Spheres Definition and 467 Threads

Homework Statement Three small spheres are placed at fixed points along the x-axis, whose positive direction points towards the right. Sphere A is at x = 46.0 cm, with a charge of –6.00 μC. Sphere B is at x = 55.0 cm, with a charge of 6.00 μC. Sphere C is at x = 59.0 cm, with a charge...

In space-time I like to think of objects going through a "stream" of movements that remain concrete in the 4 dimensions of space-time, all movements being inter-related with one another with respect to the frame of reference. But let's compress this stream so only what remains is the overall...

Hi, I'm helping my friend with a space combat game he is programming. What I'm trying to figure out is how to model the collisions between spheres in 3D. So far I've figured out how to calculate final velocities of 2 colliding spheres using conservation of linear momentum. I found a...

Homework Statement Two uncharged metal spheres, spaced 15.0 cm apart , have a capacitance of 24.0 pF. How much work would it take to move 12.0 nC of charge from one sphere to the other? Homework Equations V = Q/[4(pi)eor] (delta)K + (delta)U = 0 *I think The Attempt at a Solution...

A number of questions have come up on canoe forums relating to the “buoyancy” of different woods out of which paddles can be made. The general issue has been to make the most “buoyant” paddle. Generally, here’s the goal. In certain canoe strokes called in-water slice returns, you don’t lift...

[FONT="Arial"]Why does a sphere in a bathtub vortex spin - but a sphere in a faucet remain still ?

Hi, I understand how to get the electric field between two spheres of uniform charge, \vec{E} = \frac{\rho \vec{d}}{3 \epsilon_0} which is simplified because at a point \vec{r}, the vectors from each charge center combine to give the distance, \vec{d}, between centers (since \rho's can...

Homework Statement Two identical, uniform, frictionless spheres, each of weight W , rest in a rigid rectangular container as shown in the figure. Find, in terms of a ratio to W, the forces acting on the spheres due to the container surfaces and one another, if the line of centers of the...

Apostol 281, 4. Homework Statement Find the set of points (a,b,c) for which the spheres below intersect orthogonally. sphere 1: f(x,y,x):x^2+y^2+z^2=1 sphere 2: g(x,y,z):(x-a)^2+(y-b)^2+(z-c)^2=1 The Attempt at a Solution II know that the gradient vector, \nabla f, is normal...

Homework Statement Two arbitrarily thin concentric coplanar rings of radius a and 2a carry uniformly distributed charge density -Qe and \sqrt{27}Qe, respectively. Assuming that Z axis coincides with the rings' axes, and that the plane of the rings correspond to z=0, determine the location of...

Homework Statement Homework Equations potential, V = kq/r where k is 1/4 pi epsilon conservation of charge, sum of q = Q The Attempt at a Solution what i did is let q1 + q2 + q3 = 4*10^-4 then let V1 = V2 = V3 and solve for q3 but i end up getting q3 = 0.0002 which is...

Two insulating spheres have radii 0.3cm and 0.5cm, masses 0.1kg and 0.7kg and uniformly distributed charges of -2 \muC and 3 \muC. they are released when the distance from their center are 1m apart. How fast will each be moving when they collide. Firstly, what is the radius of the sphere use...

[b]1. The problem statement, all variables and given known data. A metal sphere with radius r_a is supported on an insulating stand at the center of a hollow, metal spherical shell with radius r_b. There is charge + q on the inner sphere and charge - q on the outer spherical shell. Take the...

Homework Statement What is the capacitance of the two metal spheres shown in the figure ? sphere one has 20nC of charge and the other has -20nC of charge. The change in voltage is 100V Homework Equations C=Q/(change in V) The Attempt at a Solution My question is how do yo...

Homework Statement In the figure, r1 = 5 and r2 = 7 cm. Before the conducting spheres are connected by the wire a charge of 5×10-7 C is placed on the smaller sphere while the larger sphere is uncharged. Calculate the charge on the smaller sphere after the wire is connected. Assume that the...

Homework Statement Four idential charged spheres are located at the corners of a square with side length 2a. The spheres are much smaller than the size of the square (r<<a) and each sphere has a mass m and carries the same charge -Q. a) What is the total electrostatic potential energy of...

Sphere A corries a net positive charge, and sphere B is nuetral. They are placed near each other on an insulated table. Sphere B is briefly touched with a wire that is grounded. What would happen to the neutral sphere? I know it woul become a neg charged but i don't know what happens when its...

