Center Definition and 1000 Threads

Homework Statement Find the center of mass of a hemisphere of radius R. Homework Equations R_cm = (rho/M) Integral[ (vector r) dv] dv = r^2 Sin[theta] dr d[theta] d[phi] The Attempt at a Solution [/B] In spherical polar coordinates, vector r = r r-hat, so the argument of the integral should...

Hi, I'm new here, great forum! I am building a boat rack for the top of my truck for a particular boat and boat dolly. The boat will be upside down with the beach dolly attached. It is a side loader, so balance is critical. I need to calculate the combined Center Of Gravity (COG) of the boat...

Hi, I'm having a discussion with someone on the plausibility of the physics in a science fiction movie (I know, very efficient use of time!). There's a scene with a space station shaped like a ring. It has a center body that is attached radially to one edge of the ring. This space station is...

Homework Statement Find electric potential at a center of charged rod with charge 'Q' and length '2a' if referent point is at infinity. Homework Equations Electric potential of a point charge: V=kQ/r Electric potential via electric field: integral (Edl) The Attempt at a Solution I used...

As we get closer to the Earth's center, clocks down there tick slower that ours in the surface. Does this have any noticeable effects? Just for example, could we notice that certain reactions such as radioactive decay happen 'too slow' down there compared to what we know as the normal rate in...

For a tapered beam of constant density the center of mass is calculated as the mean of the mass distribution along the central axis, the center of gravity is calculated by getting the equilibrium of the angular moments to the left and right of a fulcrum moving along the horizontal beam. The...

Homework Statement [/B] A shperical shell of mass = 1kg and radius 2.0cm is released from rest at the top of an inclined plane at a height of 1.00m. The ball rolls down the incline without slipping, what is the velocity of the center of mass at the bottom of the incline.Homework Equations I'm...

Hello everyone, I am trying to understand a center of gravity question regarding an object that is being lifted. I have a part that has a lifting circle that is used to put a hook through to hoist. The part needs to slide onto another part's surface that is about 30 degrees above the...

Homework Statement http://www.upload.ee/image/4762203/DSC_0009_1_.JPG I need to find the formula which is in the red circle. Beam is simply supported at both ends and there is center load. Do you think that this is correct? Homework EquationsThe Attempt at a Solution

Homework Statement If a point charge is inside a Gaussian sphere but is off center, why is its electric field still Qenc/(e0*4*pi*r^2)?Homework Equations surface integral of E*da=Qenc/e0The Attempt at a Solution If we draw cones out from the charge. the 2 surfaces from the cones' intersection...

Homework Statement A railroad flatcar of mass Mc can roll without friciton along a straight horizontal track as shown in the diagram. Initially a man of mass Mm is standing on the car which is moving to the right relative to the ground with a speed of vi. What is the change in velocity of the...

Homework Statement A dog of mass M is standing on a raft so that he is a distance L from the shore. He walks a distance d on the boat toward the shore and then stops. The boats has a mass of Mb. Assume no fricton between the boat and the water. How far is the dog from shore when he stops...

It is a classic physics problem to calculate how long it would take to fall through a hole that passes through the center of the Earth to the other side, assuming Earth is a sphere with uniform density. I also remember being posed a problem for if you were falling through a hole that passed not...

Homework Statement A 55 kg man is standing on a 65 kg and 4.0 m length canoe that floats without friction on water. The man walks from a 0.75m from one end of the canoe to another point 0.75 from the other end of the canoe. What distance does the canoe move? Homework Equations Center of mass...

First of all, I am sorry if this is in the wrong subforum; I'm not sure if astrodynamics should be under astronomy. The post is also fairly long. My problem is that in my derivation of the center of mass of a binary system, I get a conflicting result for the distances of the center of mass to...

Homework Statement Determine the center frequency and bandwidth of the bandpass filter. Homework Equations center frequency of bandpass filter = ωc occurs when the magnitude of H = 1 H = V0/Vs Center frequency occurs when Im(Z) = 0 Zc = 1/(jωC) = 1/s ZL = jωL ZR = R I don't know a formula...

At the exact center of a finite wire (i.e. a distance, say $L/2$ from each end), why can I not apply Gauss's Law in integral form to find an EXACT solution for the electric field? At the center of the wire, $E$ is entirely radial, so it seems like I should be able to draw an infinitesimally...

