Center Definition and 1000 Threads

I don't understand why we would weigh less at Earth's center(as opposed to sea level). Looking around the net, I have seen different approaches to this problem, each with different solutions. According to Newton's universal law of gravitation: F= Gm1m2/r2 If this is the case, then as...

1. Two small particles of mass m1 and mass m2 attract each other with a force that varies with the inverse cube of their separation. At time t0 , m1 has velocity v directed towards m2 , which is at rest a distance d away. At time t1 , the particles collide. How far does m1 travel in the time...

"A set in the plane is called a region if it satisfies the following two conditions: 1. Each point of the set is the center of a circle whose entire enterior consists of points of the set. 2. Every two points of the set can be joined by a curve which consists entirely of points of the set."...

Imagine that you could dig a hole up to the very center of the Earth and sit there. What will you experience? Complete weightlessness or the experience of being torn apart in every direction?

Homework Statement the electric field at the surface of a charged, solid, copper sphere with radius 0.160m is 3600N/C , directed toward the center of the sphere. what is the potential at the center of the sphere, if we take the potential to be zero infinitely far from the sphere...

i have a 20.5ft c3x5 steel channel with a point load at the exact center and i wanted to determine its maximum deflection. the point load is 921.86lbs, and moment of inertia is 1.86in^4. modulus of E= 30,000,000psi

Homework Statement 3 rods each of length 1 meter form an equilateral triangle. Two rods have a uniform charge distribution of 8\times 10^{-6} C and the third of -8\times 10^{-6} C. What is the electric field strength at the center of an equilateral triangle Homework Equations \vec{E} =...

I just wanted something to play with so I thought of this problem and solved it but now I have questions about it. Consider a charged particle with charge q and mass \mu which is constrained to move on the surface of a sphere of radius R. There is a magnetic dipole with moment \vec m=m \hat z...

Can someone show me how to resolve this question? A particular circle in the standard (x,y) coordinate plane has an equation of (x − 5)2 + y2 = 38. What are the radius of the circle, in coordinate units, and the coordinates of the center of the circle? radius center F. √38 ( 5,0) G. 19 ( 5,0)...

Think about this hypothesis: Solar activity changes the distribution of mass on the sun. This change could move the center of mass of the sun, unless the distribution were symmetric. This would move the center of mass away from the center of rotation. This would cause a fluctuation in the...

Homework Statement Prove that the center of the factor group G/Z(G) is the trivial subgroup ({e}). Homework Equations Z(G) = {elements a in G|ax=xa for all elements x in G} The Attempt at a Solution I need to prove G is abelian, because G/Z(G) is cyclic, right? Then I can say that...

Hi, how do I find the center and radius from these equations? The 2 equations represent 2 different circles, by the way. I need to draw 2 circles.

Hi, how do I find the center and radius from these equations? The 2 equations represent 2 different circles, by the way.

Consider an equilateral triangle of side 15.6 cm. A charge of +2.0uc is placed at one vertex and charges of -4.0C uc each are placed at the other two, as shown in the diagram to the right. Determine the electric field at the centre of the triangle ANgle= 60 sides--> d1= d2=d3=0.156m...

Homework Statement Find the center of mass of a planar lamina, in the form of a triangle with vertices (0,0),(0,a),(a,a), if ρ=k Homework Equations m = ∫∫f dA xbar = My/m ybar = Mx/m The Attempt at a Solution mass = ka²/2 Mx = ∫∫yk dy dx My = ∫∫xk dy dx...

Hi there I am just really confused as to how they arrived at the answer to this problem. I attached a picture of the entire question and the solution. Homework Statement Please see attached file. Homework Equations Biot Savart Law for Magnetism of a Wire where the length of wire is much...

Is it still true that most if not all galaxies have at their center a Black Hole? And that the estimated gravity is about 10% of the total mass galaxies. And is it still true that all stars or 99 % of them are moving out and a way from the black hole. I was just wondering if these black holes...