Homework Statement Two charges concentric spheres have radii of 10.0 cm and 15.0 cm. The charge on the inner sphere is 4.00 x 10 ^-8 C, and that on the outer sphere is 2.00 x 10^-8 C. Find the electric field (a) at r = 12.0 cm and (b) at r = 20.0 cm.Homework Equations I know that this is a...

Homework Statement The left-hand sphere has a positive charge Q and the right-hand sphere has a negative charge -Q . Charge is distibuted uniformly over each of two spherical volumes with radius R. One sphere of charge is centered at the origin and the other at x=2R . Find the magnitude of...

Homework Statement Sphere A, with a positive charge is located close to another Sphere B, with positive charge. The relative size of the charges is such that the charge on Sphere A = 4 (Sphere B). Locate Point P between the two spheres where the force exerted by the field is zero. State the...

Is there a solution to finding out how exactly 2 spheres of non-equal mass and radius rebound after they collide? I know how to do it for equal mass and radius, finding the line of the collision, and then the components of velocity perpendicular to that line don't change. Does that hold true for...

An experiment is performed in deep space with two uniform spheres, one with mass 30.0 kg and the other with mass 109.0 kg. They have equal radii, r = 0.20 m. The spheres are released from rest with their centers a distance 42.0 m apart. They accelerate toward each other because of their mutual...

Homework Statement Two charged spheres, 10.0 cm apart, attract each other with a force of magnitude 3.0 x10^-6 N. What force results from each of the following changes, considered separately? An uncharged, identical sphere is touched to one of the spheres and is then taken far away...

We did a lab where we dropped three spheres into two different fluids, measured their velocities, and found drag coefficients. We were also asked some theory questions, and these are what I need help with. Spheres: 3.175 mm, 0.05 g Teflon 6.35 mm, 0.375 g, aluminum 12.7 mm, 8.36 g, steel...

I've notice that our eye balls are spheres, our Earth is a sphere and our sun is a sphere.. Now that makes me wonder. If our universe is a sphere, i already know scientist think so, but its still something to even think more into. Now this is the big part, triangles are important as well. Like a...

Homework Statement Two spheres are launched horizontally from a 1.1 m-high table. Sphere A is launched with an initial speed of 4.5 m/s. Sphere B is launched with an initial speed of 1.5 m/s. -What is the time for the sphere A to hit the floor? -What is the distance that sphere A...

Homework Statement Two concentric metal spheres have radii R1 =10cm and R2=10.5cm. The inner sphere has a charge of Q=5 nC spread uniformly over its surface, and the outer sphere has charge −Q spread uniformly over its surface. Calculate the total energy stored in the electric field...

Homework Statement A spherical potential conductor of radius R1 is charged to 20kV. When it is connected by a long, fine wire to a second sphere faraway. its potential drops to 12kV. What is the radius of the second sphere. Homework Equations V=kq/r The Attempt at a Solution So...

"Two small spheres of putty, A and B, of mass M and 3M, respectively, hang from the ceiling on strings of equal length l. Sphere A is drawn aside so that it is raised to a height h0 and then released. Sphere A collides with sphere B; they stick together and swing to a maximum height h equal to "...

I was looking at this link: http://en.wikipedia.org/wiki/File:Universe_Reference_Map_%28Location%29_001.jpeg" and wondered to myself why the asteroid belt just outside of Mars is a ring...as opposed to a sphere. Then I thought, why do all the planets seem to orbit the sun on a similar plane...

Charge is placed on two conducting spheres that are very far apart and connected by a long thin wire. The radius of the smaller sphere is 5 cm and that of the larger sphere is 12 cm. The electric field at the surface of the larger sphere is 830 kV/m. Find the surface charge density on each...

Homework Statement Two identical small metal spheres initially carry charges q_1 and q_2. When they're x=1.0m apart, they experience a 2.5N attractive force. Then they're brought together so charge moves from one to the other until they have the same net charge. They're again placed x=1.0m...

Homework Statement Let B be a solid box with length L, width W, and height H. Let S be the set of all points that are a distance at most 1 from some point of B. Express the volume of S in terms of L,W, and H. Homework Equations 4/3(pi)r The Attempt at a Solution I have gotten to...