Hello everyone, As you can see, I am new on this forum. In my first thread, I decided to ask one very interesting question, maybe one of the most shocking questions which exist at this moment. We all know the data which have been provided of WMAP and Planck satellites, and what this data shows...

As per ww.physicsclassroom.com/class/refln/Lesson-3/The-Anatomy-of-a-Curved-Mirror The point in the center of the sphere from which the mirror was sliced is known as the center of curvature,I am not able to understand this.Please help.

Homework Statement There is no given data.the instruction ask to write ab essay about this topic.what will be find in the center? Homework EquationsThe Attempt at a Solution I read about sun.in the core there is fusion.neutrinos...etc.but i don't have a full idea.thanks for your helps.

Homework Statement Where's the COM Homework Equations The COM of a right triangle is a third of an edge apart of the right angle vertex The Attempt at a Solution Edge AC: ##\frac{50}{\cos 20^0}=53.2## Two thirds of edge AB: ##\frac{53.2\cdot 30^0\cdot 2}{3}=30.7## One third of edge BC...

Homework Statement Problem and solution attached Homework Equations B = [4uI/(4pi)]sin(theta1-theta2] The Attempt at a Solution I understand fully how to do it except determining the value of theta1 and theta2. The solution says theta1 is 45(deg) and theta2 is -45(deg). How did they get those...

Homework Statement Consider a slender rod satellite in a circular orbit. Show that the position of the center of gravity, ##\rho_G##, can be written in terms of the position of the center of mass, ##\rho_C##, as: ##\rho_G = \rho_C (1+\frac{l^2}{4\rho_C^2})^\frac{1}{4} ##, where ## l## is the...

Suppose we have a free rod on a frictionless surface: if we hit it on a tip it will translate and rotate around its CM. What happens if we hit it at any other point between tip and CM? will it still rotate around CM?, if not, is it easy to find the center of rotation? If not, are the 3...

Homework Statement A frog sits on the end of a long board of length L=5m . The board rests on a frictionless horizontal table. The frog wants to jump to the opposite end of the board . What is the minimum take-off speed (in s.i. Units) i.e.,relative to ground 'v' that allows the frog to do the...

1. The problem statement: A removable plate is mounted in the end of a swimming pool. The plate is 60cm square with the top edge 30cm below surface of water. Compute the force on plate and distance to centre of pressure below surface of water. 2. Homework Equations . 3. The attempt at...

Homework Statement My question is this: When finding center of mass, can you do so using spherical/cylindrical coordinates, or must you put it in cartesian coordinates? If you can use spherical/cylindrical coordinates, how do you set up the triple integrals ? Thank you. Homework...

Homework Statement Suppose we had a straight tunnel, through Earth's center, to a point on the opposite side of the planet, and used it to deliver mail to the other side. With what speed would our packages pass through Earth's center. Homework Equations ag = (GM)/R2 Mins = (4/3)πR3*ρ The...

Homework Statement Consider a solid hemisphere of uniform density with radius R. Where is the center of mass? z=0 0zR2 z=R2 R2zr z=R Image is provided. Homework EquationsNoneThe Attempt at a Solution Answer A and E do not seem logical. I thought it was answer C from my eyes. Center of...

I am doing a mini hovercraft project. Regarding my design, I plan to place the fan (LIFT) in the middle of a rectangular styrofoam board (15 inches by 8inches). The position of my fan would be (x=7.5, y=4in); this would also be my center of gravity. My origin (coordinate) is at the corner of...

-Hello everyone. At school, I studied about convex lense and concave lense. They are very interesting, we learned about how lights would be after going through the lense. But what I want to ask is how we can calculate the distance between optical center and focal (I means focal length). Focal...

Homework Statement Homework Equations I don't know how is it related to center of mass. The Attempt at a Solution I don't know how to begin. Thanks a lot for your help !

Homework Statement A meter stick is 200 g. A mass of 1 kg is placed in 20 cm, and another mass of 5 kg is placed in 100 cm. So the diagram will be like: Homework Equations Why do we have to include M2? And why is the mass of M2 is 200g? Isn't the whole meter stick weight...

