Thank you, I understand now. When you say
this means that all the ## v ## perpendicular to the ## k##-dimensional plane satisfy ## \overline{A} v = 0##.
Let A = (a_{ij}) be a k\times n matrix of rank k .
The k row vectors, a_i are linearly independent and span a k-dimensional plane in \mathbb{R}^n .
In "Geometry, Topology, and Physics" (Ex 5.5 about the Grassmann manifold), the author states that for a matrix g\in...
That's a mistake. I realize now that total speed + v_y is a constant, \sqrt{v_x^2 + v_y^2} + v_y = C . I will check out the link you posted, which is the same problem, and try to redo my math.
Right, the total speed should be v^2 , not v . Then the square root makes it v .
Seperating the equation for \dot y ,
\dot y \, = \, v \, (1 \, - \, \frac{\ddot y}{g\,sin\theta}) .
As t -> \infty , \ddot y -> 0 because the block will be moving straight down the incline. This can't be...
Homework Statement
I was looking at the problem discussed in the thread below.
https://www.physicsforums.com/showthread.php?t=502417
A block is initially kicked in the direction perpendicular to the downslope of the plane with initial speed V.
The problem asks for the speed of the block...
I have some questions. What does the "volume" the figure should scale by mean? In this case, aren't we concerned with the area? And how is the dimension of the figure not 2 if it's on paper (having a length and a width and being flat)? I'm not familiar with the terms Hausdorff and gasket either...
Sierpiń́ski's fractal and calculating the total "blank" space
Homework Statement
Connect the midpoints of the sides of an equilateral triangle to form 4 smaller
equilateral triangles. Leave the middle small triangle blank, but for each of the
other 3 small triangles, draw lines connecting the...
If a vertical spring is hanging and at rest, its net force = 0.
So that means F = 0 = -kx - mg, but doesn't the force of the spring oppose the force of gravity? How does this make sense? The force of gravity always points downward ( is negative), but -kx is negative when the spring is stretched...
Homework Statement
Whether or not the spring is vertical or not, assuming that the spring is ideal, is Fnet always equal to -kx?
Is it incorrect to write the sum of the forces of a vertical spring as Fnet = -kx - mg?
And does hooke's law account for the force of friction on a horizontal...
For the first problem, the fingers would point upwards if they represent the magnetic field. The thumb could point either clockwise or counter clockwise depending on whether the palm faces towards or away from you. I don't understand how this "conventional" way is supposed to work.
Okay. For first problem, thumb represents the direction of the magnetic field (pointing up). The fingers curl counter clockwise.
For the second problem with the bars, thumb again represents the magnetic field (pointing up). And again, the fingers curl counterclockwise, which represents the...
I guess I don't. I tried using F = I L B sin theta, but it didn't work out well.
There is another right hand rule mentioned in my book:
"The magnetic field 'lines' are actually circles whose centers are on the wire. The direction of these circles is determined by a variation of the right-hand...
Homework Statement
Attached below
Homework Equations
Emf = - \Delta\Phi / \Deltat
emf = vBl; motional emf
The Attempt at a Solution
In the two attached files, there are problems that ask for the direction of the induced current.
I understand that the induced current flows in the...
Okay. Thanks everyone. I understand the problem now. I have just one last question. Why does the current NOT flow through the wire past the grounded point?
When grounding occurs, does all the current/charges flow to the ground, leaving none for the part of the circuit past the grounded point...