Wedge Definition and 267 Threads

If I want to take the wedge product of $$\alpha = a_i\theta^i $$ and $$\beta = b_j\theta^j$$ I get after applying antisymmetrization,$$ \alpha \Lambda \beta = \frac{1}{2}(a_ib_j - a_jb_i)\theta^i\theta^j$$ My question is it seems to me that antisymmetrization technique doesn't apply to the...

Homework Statement Given that two masses are connected by a light string over a pulley.They are initial at rest.Suppose all the surfaces are smooth.Find the resultant acceleration of the system Homework Equations F=ma Fpseudo=-ma The Attempt at a Solution Suppose I let the resultant a be A,and...

Homework Statement Consider a wedge of mass m whose upper surface is a quarter circle and is smooth. The lower part is rough. A small block of same mass is kept at the topmost position and the initial position is shown in figure. The block slides down the wedge. Find the minimum value of...

Hello, Can anyone give me a heads up for a lens manufacturer that sells 12.7mm or 13mm dia wedge prisms? It seems all my sources only have 25.4mm. Thanks in advance, Mike

Homework Statement please refer to the question, since at the positon Q , the lighr ray is blocked by the substance , (as in the diagram) , why the bright fringe is seen at Q , In my opinion , it it should be a dark fringe. whereas at P , the lighr ray is not blocked , so it should be bright...

Homework Statement i can't understand why the optical path diffrence is 2nt+0.5λ. why is it so? the 0.5λ is due to the path difference change of 180 degree of when it is reflected lower ray when it is reflected from the lower glass surface... why there's also phase change of 2nt. since both...

Homework Statement Consider a fixed wedge, whose part is a quarter circle of radius as shown. A small block of mass 'm' slides down the wedge and leaves horizontally from a height 'h' as shown.The coefficient of friction between wedge and block is 'μ_{k}' . Compute the value of in centimetres...

Homework Statement A thin rod of mass m = 1 kg and length l=1m is placed along the hypotenuse side of a wedge lying on a frictionless floor having mass M =5kg and angle 60° . At t= 0 the system is released from rest. Both the objects are free to move .Find the speed of the wedge when the rod...

Homework Statement I think that the image is clear. There isn't friction, not the material point with wedge, not the wedge with the floor. At time t=0 the material point start to move, I need to find the final speed of the two objects at time t\rightarrow\infty. Homework Equations...

Homework Statement A 45 degree wedge is pushed along a table with constant acceleration A. A block of mass m slides without friction on the wedge. Find the block's acceleration. Gravity is directed down. Homework Equations Constraint Equation...

Homework Statement This is problem 2.17 from Kleppner and Kolenkow, 2nd edition. It is the first problem involving friction, and I want to check my reasoning. A block rests on a wedge on a horizontal surface. The coefficient of friction of the block on the wedge is ##\mu##. Gravity is directed...

Homework Statement This is problem 2.11 from Kleppner and Kolenkow, 2nd edition. I have completed the problem but I'm not 100% sure I did it right and would like to check my understanding. A ##45## degree wedge is pushed along a table with constant acceleration ##A##. A block of mass ##m##...

Homework Statement Find the displacement of wedge when the smaller block reaches the bottom of wedge. Homework Equations See attached diagram. The Attempt at a Solution For the smaller block, N = mg \cos \theta \\ mg \sin \theta = m v \dfrac{dv}{dx} For wedge N \sin...

Hi, All: Just curious if anyone knows of any online or otherwise software to help compute the wedge of forms, or maybe some method to help simplify. Not about laziness; I don't have that much experience, and I want to double check; I have around 30 terms ( many of which may cancel out) , and...

Homework Statement The height of the slope shown in the figure is 30 cm, and its base is 40 cm. A solid cylinder of uniform density, which has the same mass as the slope, rolls down along the slope without slipping. What is the least value of the coefficient of friction between the inclined...

Homework Statement We have a wedge and at the top of it a block(consider it dimensionless)and the whole system initially is at rest.Given the gravitational acceleration g, the angle φ of the inclined plane,the mass m of the block,the mass M of the wedge,the coefficient of friction fs between...

Homework Statement A wedge of mass M rests on a horizontal table. A block of mass m rests on the wedge. http://imgur.com/cS02MvM (a) What horizontal acceleration, a, must M have relative to the table to keep the block stationary relative to the wedge, assuming no friction? (b) What...

