The Synchronized Position Hold Engage and Reorient Experimental Satellite (SPHERES) are a series of miniaturized satellites developed by MIT's Space Systems Laboratory for NASA and US Military, to be used as a low-risk, extensible test bed for the development of metrology, formation flight, rendezvous, docking and autonomy algorithms that are critical for future space missions that use distributed spacecraft architecture, such as Terrestrial Planet Finder and Orbital Express.Each SPHERES satellite is an 18-sided polyhedron, with a mass of about 4.1 kg and a diameter of about 21 cm. They can be used in the International Space Station as well as in ground-based laboratories, but not in the vacuum of space. The battery-powered, self-contained units can operate semi-autonomously, using CO2-based cold-gas thrusters for movement and a series of ultrasonic beacons for orientation. The satellites can communicate with each other and with a control station wirelessly. The built-in features of the satellites can be extended using an expansion port.From 2006, three SPHERES units are being used in the International Space Station for a variety of experiments. The SPHERES Guest Scientist Program allow scientists to conduct new science experiments using SPHERES units, and the Zero Robotics Program allow students to participate in annual competitions that involve developing software to control SPHERES units.The SPHERES program is expected to continue until 2017, and possibly further.The SPHERES project lead to a newer project called Astrobee.
Homework Statement
In deep space, three spherical masses are held in fixed positions (by rods light compared to the masses) at three corners of a square of side length sqrt(18) m as shown. The masses of the three spheres are m1 = m3 = 1.76×10^9 kg, and m2 = 2.75×10^9 kg. A relatively small...
Homework Statement
Two small spheres, each of mass 4.00g, are suspended by light strings 15cm in length. A uniform electric field is applied in the x direction. The spheres have charges equal to -7*10^-8 C and +7*10^-8 C. Determine the electric field that enables the spheres to be in...
Hey guys! This problem has been perplexing me for ages, and everything I do to try to solve it doesn't seem to work. So I was wondering if you guys could help point me in the right direction. Anyway:
Homework Statement
The figure below shows six concentric conducting spheres, a, b, c, d, e...
Homework Statement
The volume of a spherical balloon is increasing at a rate of 4m^3/min. How fast is the surface area increasing when the radius is three meters?
Homework Equations
V=4/3piR^3
A=4piR^2
The Attempt at a Solution
V=s.a.*R/3
dv/dt=d(s.a.R/3)/dt...
Homework Statement
Find the volume of a sphere bounded above by the sphere x^2 + y^2 + z^2 = 1 and below by the sphere X^2 + y^2 + (z-1)^2 = 1.
Homework Equations
The Attempt at a Solution
In class we have been doing double integrals with rectangular and polar, but I kinda feel...
X and Y are two identical conducting spheres separated by a distance d. X has a charge of +6µC and Y has a charge of -2µC. The electric force between them is +F (i.e. attractive). The spheres are touched together and are then returned to their original separation d. What is the new value of the...
Homework Statement
Two spheres of mass M1 and M2 are arranged one above the other as shown. They are separated by a fraction of a mm. They are released from rest and allowed to fall to the ground, a distance h = 6.5 m below. Mass M2 collides elastically with the ground and then elastically...
Homework Statement
Two spheres have equal radius R = 14m and mass m = 1420kg. Their centers are separated a distance 4R. The spheres are released from rest. What will be their speed when they collide? Answer in m/s.
Homework Equations
U(g) = -G*m1*m2/R
The Attempt at a Solution
We...
Homework Statement
A hollow sphere of radius r_1 is placed at the centre of a larger hollow sphere of radius r_2.
Both spheres have a uniformly distributed total charge of +q
Find the preassure p(r_2 , q) which acts on the outer sphere.
Homework Equations
\oint\textbf{E.n}dS = 4\pi k Q
p =...
Homework Statement
Two spheres, each of radius R and carrying uniform charge densities +\rho
and -\rho, respectively, are placed so that they partially overlap.
