So we can rewrite the flux variation as
[tex]\Delta \Phi_B = A \Delta B [/tex]
where [tex]\Delta B = 0.069 T-(-0.044 T)=0.113 T[/tex]
By using [tex]\Delta t=0.46 s[/tex], we can find the magnitude of the emf induced:
[tex]\epsilon = \frac{A \Delta B}{\Delta t}= \frac{(\pi (0.04 m)^2)(0.113 T)}{0.46 s}=1.2 \cdot 10^{-3}V [/tex]
how does a shovel make work easier for digging a hole?
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what was perphaps the greatest challenge of human space flight?
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Johnny was playing baseball with his friends and they noticed a bolt of lightning. They heard thunder seven seconds later. How far away is the storm?
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That particular strike was very roughly 2.4 km (1.5 miles) away from them.
That's if you use 340 m/s (1120 ft/sec) for the speed of sound.
But the air in the region for several thousand feet around a thunderstorm
is doing weird things to sounds that pass through it, so you can't use any
exact number for the speed of sound in a stormy area.
The only thing you can be absolutely sure of is that Johnny and his friends
need to round up their equipment and get in the house. NOW !
2,317 meters on edg!!
Wrap a fur coat around a thermometer. how does the temperature change?
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if you conduct an expiriment that uses lots of paper and plastic how can you practice good science ethics ?
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What is the main reason why many nuclear power plants are located near bodies of water?
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Hope this helps!:)
~Scarlett
Which statements describe chemical changes? Check all that apply.
The after-rain smell is produced by an interaction between rain and the oils released by plants.
A homemade volcano can be created by combining baking soda and vinegar. When it erupts, carbon dioxide gas is released.
Sheep are sheared for their wool. The wool is cleaned and twisted into yarn. The yarn is dyed and used to knit clothing.
The Statue of Liberty has turned green over time due to the reaction of copper with carbon dioxide and water.
Mosaic art is created by smashing colored glass tiles and rearranging them to form a picture or design.
Answers
The answers are a,b and d
Answer: A, B, and D
A fixed mass of an ideal gas is heated from 50 to 80℃ at a constant pressure of (a) 1 atm and (b) 3 atm. for which case do you think the energy required will be greater? why?
Answers
The energy required to heat a fixed mass of an ideal gas from 50 to 80℃ is the same at both 1 atm and 3 atm, as it depends on the gas's heat capacity and the temperature change, not pressure.
Explanation:The energy required to heat a fixed mass of an ideal gas from 50 to 80℃ would be the same for both cases of constant pressure at 1 atm and 3 atm. The reason behind this is that the amount of energy required to raise the temperature of an ideal gas is dependent on its heat capacity and the change in temperature, not the pressure at which it is heated. In both cases (a) and (b), the change in temperature is the same, so the energy required will also be the same.
The potential energy of a book on a shelf is 50 J. If the book is now on the floor (below the shelf), its potential energy is
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If the book is now on the floor (below the shelf), its potential energy is 0 J.
Potential Energy is defined as the energy that is capable of generating work as a consequence of the location of the object.
When the book is on a shelf, it is capable of generating work by falling from the shelf onto the floor by the force of gravity. This is called gravitational potential energy.
When the book is on the floor, it is no longer capable of generating work by falling, and its potential energy is 0 as it can't fall anymore and generate work.
Have a nice day!
Answer:
shelf a is increase shelf b is stay the same and shelf c is decrease
Explanation:
i did it on edu
A two-phase, liquid–vapor mixture of h2o, initially at x 5 30% and a pressure of 100 kpa, is contained in a piston– cylinder assembly, as shown in fig p3.77. the mass of the piston is 10 kg, and its diameter is 15 cm. the pressure of the surroundings is 100 kpa. as the water is heated, the pressure inside the cylinder remains constant until the piston hits the stops. heat transfer to the water continues at constant volume until the pressure is 150 kpa. friction between the piston and the cylinder wall and kinetic and potential energy effects are negligible. for the overall process of the water, determine the work and heat transfer, each in kj.