1. How many apples can you put into a box in the following dimensions: Width: 1.25 meters Length: 3 meters Hight: 2.1 meters 2. Close packing of spheres 3. All I could find is the efficiency of close packing of spheres in face-centered cubic, which is 0.74048. Is there an...

Homework Statement Find the volume of the solid that lies inside both the spheres x^2+y^2+z^2=4 x^2+y^2+z^2+4x-2y+4z+5=0 Homework Equations none The Attempt at a Solution I completed the square on the 2nd equation to get (x+2)^2 + (y-1)^2 + (z+2)^2 = 4 So I have the two...

A hollow spherical conductor of radius 3.00 cm has 6.00 nC of charge distributed uniformly over its surface. (a)What is the electric potential at the center of the sphere(in volts)? (b) If the conductor is solid rather than hollow, what is the potential at the center of the sphere? I know...

...if the spheres are separated by a large distance - one with charge Q, the other with charge -Q - isn't the force between them just the same as the force between two oppositely charged point charges, since the electric field produced by one of the spheres "looks like" the field of a point...

Homework Statement A small metal sphere, carrying a net charge of q_1 = -2.60 \mu C, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q_2 = -7.70 \mu C and mass 1.40 g, is projected toward q_{1}. When the two spheres are 0.800 \rm m...

Homework Statement We're supposed to find the capacitance of a system of two conducting spheres, one of radius r_1 and charge Q, the other of radius r_2 and charge -Q, separated by a distance L (this is the distance between their centers) that's very large compared to either r_1 or r_2.Homework...

Homework Statement Two spheres, each radius R and carrying uniform charge densities +rho and -rho are placed so that they partially overlap. Call the vector from the positive center to the negative center dhat. Show that the field in the region of overlap is constant and find its value.Homework...

Homework Statement Figure 23-30 shows two nonconducting spherical shells fixed in place. Shell 1 has uniform surface charge density +6.0 µC/m2 on its outer surface and radius 3.0 cm. Shell 2 has uniform surface charge density -3.8 µC/m2 on its outer surface and radius 2.0 cm. The shell centers...

Homework Statement Find an equation of the plane that contains both the center and "south pole" of the sphere (x-3)^2+(y-2)^2+(z-3)^2 = 400 and is parallel to the line given in vector form by r(t) = [-43*t-82, -44*t+39, -84*t+94]. Write your answer in the form ax + by + cz = d Homework...

Homework Statement Two identical like-charged conductive spheres are placed very close to each other, the charges willl redistribute themselves on the sphere's surface with an effective center-to-center distance rc so as to approximately satisfy the Coulomb's law, F = ke q1 q2 / (rc)^2. Is the...

Homework Statement Problem: 2 spheres each one of them with a radius R and uniformly charged with ro+ and ro-, are situated in a way they superimpose partially ( see figure). Let be "d" the vector from the positive center to the negative center...

Suppose I have a bunch of spheres, all with the same radius r. Now, take one sphere and set it aside in R3. The question then, is, how many spheres can I place around this sphere such that at least one part of them is touching the central sphere? I've arrived at a very strict upper bound of...

Homework Statement Find the volume of the intersection of two spheres of radius 2, give that the center of each sphere lies on the surface of the other. The Attempt at a Solution I was trying to do this problem with volumes of revolution. I drew two circles, one with a center at -1, the...

Homework Statement Figure 21-36 shows four identical conducting spheres that are actually well separated from one another. Figure 21-36 Sphere W (with an initial charge of zero) is touched to sphere A and then they are separated. Next, sphere W is touched to sphere B (with an initial...

Whilst following my textbooks advice and "proving to myself that the inertia listed are true" I considered the Moment of Inertia of a hollow sphere by adding up infinitesimally thin rings: dI = y^2 dm = y^2 \sigma dS = y^2 \sigma 2\pi y dz = 2\pi y^3 \sigma dz This didn't work...

Homework Statement Two small, positively charged spheres have a combined charge of 14.0 × 10-5 C. If each sphere is repelled from the other by an electrostatic force of 0.9 N when the spheres are 1.7 m apart, what is the charge (in Coulombs) on the sphere with the smaller charge? Homework...

Homework Statement Consider two small conductive spheres in radius a and b located far from each other. In t=0 "a" sphere charged with Q and "b" sphere neutral. We connect the spheres by wire with resistance R. Find the charge on each sphere as a function of time. Homework Equations...