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Homework Statement A block of mass 0.80 kg rests on the inclined surface of a wedge of mass 2.0 kg. The wedge is acted on by a horizontal force F and slides on a frictionless surface. If the coefficient of static friction between the wedge and the block is µs = 0.40, and the angle of the...

Hi guys, Would you please help me by telling me the meaning of the wedge symbol in the equation attached? I=inertia. ω=angular velocity. Since the inertia is constant, then why do we need to add the second term? I mean why isn't the differentiation of (Iω) simply equal to (Iω')?

Homework Statement A block A of mass m is placed over a wedge B of same mass m. Assuming all surface to be smooth. The displacement of block A is 1 sec if the system is released from rest is : Homework Equations The Attempt at a Solution i have made fbds and have the relations-...

Homework Statement A 45 degree wedge is pushed along a table with constant acceleration A. A block of mass m slides without friction on the wedge. Find its acceleration. (Gravity is directed downwards.) Homework Equations The Attempt at a Solution Let the acceleration of block...

Hi, I'm trying to get my head around the Hodge dual and how it exactly works. In the book "Gauge Fields, Knots and Gravity" by John Baez and Javier P. Muniain they define: \begin{equation} \omega \wedge * \mu = \langle \omega , \mu \rangle \mathrm{vol} \end{equation} for two p-forms...

Homework Statement This is a 2 part question. A block of mass m rests on a frictionless wedge that has an inclination of theta and mass M. a) Find the acceleration of the wedge M to the right such that the block m remains stationary relative to the wedge. c) You now find out that a force...

I'm interested in calculating the resistance of an object using the formula: R=ρ (L/(T*W)) where L is the length and T*W is the cross sectional area. My object is however, a wedge, so I do not know exactly how to calculate the resistance without doing an integral...

Homework Statement (context: I'm studying for a test, and this is a question from a past exam paper.) "A wedge of mass M with angle \phi is free to slide on a frictionless horizontal table. A solid ball of radius a and mass m is placed on the slope of the wedge. The contact between the ball...

Homework Statement In the figure a block of mass 'm' is placed on a wedge of mass M. The wedge is subject to a horizontal force 'F' and slides on a friction less surface. The coefficient of static friction between the block and wedge is μs. Find the range of values of 'F' for which the block...

Consider ##\vec{a}=\begin{bmatrix} a_1 \\ a_2 \\ a_3 \end{bmatrix}## and ##\vec{b}=\begin{bmatrix} b_1 \\ b_2 \\ b_3 \end{bmatrix}##. Is any part of the following NOT true? $$\vec{a}\wedge\vec{b}=\frac{1}{2}(\vec{a}\otimes\vec{b}-\vec{b}\otimes\vec{a}) = \frac{1}{2}\begin{bmatrix} 0 &...

Homework Statement Block B of mass 10 kg is initially at rest as shown on the upper surface of a 20-kg wedge A which is supported by a horizontal surface. A 2-kg block C is connected to block B by a cord which passes over a pulley of negligible mass. Using computational software and denoting...

Homework Statement Homework Equations Conservation of energy The Attempt at a Solution All I'm thinking for this problem is to just use conservation of energy, since the cube is frictionless and it is just sliding down the wedge, aren't the only forces that are at play is just...

Homework Statement The question is: Let \phi: \mathbb{R}^n\rightarrow\mathbb{R}^n be a C^1 map and let y=\phi(x) be the change of variables. Show that dy_1\wedge...\wedge dy_n=(detD\phi(x))\cdotdx_1\wedge...\wedgedx_n. Homework Equations n/a The Attempt at a Solution Take a look at here and...

The question is: Let $\phi：\mathbb{R}^n\rightarrow\mathbb{R}^n$ be a $C^1$ map and let $y=\phi(x)$ be the change of variables. Show that d$y_1\wedge...\wedge $d$y_n$=(detD$\phi(x)$)$\cdot$d$x_1\wedge...\wedge$d$x_n$.Take a look at here and the answer given by Michael Albanese: differential...

Homework Statement A symmetric wedge of depth h and width A is filled to the brim with water of mass m, where acceleraton due to gravity is g. What is the potential energy of the water with respect to the base of the wedge? Homework Equations E = mgh The Attempt at a Solution E =...