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Final answer:
In this scenario, the work done by the external agent can be calculated using the change in volume, and no heat is exchanged during this process.
Explanation:
Work: In the given scenario, since the gas volume doubles at constant temperature, the work done by the external agent can be calculated using the formula W = -PΔV, where P is the pressure and ΔV is the change in volume.
Heat Transfer: As the gas volume doubles at constant temperature, no heat is exchanged during this process. Hence, the heat exchanged is zero.
The second law of thermodynamics dictates that ____. 1 point low-quality energy becomes static some high-quality energy is always degraded the amount of energy in the universe is constantly changing low-quality energy is required to get high-quality energy
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The second law of thermodynamics dictates that "Some high-quality energy is always degraded.
It is important to know that the "Thermodynamics" is defined as a branch of physics that studies the mechanical action of heat and the others forms of energy.
Final answer:
The second law of thermodynamics states that in any energy transfer, some high-quality energy is always degraded, leading to increased disorder or entropy in the system.
Explanation:
The second law of thermodynamics dictates that some high-quality energy is always degraded to a lower quality form during energy transfers. This law further implies that no energy transfer is completely efficient, thus resulting in an increase in entropy, or disorder, within a system. This is a fundamental concept in physics that puts an arrow on the transformations of matter and energy, signifying a one-way flow from usable to less-usable forms of energy. It is most commonly observed through heat loss, where energy spontaneously transfers from a hotter object to a cooler one, increasing the disorder of the system.
Suppose we are told that the acceleration a of a particle moving with uniform speed v in a circle of radius r is proportional to some power of r, say rn, and some power of v, say vm. Determine the values of n and m and write the simplest form of an equation for the acceleration.
Answers
[tex]a = r^nv^m[/tex]
The units for that equation must be:
[tex](\frac{m}{s^2}) = (m)^{-1} ( \frac{m}{s} )^2[/tex]
Answer:
Acceleration, [tex]a=k\dfrac{v^2}{r}[/tex]
Explanation:
It is given that, the acceleration a of a particle moving with uniform speed v in a circle of radius r is proportional to some power of r and some power of v. Mathematically, it can be written as :
[tex]a\propto r^nv^m[/tex]
or
[tex]a=r^nv^m[/tex]...........(1)
Dimensional formula of a = [tex][LT^{-2}][/tex]
Dimensional formula of r = [tex][L][/tex]
Dimensional formula of v = [tex][LT^{-1}][/tex]
Using dimensional analysis in equation (1) as :
[tex][LT^{-2}]=[L]^n[LT^{-1}]^m[/tex]
[tex][LT^{-2}]=[L]^{n+m}[T^{-m}][/tex]
Equation both sides of equation as :
n + m = 1, m = 2
This gives, n = -1
Use the value of m and n in equation (1) in order to get the formula :
[tex]a=kr^{-1}v^2[/tex]
[tex]a=k\dfrac{v^2}{r}[/tex]
Hence, this is the required solution.
What does it mean to say that science is a “systematic” process?
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Science is a systematic process, which means it follows a careful method that involves observation and experimentation. Through experimentation, information is collected that supports or refutes a scientist’s hypothesis.
edginuity answer
Estimate the first three standing-wave frequencies of the vocal tract. use v=344m/s. (the answers are only an estimate, since the position of lips and tongue affects the motion of air in the vocal tract.)
Answers
The fundamental frequency for a stopped pipe is given with the following formula:
[tex]f_0=\frac{v}{4L}[/tex]
Higher harmonics are simply:
[tex]f=nf_0; n=1,3,5,7,9...[/tex]
Keep in mind that the stopped pipe produces only odd harmonics.
Lenght of a human vocal tract is 17cm(for males, females have slightly shorter vocal tract). We can now calculate the answers.