Is the value of g at the center of the Earth zero or infinite ?

I was googling to see if a bomb could disrupt a tornado and I came across this thread here ( https://www.physicsforums.com/showthread.php?t=692975 ) and I saw this graphic posted there (see attached thumbnail below). And it got me to wondering, if you made a giant, massive, strong metal plate...

Suppose there were a supermassive, superdense hollow sphere. Inside of the sphere, would time move more slowly relative to outside? Would objects inside the sphere be contracted relative to outside? I did this calculation once about the center of a neutron star. (Of course, it isn't...

This is my first thread, and I am excited to post it.:biggrin: My question is that, did any Scientists do any research about Center of Gravity and formulated any laws or gave explanation to it's fundamental behavior? If so, then have they considered the Center of Gravity of liquids and...

Was thinking about this why is it a requirement that the center of a black hole be a singularity? If the event horizon contained all the mass of a black hole would it still not have the same effect on it's surroundings? Why could it not be similar to a a crystal where as each molecular link or...

Consider the motion of a system composed of a rigid bar and a rigid ring attached to it as is shown in the attached figure.The rigid system is rotating around the point O. Why we can not treat this motion as rotational motion of "the center of mass"? Namely why we can not get the correct result...

I have attached the image as an attachment Homework Statement I am reading a classical mechanics textbook and I don't understand how they found that. r1' = -\frac{m_{2}}{m_{1}+m_{2}}r and r2' = \frac{m_{1}}{m_{1}+m_{2}}r r1' is the vector from the center of mass R to m1 and...

Homework Statement Pic: http://i.imgur.com/Ny4YAKf.jpg Rod has radius R, and mass M. Small mass has mass m. I have to find gravitational force exerted on mass m by rod and potential energy of the whole thing. Homework Equations The Attempt at a Solution So my idea is that...

Not sure how speculative this is but thought it would be of interest- http://www.iflscience.com/space/could-supermassive-black-holes-center-galaxies-be-wormholes and the related paper- http://arxiv.org/abs/1405.1883v1 Distinguishing black holes and wormholes with orbiting hot spots by...

Is it true that the center of mass of an object will be accelerated with the same direction and magnitude from the same force no matter if the force is applied to the center of the object or to the edge of the object? I have heard some people say this is not true because some of the "force"...

Hi ! 2 Objects turn at constant rotational velocity ω rd/s around axis noted "axis" on image (ω clockwise). An external system not drawn force the study to turn at ω rd/s if necessary. From blue object, forces F1 and F2 are applied to orange object. F1 = -F2 in vector. I would like to know if...

Homework Statement I have a conceptual question which is not HW, although the moderators of this forum think different. In the "hoop" example, and the example after that here: http://tonic.physics.sunysb.edu/~dteaney/F06_Ph2034/lectures/lexam3.pdf do you ALWAYS have the change in...

Homework Statement Two stars, each of mass M, move in a circular orbit of radius R around their common center of mass C. a) what is the gravitational force on each star? b) what is the period of each star's orbit? c) what is the total mechanical energy (potential + kinetic) of this...

Homework Statement I need to find a vehicles center of gravityHomework Equations I'm thinking euler's equations but I am new to them.The Attempt at a Solution I'm designing a rig as part of a project that would allow a race car to be suspended from a lift on 4 ropes and then allow to move in on...

Homework Statement Assuming that the combined mass of the balls is greater than the combined mass of the cords, but that the cords do have some mass, where is the center of mass for the system shown below? Homework Equations None The Attempt at a Solution I tried approaching...

Homework Statement Image 1 Shows both system 1 and system 2 at rest Images 2 and 3 show answer choices: Given M2 > M1, which of the following pendulum systems has the GREATEST change in potential energy from a state of rest? Passage says: The greatest Potential energy is always associated...

My textbook says that at the center of a square conducting wire of length ω, the magnetic field is: B=\sqrt{2}μ_{0}I/(\piR) I am not sure how to calculate this...? Because the Biot Savart law has a closed loop integral, we do not use piecewise addition of line integrals to find the...