Homework Statement Where is the difference between center of support of equilibrium and center of mass of system. For example we are given a ruler with length L and mass M and two builds with mass m1 and m2 on its edges. Homework Equations http://imgur.com/PiGA817 The Attempt at a Solution I...

Homework Statement What is the distance between the center of gravity and the center of mass of a vertical rod of length 2 meters, and with a uniform mass distribution? (Center of gravity is defined like the center of mass with weight replacing mass in the formula). Homework Equations nothing...

I have just begun studying electrostatic and I'm trying to do this exercize: We have a square with charges +q , -2q, +2q, -q1)Compute the electrostatic field \vec{E}at the center of the square. I did this way : I find \vec{E_A}=\frac{q}{2 \pi \epsilon_0} \vec{u} {E_B}=\frac{-q}{ \pi...

Homework Statement 3.) What is the moment of inertia of the object about an axis at the center of mass of the object? (Note: the center of mass can be calculated to be located at a point halfway between the center of the sphere and the left edge of the sphere.)...

In the above figure, a small weight is placed at 2 cm (0.02 m) from the center of the rectangular prism. Let's call the mass of this small weight (M1) and the mass of the entire body including the small weight (M) Given the dimensions above, I want to know how to calculate the height of center...

Hey everyone! I recently worked through finding the moment of inertia of a cylinder with a cylindrical cavity off center, and I wish to further deepen my understanding of calculating the center of mass of such objects. So I made up the following problem: Homework Statement Find the center of...

Homework Statement mass = M radius = r rot. inertia = i height = h Sphere of mass M is released from rest at the top of an inclined plane. The speed of the center of mass at the bottom of the incline, without friction, is sqrt(2gh). I need to find the velocity of the center of mass assuming...

Homework Statement I would like to calculate the position of the center of mass of the body on the figure. http://kepfeltoltes.hu/150302/161353224K_pkiv_g_s_www.kepfeltoltes.hu_.jpgHomework EquationsThe Attempt at a Solution I read a way of solution: Theorem of Pappus It states that if we...

Homework Statement A Cessna C-172M has empty weight 1350 lbs. When it is weighed, the load on each of the main wheels is 474 lbs. The load on the nose wheel is 402 lbs. Where is the center of gravity of the empty Cessna? Ok so the question assumes you know what a Cessna looks like, but it's...

Homework Statement A partially loaded plane weighs 115,000 pounds. A famous actor's steamer trunk, weighing 300 pounds, is put into the rear cargo hold 250 inches behind the center of gravity. How much does this extra hold shift the center of gravity. Homework Equations W1 = W x (L2 / L) W2...

Homework Statement The force of attraction on an object below Earth's surface is directly proportional to it's distance from Earth's center.Find the work done in moving a weight of ##w## lb located ##a## miles below Earth's surface up to the surface itself. Assume Earth's radius is a constant...

Homework Statement I really think my answer is correct - could someone verify this or let me know where I went wrong? This is problem submitted online, the "correct" answer looks like my teacher accidentally hit the button 3 twice. PROBLEM: The toriod in example 5-1 from the textbook has an...

Homework Statement A man with mass m1 = 55 kg stands at the left end of a uniform boat with mass m2 = 175 kg and a length L = 2.7 m. Let the origin of our coordinate system be the man’s original location as shown in the drawing. Assume there is no friction or drag between the boat and water...

Homework Statement A conductor consists of a circular loop of radius R = 14.4 cm and two long, straight sections as shown in the figure. The wire lies in the plane of the paper and carries a current I = 1.60 A. Find the magnetic field at the center of the loop. Homework Equations...

Homework Statement I am trying to understand a substitution used to solve for the center of mass of a solid uniform hemisphere as in this post: https://www.physicsforums.com/threads/solid-hemisphere-center-of-mass-in-spherical-coordinates.650663/#post-4151797[1] I completely understand the...

what's the center of a globular cluster , is it a star or can it be a black hole ? how are they formed and bound to gravitational pull of the milky way

Homework Statement A total charge Q is uniformly distributed on a thread of length L. This thread forms a semicircle. what is the potential at the center? (assume V=0 at large distances) Homework Equations V = -∫Edl E = kQ/r^2 The Attempt at a Solution V = - ∫Edr = -E∫dr = -Er = - kQr/r^2 =...