[tex]f_0=\frac{344}{4\cdot 0.17}=505.88$Hz[/tex]
Now we can calculate higher harmonics:
[tex]f_3=3f_0=1517.64$Hz[/tex]
[tex]f_5=5f_0=2529.4$Hz[/tex]
Using _________ permits scientists to temporarily enhance or depress activity in a specific area of the brain. A. TMS B. EEG C. MRI D. ESB
Answers
Using TMS permits scientists to temporarily enhance or depress activity in a specific area of the brain.
What is Transcranial magnetic stimulation ?
Transcranial magnetic stimulation (TMS) is a noninvasive procedure that uses magnetic fields to stimulate nerve cells in the brain to improve symptoms of depression. TMS is typically used when other depression treatments haven't been effective.
The electromagnet painlessly delivers a magnetic pulse that stimulates nerve cells in the region of your brain involved in mood control and depression. It's thought to activate regions of the brain that have decreased activity in depression.
a single Transcranial magnetic stimulation (TMS) pulse can cause disruption in the contralateral hand muscles for ∼200 ms. These different temporal windows of disruption across different brain regions
Transcranial magnetic stimulation targets the activity of nerve cells in your brain, which may alleviate depression symptoms. It could also have benefit for disorders like OCD, anxiety, and PTSD as well.
hence , correct option is A. TMS (Transcranial magnetic stimulation)
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Rocket engineers use newton's third law during launch. identify the action force.
A. exhaust gases push down on the earth
B. rocket travels upward
C. earth pushes back on the exhaust gases
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The action force in this scenario is earth pushes back on the exhaust gases.
Explanation:The action force in this scenario is option C: earth pushes back on the exhaust gases.
Newton's third law states that for every action, there is an equal and opposite reaction. In this case, the action force is the exhaust gases pushing downward on the earth as the rocket launches. The reaction force is the earth pushing back on the exhaust gases with an equal force in the opposite direction.
So, while the rocket is traveling upward, the action force is the exhaust gases pushing downward on the earth and the reaction force is the earth pushing back on the exhaust gases.
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A 60-kg skier starts from rest from the top of a 50-m high slope. if the work done by friction is -6.0 kj, what is the speed of the skier on reaching the bottom of the slope?
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Answer:
27.9 m/s
Explanation:
You want the speed of a 60 kg skier at the bottom of a 50 m high slope if 6 kJ of energy is lost to friction.
Potential energyThe potential energy of the skier at the top of the slope is ...
PE = mgh
PE = (60 kg)(9.8 m/s²)(50 m)
Kinetic energyThe kinetic energy of the skier at the bottom of the slope is this potential energy, less the energy lost due to friction.
KE = PE -6000 J
That is related to the skier's speed by ...
KE = 1/2mv²
So, the speed is ...
[tex]v^2=\dfrac{2\cdot KE}{m}=\dfrac{2(mgh-6000)}{m}=2\left(gh-\dfrac{6000}{m}\right)\\\\\\v^2=2\left(9.8\cdot50-\dfrac{6000}{60}\right)=780\\\\\\v=\sqrt{780}\approx27.9\quad\text{m/s}[/tex]
The speed of the skier at the bottom of the slope is about 27.9 m/s.
What does 34.9cL equal in hL
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The answer is "0.00349 hL".
Reason:
34.9cL=0.00349hL
(Remember to go left 6 places when doing this question)
If you need anymore help feel free to ask me!
Hope this helps!
~Nonportrit
which jet stream affects weather in south Africa
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A spring with a spring constant of 95 n/m is compressed a distance of 0.45 m from its relaxed position. by how much does the spring\'s potential energy change?
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The potential energy change of a spring with a spring constant of 95 N/m compressed by 0.45 m is approximately 9.62 J, calculated using the formula U = 1/2 kx².
Explanation:When a spring with a spring constant of 95 N/m is compressed a distance of 0.45 m from its relaxed position, the potential energy of the spring changes according to the formula for elastic potential energy, U = 1/2 kx², where 'k' is the spring constant and 'x' is the distance of compression or extension from the equilibrium position. In this case, the spring's potential energy change is calculated as U = 1/2 × 95 N/m × (0.45 m)².