Hello! I have data of a damped oscillation (the movement on Y as it dies down in time). Imagine for example a ball that is hanging from a spring and it keeps bouncing up and down under the spring until it stops. The problem is I do not know how to find the axis around which the oscillation...

Homework Statement An object with kinetic energy K explodes into two pieces, each of which moves with twice the speed of the original object. Compare the internal and center-of-mass energies after the explosion. The Attempt at a Solution Let K1 be the kinetic energy of the main...

Attachments Figure # 1 Figure # 2 reproduced from http://www.lmnoeng.com/Volume/InclinedCyl.htmhttp://www.lmnoeng.com/Volume/InclinedCyl.htm Description The blue is the mass inside a cylinder. In steady condition, I would want to know where its Center of gravity point shall be from either of...

Homework Statement How could I express a parametric formula for a right circular cylinder centered at (-2, 10, 3)? with radius 3 and length 12 Homework Equations Parametric equations for a right circular cylinder are: x=rcosΘ y=rsinθ z = h The Attempt at a Solution Not sure...

So I have a question. I (moment of inertia) is basically mr^2 right? And r is supposed to be the distance from the axis of rotation. When the axis of rotation is directly through the center of mass, how is there Icm (moment of inertia about the center of mass). It's confusing to me, because so...

Homework Statement 1. A non-uniform beam with a mass of 85kg has a length of 6.2m and is attached to a wall and supported at an angle of 28 degrees from the wall by a horizontal rope which is attached to the wall above the beam . The tension in the rope is found to be 310N. How far from the...

I got one multiple choice on our exam incorrect, and I was wondering exactly why this answer is correct: When you accelerate your car, the front of the car lifts up slightly. Or when you brake, the front dips down. The primary reason is because the A) center of mass of the car and its...

Take a uniform density bar in space for example. Would the center of mass move if the bar was struck at the very tip perpendicularly by some weight? If so, please explain.

Hi I need some help explaining kinetic moment and moment of the center of mass. This is an example: http://session.masteringengineering.com/problemAsset/1529176/3/Hibbler.ch17.p107.jpg Okay I know that when you do moment equations: The Moment forces about some point is = to the kinetic...

Homework Statement A nonuniform, horizontal bar of mass m is supported by two massless wires against gravity. The left wire makes an angle ϕ1 with the horizontal, and the right wire makes an angle ϕ2. The bar has length L. Find the position of the center of mass of the bar, x, measured from...

Hello there, If a mass, m, is placed at one end of an boat of mass M, which is located on a frictionless ocean. If the mass, m, is moved from one end of the boat to the other end, conservation of center of mass position ensures that the boat shifts a small distance in the opposite direction...

Hello again, Two days ago, I started a thread asking about the same question more or less, and I was thinking that the matter was clear now in my mind, because I had made an error in my calculations... Before I begin, I want to admit that my English is not very good, and my exposition to...

Homework Statement Find B at the center of the 3.2-cm-radius semicircle in the figure(Figure 1) . The straight wires extend a great distance outward to the left and carry a current I=6.4A. Homework Equations (Magnetic field for a current carrying loop)...

Homework Statement A uniformly charged insulating rod of length 12.0 cm is bent into the shape of a semicircle as shown in the figure below. The rod has a total charge of −7.50 µC. Find the magnitude of the electric field at O, the centre of the semicircle. Homework Equations E = 2kq /...

Homework Statement A cubical box has been constructed from uniform metal plate of negligible thickness. The box is open at the top and has edge length L=40cm. Find (a) the x coordinate (b) the y coordinate, and (c) the z coordinate of the center of mass of the box. Ok, so my professor...

Homework Statement image attachment Homework Equations The Attempt at a Solution i have the solution , but in it , he assumes the center of mass is on the vertical and thus the distance of the vertical from the center is rsin(1/4∏)/(1/4∏) where r is the radius , so why did he...