Call the vector from the positive centre to the negative centre \vec{d}. Show
that the field in the region of overlap is constant...
Two metal spheres are connected by a long wire with a switch. The radius of the larger sphere (B) is b= 0.20 m and the radius of the smaller sphere (A) is a= 0.080 m. Initially the switch is open and both spheres have zero charge. Then charge Q0 = 1.0 μC is placed on the larger sphere.
B)...
Hello,
I am constructing a MATLAB script to tightly pack an arbitrary given geometry with spheres of a predefined radius. Coordinates of the vertices of the geometry (a polyhedral model) are given; I am thereby developing an algorithm to plot/track all spheres that fit within the boundaries...
Homework Statement
I have found this problem in Feynman Lectures on Physics vol. 2:
Two equal conducting spheres, one with the total charge of +Q and the other with a total charge of -Q, are placed at some distance from each other. What is the force between them?
Homework Equations...
Homework Statement
I would really appreciate help understanding how the answer is reached in this question:
Setting the scene: three metal sphere's are in fixed positions R (+Q), S (+2Q) and T (+3Q):
+Q +2Q +3Q...
I thought this would be a basic physics problem, but I'm not getting the right answer, here's the problem:
There are two identical small metal spheres with charges 27.5 μC and −19.119 μC. The distance between them is 8 cm. The spheres are placed in contact then set at their original...
Homework Statement
2 conducting spheres of radius r=0.5cm are connected by a long thin piece of conducting wire of length L=2metres. A charge of 60 micro Coulombs is put onto one of the spheres, find the tension T in the wire. Assume the charge is evenly distributed along the surface of the...
Hello all!
I hope this question has not been raised previously, so that I wouldn't exhaust your time in vain, and if it had been, please forgive me, though extensive combing of the web yielded largely nothing.
My problem concerns something extremely trivial: the derivation of the electric...
Homework Statement
Two small spheres, each of mass 2.00 g, are suspended by
light strings 10.0 cm in length. A uniform
electric field is applied in the x direction. The spheres
have charges equal to -5.00 x 10^-8 C and +5.00 x
10^-8 C. Determine the electric field that enables the
spheres to...
Suppose you have two similar particles that have gone through similar half life periods. They each have been reduced to practically infinitely small spheres. Within each sphere is a hollow space. They are both touching during a process in which they are constantly decaying, with two small...
Homework Statement
A conducting sphere of radius, R = 5.5 cm with an excess charge of Q = -35.5 nC is surrounded by a concentric, conducting, spherical shell of inner radius, Rin = 9.5 cm and outer radius, Rout = 11.5 cm that carries an excess charge of q = -13.0 nC...
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...
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
Given the figure below and knowing that the coefficient of restitution is e=0.8 find the final velocities of the spheres.
Homework Equations
m1v1 + m2v2 = m1v1' + m2v2'
e = v2' - v1'/v1 - v2
The Attempt at a Solution
I have tried this a bunch of different ways...
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
Consider two concentric conducting spheres. The outer sphere is hollow and initially has a charge Q1 = -6Q deposited on it. The inner sphere is solid and has a charge Q2 = +1Q on it.
(a) How much charge is on the outer surface?
How much charge is on the inner surface...
Homework Statement
A solid metal sphere has a radius of 10.0 cm and a concentric metal sphere has a radius 10.5 cm. The solid sphere has a charge 5.00 nC. (a) Estimate the energy stored in the electric field in the region between the sphere. Hint: you can treat the pheres essentially as...
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...
Hi. I am having trouble finding sources to the information that i am seeking (sometimes you find really good phyisics/chemistry books through google).
Nm particles of iron 100 nm has the same melting point as iron in bulk. Is there any chemistry books online that shows why even small...
Hi. I am having trouble finding sources to the information that i am seeking (sometimes you find really good phyisics/chemistry books through google).
Nm particles of iron 100 nm has the same melting point as iron in bulk. Is there any chemistry books online that shows why even small...
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...