By computing this, U = 1/2 × 95 × 0.45² = 0.5 × 95 × 0.2025 J. This results in U = 9.61875 J, so the potential energy of the spring changes by approximately 9.62 J.
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the potential energy of an apple is 6.00 joules. the apple is 3.00 meters high. what is the mass of the apple?
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By rearranging the formula for gravitational potential energy, we calculate that the mass of the apple is approximately 0.2041 kg when its potential energy is 6.00 joules at a height of 3.00 meters.
To calculate the mass of the apple using its potential energy (PE) and the height (h) at which it is located, we use the formula for gravitational potential energy:
PE = mgh
where:
m is the mass in kilograms,g is the acceleration due to gravity (9.8 m/s² on Earth), andh is the height in meters.Given that PE = 6.00 Joules and h = 3.00 meters, we rearrange the formula to solve for m:
m = PE / (gh)
Substituting in the known values:
m = 6.00 J / (9.8 m/s² * 3.00 m) = 0.2041 kg
Therefore, the mass of the apple is approximately 0.2041 kg.
A 58.5-kg athlete leaps straight up into the air from a trampoline with an initial speed of 8.8 m/s. the goal of this problem is to find the maximum height she attains and her speed at half maximum height.
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This is a uniformly accelerated motion with initial speed [tex]v_0 = 8.8 m/s[/tex] and acceleration [tex]a=g=-9.81 m/s^2[/tex] (the negative sign is required because the acceleration is directed downward, in the opposite direction of the motion, which is directed upward). The distance covered (S) in a uniformly accelerated motion is related to the acceleration and the initial and final velocity by the relationship
[tex]2aS=v_f^2-v_i^2[/tex]
At maximum height, S=h and the final velocity is zero: [tex]v_f =0[/tex]. So we can solve for h and find the maximum height:
[tex]2ah=-v_i^2[/tex]
[tex]h= \frac{-v_i^2}{g}= \frac{-(8.8 m/s)^2}{-9.81 m/s^2}=3.95 m [/tex]
2) Speed at half maximum height
Half maximum height corresponds to [tex] \frac{h}{2}= \frac{3.95 m}{2}=1.975 m [/tex]. To find the speed at this height, we can use the same relationship used in the previous step:
[tex]2a \frac{h}{2}=v_f^2-v_i^2 [/tex]
where [tex]v_f [/tex] is the speed at half maximum height.
Re-arranging and substituting numbers, we find
[tex]v_f = \sqrt{v_i^2+(2g \frac{h}{2}) }= \sqrt{(8.8m/s)^2+2(-9.81m/s^2)(1.975m)}=6.22m/s [/tex]
A transformer changes the 10,000 v power line to 120 v. if the primary coil contains 750 turns, how many turns are on the secondary?
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[tex] \frac{N_p}{N_s}= \frac{V_p}{V_s} [/tex]
Where [tex]N_p[/tex] and [tex]N_s[/tex] are the number of turns in the primary and secondary coils, while [tex]V_p[/tex] and [tex]V_s[/tex] are the voltages on the two coils.
Using the data of the problem: [tex]N_p=750[/tex], [tex]V_p=10000 V[/tex] and [tex]V_s=120 V[/tex], we can find [tex]N_s[/tex], the number of turns of the secondary coil:
[tex]N_s=N_p \frac{V_s}{V_p}=750 \frac{120 V}{10000 V}=9 [/tex]
A volleyball is dropped from a cliff and a soccer ball is thrown upward from the same position. When each ball reaches the ground at the bottom of the cliff, the volleyball will hit the ground with greater velocity.
Answers
The answer if false.
Explanation:
It is exactly the opposite. The soccer ball will hit the ground with greater velocity.
Since the soccer ball is thrown upward, when it returns to the same heigth from which it was throwm it will have a velocity downward, which will make that the soocer ball reaches the ground at the bottom of the clif with greater velocity than the volleball.
The greater the velocity with which the soccer ball is thrown upward, the greater its velocity when reaches the same point from which it was thrown, and the greater the velocity with which it will hit the ground at the bottom of the clif.
