Volume Definition and 1000 Threads

hey guys. bellow is an upside down cone frustum with the dimensions given bellow where the green R is the radius of the larger circle and the blue r is the radius of the smaller circle and the red h to be the height of the object knowing that volume of this shape is calculated as...

Homework Statement Find the centre of mass of solid cone. Homework Equations $$y_{cm}=\frac{1}{M}\int_0^Hydm$$ The Attempt at a Solution First I took thin disks. I got the answer when I assumed its thickness to be dy but then dysecθ would be more accurate if half angle of cone is θ since...

Homework Statement (3 i) Using \nabla . \mathbf{F} = \frac{\partial \mathbf{F_{\rho}}}{\partial \rho} + \frac{\mathbf{F_{\rho}}}{\rho} + \frac{1}{\rho} \frac{\partial \mathbf{F_{\phi}}}{\partial \phi} + \frac{\partial \mathbf{F_{z}}}{\partial z} calculate the divergence of the vector field...

A solid is generated by revolving the region bounded by y=(1/2)x2 and y= 2 about the y-axis. So what I did is set up my integral V= 2pi (integral sign from 0 to 2) x(1/2)(x)2 dx When I solve i get 4pi, and then I have to find the radius of the hole which has one fourth of the volume. So the...

Homework Statement Find the volume V of the region that lies inside the quarter cylinder 0 ≤ r ≤ 1, 0 ≤ θ ⇐ 1/2 π and between the planes x+y+z=4 and z=0, where (r, θ, z) are cylindrical polar coordinates. Homework Equations integral dV = integral r drdθdz The Attempt at a Solution I...

Homework Statement Dear Mentors and PF helpers, I can do part (a) and (b) but don't really know how to do (c) and (d). Can somebody teach me how to go about solving it. Homework Equations Volume of cone: $$\frac{1}{3}πr^2h$$ Volume of cylinder: $$πr^2h$$ Volume of sphere...

Hey, I am new in this forum and looking forward to learn physics which I hate :) My first question concerns possibility, in theory. Say, there is a water tank. Let us say that we made a nanometer hole. The tank is full. Then, we put even more water through that hole. But the hole has something...

Homework Statement The region bounded by the graphs of the curves y=4√x , y=0, x=5, x=12 is revolved about the x-axis. a) Find the religion lateral surface area of the generated volume. b) Find the total surface area of the generated volume, including both ends. Homework EquationsThe Attempt at...

Homework Statement Problem - If the volume of the carry-on luggage is 2000 cubic inches, determine two possibilities for its depth. Where necessary, round to the nearest tenth of an inch Homework Equations V(x) = x(x+10)(30-2x) Volume function is given above The Attempt at a Solution I...

Homework Statement Find the volume generated by x=0 x=π y=2sin(x/2) y=sin(x) using the shell method. Homework Equations x=2arcsin(y/2) x=arcsin(y) The Attempt at a Solution So to setup my integral I got the following values, Outer Radius=(2-arcsin(y)) Inner Radius=(2-2arcsin(y/2)) I'm...

Homework Statement 5 lbs of nitroglycerin detonates. What is the total volume of the gases produced? Homework Equations PV=nRT The Attempt at a Solution I used the balance chemical equation of the decomposition of nitroglycerin and used stoichiometry to find the number of moles of nitrogen...

I need a website or a program that I can write an equation then find volume in Disk or washer or cylindrical and draw it ? it should be Free

Question: The height of the given vessel is h,and the width of the given vessel is b (as given in the diagram). The density of the liquid is r.Find the force exerted by the liquid on the slant wall. Relevant formulae : P = F/A F = Vdg An attempt at the solution...

At STP, a mole of hydrogen gas would take up 22.4 L. If that hydrogen gas was ionized and stripped of 100% of the electrons, would the remaining protons have a larger volume than 22.4 L? I'm not sure because on one hand, taking away the electrons leaves each proton with much less volume, but on...

Homework Statement What equation is needed to calculate the height of a spherical cap with a fixed volume and radius? Homework Equations V=πh/6 (3a^2 + h^2) Where V = volume, h is cap height, a is cap radius The Attempt at a Solution I have tried to separate the h out and got as far as...

Hey! :o A liquid flows through a flat surface with uniform vector velocity $\overrightarrow{v}$. Let $\overrightarrow{n}$ an unit vector perpendicular to the plane. Show that $\overrightarrow{v} \cdot \overrightarrow{n}$ is the volume of the liquid that passes through the unit surface of...