Hi guys. I saw this in one of my Engineering Design slides about embodiment designs and saw these slides using uniform stresses as an example and had a hard time figuring out how is this structure supposed to ensure uniform stress. Shown in here is taken from the slides I was...

On a smooth triangulation of a manifold differential forms can be viewed as real cochains by integration. The wedge product of two forms gives another real cochain. So does their cup product. - are they cohomologous? - Is there a limiting process that relates them?

Homework Statement We have a body of mass M placed in a kind of sledge like on the picture: Coefficient of fristion between the mass and the sledge is zero, but the coefficient of friction between the wedge and the sledge is μ. Angle of the wedge is α. The sledge is massles. The slegde is...

Hi, I am currently reading about differential forms in "Introduction to Smooth Manifolds" by J. M. Lee, and I was wondering exactly how you define the wedge product on the exterior algebra \Lambda^*(V) = \oplus_{k=0}^n\Lambda^k(V) of a vector space V. I understand how the wedge product is...

Homework Statement If a block is let go from the top of a wedge elevated at a certain angle and slides down will it reach the bottom at the same time as if the wedge was moving and then we let the block slide? so neglect friction and air resistance and basically just let the block slide down...

Homework Statement http://imageshack.us/a/img594/4821/fileeq.jpg So, the problem is to find the minimum acceleration required to keep the block on the ramp, when the ramp is being pushed at an angle to the horizontal (so going diagonally) I know that the coefficient of static friction...

sry for typo..it should be acceleration Homework Statement A block m slides down from a frictionless inclined surface (theta = 45) of a wedge, mass m, which is on a horizontal plane with coefficient of friction u. Prove that the wedge moves to the right with acceleration equal to...

A wedge with mass M rests on a frictionless horizontal table top. A block with mass m is placed on the wedge. There is no friction between the block and the wedge. The system is released from rest. Figure http://tinyurl.com/9zcf7uq 1. Calculate the acceleration of the wedge. Express...

I'm having problems in my differential geometry class. Does anyone know of a good tutorial or set of notes? The 1-form, 2-form, 3-form stuff is confusing and so is the wedge product. Anyways, here's the problem. After some algebra I arrived at my answer, but I'm unsure of how to incorporate...

Homework Statement The problem is attached in the picture. The Attempt at a Solution What bothers me is that they say the wedge is bounded by x + z = a. Doesn't this imply that the calculated volume should only be half of what is written in the answers? I'm aware that the plane x +...

Homework Statement Two masses m1 and m2 (m1 > m2) are connected over a wedge shaped block. Assuming both inclined planes are frictionless along with frictionless and massless pulley, calculate an expression for the acceleration of the system. Here's what it sort of looks like...

Is the following the definition of wedge product in tensor notation? Let A \equiv A_i be a matrix one form. Then A \wedge A \wedge A \wedge A \wedge A = \epsilon^{abcde}A_a A_b A_c A_d A_e ? in 5 dimensions. This question is in reference to the winding number of maps.

Homework Statement The situation is indicated in the diagram below. Block m is at rest, and the block M has an initial velocity upward. Need to find the Lagrangian of this system, and then the Euler-Lagrange equations. The Attempt at a Solution This is the Lagrange that I came up with...

Homework Statement Monochromatic beam of incident light on the surface of the glass wedge, whose upper edge is inclined at an angle of γ = 0.05 ° from the base. In reflected light observe a number of interference fringes, the distance between adjacent dark streaks is △X = 0.21 mm. Calculate...

Homework Statement Find the volume of the enclosed by the surfaces z=qx z=0 and x²+y²=2ax Homework Equations This is meant to be done with calculus but can verify my answer with simple geometry - should be \pi a^3q The Attempt at a Solution So the top of the wedge will be when x=2a...

Homework Statement Find the solution of Laplace's equation for \phi(r,\theta) in the circular sector 0 < r < 1; 0 < \theta < \alpha with the boundary conditions \phi(r,0) = f(r), \phi(r,\alpha) = 0, \phi(1,\theta) = 0. (also, implicitly, the solution is bounded at r = 0). Use two different...

Hi, I need help with following problem: I need to solve scattering of the planewave incident on the metal wedge. Let's say that wave travels in $z$ direction. Angle of wedge is $\alpha$, it is formed in $x-z$ plane. Wedge is infinite in $y$ direction (metal corner, if $\alpha = \pi / 2$, it will...