The standard unit of work in the metric system is named after the scientist _____. 1 Albert Einstein 2 James Joule 3 Isaac Newton 4 James Watt
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Hope it helped!
A torque applied to a flywheel causes it to accelerate uniformly from a speed of 161 rev/min to a speed of 853 rev/min in 5.0 seconds. determine the number of revolutions n through which the wheel turns during this interval. (suggestion: use revolutions and minutes for units in your calculations.)
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[tex]60 s: 1 min = 5 s: x[/tex]
we find
[tex]\Delta t = \frac{5.0 s}{60 s/min}=0.083 min [/tex]
Then we can find the angular acceleration of the flywheel:
[tex]\alpha = \frac{\omega _f - \omega_i}{\Delta t}= \frac{853 rpm-161 rpm}{0.083 min}=8337 rev/min^2 [/tex]
At this point, we can use the law of motion of an uniformly accelerated rotational motion. The angular displacement after a time [tex]\Delta t[/tex] is given by
[tex]\theta (\Delta t)= \omega_i t + \frac{1}{2} \alpha t^2 = [/tex]
[tex]=(161 rpm)(0.083 min)+ \frac{1}{2}(8337 rev/min^2)(0.083 min)^2 =42.1 rev[/tex]
So, the flywheel covers 42.1 revolutions.
Which graphic design tools help you draw circles and rectangles?
Freehand tool
Geometric Shape tools
Vector Splines
Drawing tool
Answers
Geometric shape tools help you draw circles and rectangles. Option B is correct.
What is graphic design?Graphic design is the practice of using words, pictures, and other visual elements to communicate ideas to an audience, often in order to achieve a certain result.
In other words, graphic design serves as a tool for communicating ideas through imagery and design.
For those with imaginative thinking skills who appreciate art, technology, and communication, graphic design is a terrific job.
Every business has a need for design, therefore graphic designers have a lot of opportunities to work on a variety of brand-new, fascinating projects.
You can draw circles and rectangles using geometric form tools.
Hence, option B is correct.
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A satellite of mass 6500 kg orbits the earth in a circular orbit of radius of 7.5 106 m (this is above the earth's atmosphere).the mass of the earth is 6.0 1024 kg. what is the speed of the satellite?
Answers
The two forces, centripetal force and gravity are
equal
So, G M m / r^2 = (m V^2) / r
so sqrt (GM/r)= V
G is a gravitational constant which is G=6,67.10exp(-11)
Sqrt (6.67 x 10^-11) (6 x 10^24)/7.5 x 10^6
so V= 7.30479295e9 or 7305 m/s
Final answer:
To find the speed of a satellite in Earth orbit, we use the formula for orbital speed with the Earth's mass and the orbit's radius. After calculation, the satellite's speed is found to be approximately 7357.7 m/s.
Explanation:
The question asks for the speed of a satellite of mass 6500 kg orbiting the Earth in a circular orbit with a radius of 7.5 × 106 m. The mass of the Earth is given as 6.0 × 1024 kg. To find the speed of the satellite, we use the formula for the orbital speed:
v = √(GM/r)
where v is the orbital speed, G is the gravitational constant (6.674 × 10−12 Nm2/kg2), M is the mass of the Earth, and r is the radius of the orbit. Plugging in the given values:
v = √((6.674 × 10−12 × 6.0 × 1024) / 7.5 × 106)
After performing the calculation, we find that the speed of the satellite is approximately 7357.7 m/s.
A lunar exploration vehicle was created by a research team. It weighs 3,000 kg on the earth. It needs an acceleration of 10 m/s2 on the moon. In order to have the same acceleration, what will be the net force acting on the vehicle on the earth?
Answers
EXPLANATION
Applying Newton’s second of law of motion, which in summary, states that the acceleration of an object... is directly proportional to the magnitude of the net force... and inversely proportional to the mass of the object.
Therefore, Force = Mass * Acceleration
F = ma
Mass, m = 3,000 kg
Acceleration, a = 10 m/s²
Force, F = 3,000 × 10
= 30,000 N