Homework Statement [/B] (a) Find the proper distance (b) Find the proper area (c) Find the proper volume (d) Find the four-volume Homework EquationsThe Attempt at a Solution Part (a) Letting ##d\theta = dt = d\phi = 0##: \Delta s = \int_0^R \left( 1-Ar^2 \right) dr = R \left(1 -...

I am working on a take home with a group of students and we all got different answers for this problem... can anyone look over it and tell me where I am going wrong?? Let me know if any of my work is confusing...

I understand why entropy (a state function) is very useful in chemistry. Since most chemistry systems are at constant pressure, ##\Delta H=Q_v## from the derivation below: ##H=U+PV## ##dH=dU+dPV+PdV## ##dU=\delta Q-\delta W## ## dU=\delta Q-PdV## ## dH=\delta Q+dPV## ##dPV=0## ## dH=\delta...

For a van der Waals gas, there are London dispersion forces causing the gas particles to be attracted to each other while the law of excluded volume provides repulsive forces. How do each of these characteristics effect the pressure, volume, and temperature of the gas? I assumed that for the...

The question is... So of course I rearrange my ellipse formula to get $$y=\pm\sqrt{1-\frac{{x}^{2}}{4}}$$ Then I calculate my radius as $$x-(-2)=r \implies x+2=r$$ I know the formula for finding volume with the Shell Method is $$V=\int_{a}^{b}2\pi x\cdot f(x) \,dx$$ To make it easier I...

Homework Statement A question in my chemistry 151 lab book: A student measures the volume of water displaced by the same metal sample as 5.4 mL, 5.8 mL, and 5.5 mL for his three determinations. Determine the median volume. Homework Equations Unknown or N/A The Attempt at a Solution How do...

Homework Statement A tank for scuba diving is designed to contain 50 standard cubic feet of air when filled to a pressure of 3,000 pounds per square inch (gage) at an ambient temperature of 80 F. Calculate the interior volume of the tank. A standard cubic foot occupies one cubic foot at T=15...

Hi can anyone please suggest me how to find out the rate at which gas in LPG cylinder reduce.Initially before use gas cylinder will be full as the consumer start using the gas it starts reducing how do i calculate how much is left out and the rate at which it is getting reduced ,And also if a...

Homework Statement Find the volume of the solid bounded by the cylinder y^2+z^2=9 and the planes x=0, y=0, z=0, and 2x+y=2. Homework Equations None. The Attempt at a Solution This is double integral problem. I know how to find the double integral but I don't know how to set it up. How do I...

Homework Statement Find volume when the area rotates around a line. Homework Equations x=y^2 x=1-y^2 about x = 3 The Attempt at a Solution Could someone please check my formula for Area? I have pi[ (3-(y^2))^2 - (2-(y^2))^2 ] which gives me the integral pi[5y-(2/3)y^3]. I think...

Homework Statement How do you find the volume of the solid obtained by rotating the region bounded by the given curves about the specified lines? I keep getting a negative number and I"m becoming so frustrated! 11pi/30 is the answer in the textbook. Thank you so very much in advance...

Can a singularity expand in volume?

Imaginary numbers enable one to envision a lot of ideas. But what kind of numbers/algebras would enable us to work with imaginary volumes? Volumes, by definition, always seem to be positive, since any cubes are. What kind of numbers would give/allow a more complex picture?

Homework Statement Of the objects below, which is the most dense? A. an object with a volume of 13 dm3 and a mass of 1.29 × 103 g B. an object with a volume of 0.00212 m3 and a mass of 4.22 × 104 mg C. an object with a volume of 3.91 × 10-24 nm3 and a mass of 7.93 × 10-1 ng D. an object with...

Hallo, Working on building a cloud chamber based on thermoelectric coolers rather than dry ice or other "consumable" cooling methods, and having some difficulty working out some of the numbers. Say I have a volume of air at room temperature, for arguments sake 1600cm³, and I want to cool this...

Homework Statement I've seen this problem appear in more than one textbook almost without any changes. It goes like this: Assume the entropy ##S## depends on the volume ##\bar{\Omega}## inside the energy shell: ##S(\bar{\Omega})=f(\bar{\Omega})##. Show that from the additivity of ##S## and the...

Homework Statement Hi guys, My first post here, I hope someone can help me out with a quick fluid mechanics problem. I'm looking to calculate the pressure increase inside a closed tube full of water when the tube is crushed and therefore its volume reduced. The tube is filled completely...

I am trying to figure out what the total thermal energy emitted by completely transparent matter. It seems Planck's law can't do this because the thickness or geometry of the mass is not given, only it's surface area. The spectral radiance of a black body is given by Planck's law...

This is just a question I posed to myself while learning about waves, I was wondering how the volume of an audible noise is increased or decreased, is it related to the compression of the wave and therefore the force generating it? If somebody could explain this in mathematical terms or provide...

Homework Statement Take an elastic balloon of volume V in vacuum. The surface of the balloon has tension T. Find the pressure inside the balloon in terms of V and T, then combine this to the ideal gas law to find an expression for V. Homework Equations See below The Attempt at a Solution I...

Hello there, so I have answered my question from fluid systems but the answer doesn't look right ;/ and I have no idea what have I done wrong. Can you please check and correct where it's wrong ? ;) here is the question: A pipe contains a gradually tapering section in which its diameter decreases...

Homework Statement An infinite line of charge with linear density λ1 = 6.7 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.4 cm and outer radius b = 4.7 cm. The insulating shell is uniformly charged with a volume density of ρ = -722 μC/m3. What is λ2, the...

Homework Statement The problem says: "A record rainstorm produced 304.8 mm (approximately 1 ft) of rain in 42 min. Estimate the average force that the rain exerted on the roof of a house that measures 10 m * 16 m. Indicate any assumptions you made. (Note: density of water is 1000 kg/m3"...

Hi everyone, If you know the temperature rise of 2 moles of an ideal gas when a known amount of energy is transferred to it as heat, (hence are able to calculate cv by dU/dT); is the molar heat capacity simply half this value as it is half the number of moles?

There is a nice equation made by Nobuo Yamamoto which describes the curve of an egg and it is: (x^2 + y^2)^2 = ax^3 + (3/10)xy^2, where a is the length of the major axis of the egg. Solve this equation for y, we get: y=+/- sqrt((3/20)ax - x^2 + xsqrt((7/10)ax + (9/400)a^2)) When I rotate the...

Homework Statement The Biot-Savart law for a current density j in a volume V is: d\vec{B} = \frac{\mu_0\vec{j}\times\vec{r}}{4\pi r^3} dV Derive the formula for the magnetic field created by a single point-like particle carrying charge q moving with velocity \vec{v}. Explain and justify all...

I am an EMT and have a concern. Some patients require high volumes of oxygen (as high as 15 liters per minute sometimes). Many times oxygen concentrators only go up to 5 lpm. It may be misleading to say 5 lpm because the machines have to operate based upon pressure rather than volume. 5 lpm...

I asked my teacher, and I was told that volume is the independent variable, and that pressure is dependent. The textbook I'm using said the same thing. After looking up some graphs of the law, I found that both pressure and volume were used as independent variables. It seems counter-intuitive...

If we take two planets One Earth and another one with half the radius of Earth. The planet with half the radius has lesser than half of the volume of the Earth. Also given that mass is half. Why? Is it because lower radius and lesser mass means lesser gravity and lesser gravity can pull lesser...

If I where to take a volume of water that is at atmospheric pressure and then add more water molecules to it without allowing the volume to increase I understand that the pressure will increase but does this also mean the temperature will increase? My guess is that is does but I don't...

hello my friend I need to know the Molar volume of sodium at the boiling point I can't find any thing about this please help me thanks

Homework Statement An air bubble of volume 20 cm^3 is at the bottom of a lake 40 m deep, where the temperature is 4.0°C. The bubble rises to the surface, which is at a temperature of 20°C. Take the temperature of the bubble’s air to be the same as that of the surrounding water. Just as the...

Homework Statement What is the volume of a tank that is 8 ft in diameter and 15 feet high Homework EquationsThe Attempt at a Solution Π x (4ft) 2 x 20ft 3.14 X 24ft x 15ft = 1130.4

Homework Statement How would you calculate the volume of a cylindrical tank that is on its side (called a horizontal tank)? Calculate the volume if that tank that is 10 ft. in diameter and 18 ft. long. I already know the answer i just need help understanding how they got the answer Homework...