Wedge Definition and 267 Threads

Hi PF! Does anyone know the conformal map that takes a wedge of some interior angle ##\alpha## into a half plane? I'm not talking about the potential flow, just the mapping for the shape. Thanks!

Homework Statement If a beam with square cross-section and very low density is placed in water, it will turn one pair of its long opposite faces horizontal. This orientation, however, becomes unstable as we increase its density. Find the critical density when this transition occurs. The density...

Homework Statement Homework Equations - The Attempt at a Solution Flux on opposite sides = 0 The answer is (E) , right ?

Homework Statement A block of mass m is placed on a rough wedge inclined at an angle α to the horizontal, a distance d up the slope from the bottom of the wedge. The coefficient of kinetic friction between the block and wedge is given by µ_0x/d, where x is the distance down the slope from the...

Homework Statement On the axis of an infinite wedge that moves with velocity ##\vec{V}##, the body decays with the formation of a lot of splinters that fly away uniformly in all directions with velocity ##\vec{u}##. What should be the angle of the wedge that half of the splinters fall on its...

Hello! The cohomology ring on an M-dim manifold is defined as ##H^*(M)=\oplus_{r=1}^mH^r(M)## and the product on ##H^*## is provided by the wedge product between cohomology classes i.e. ## [a]## ##\wedge## ##[c]## ##= [a \wedge c]##, where ##[a]\in H^r(M)##, ##[c]\in H^p(M)## and ##[a \wedge...

Homework Statement A block of mass 0.5Kg rests on the inclined surface of a wedge of mass 2kg. The wedge is acted on by a horizontal force that slides on a frictionless surface. If the coefficient of static friction between the wedge and the block is 0.8 and the angle is 35 degrees, find the...

Hello! I am reading something about differential geometry and I have that for a manifold M and a point ##p \in M## we denote ##\Omega_p^r(M)## the vector space of r-forms at p. Then they say that any ##\omega \in \Omega_p^r(M)## can be expanded in terms of wedge products of one-forms at p i.e...

Homework Statement Two rectangular pieces of plane glass 11.0 cm long are laid upon the other on a table. At one end they are in contact, at the other end they are separated by a piece of paper, which forms a thin wedge of air. The plates are illuminated at normal incidence by 510 nm light...

Homework Statement There is no friction between any surfaces mass is known. Find acceleration of the blocks. Homework Equations F=ma The Attempt at a Solution I'm almost certian Amx=g sin θ AMy=0

I don't understand the motion of an accelerating wedge and a block. I'd really appreciate if you make me understand the motion in both an inertial and a non inertial reference frame. Here's a figure I have made, a0 is the acceleration on the wedge with respect to an inertial frame, towards right.

Hello! I was trying to show that the wedge product of 2 one-forms is a 2-form. So we have ## (A \wedge B)_{\mu \nu} = A_\mu B_\nu - A_\nu B_\mu ##. So to show that this is a (0,2) tensor, we need to show that ##(A \wedge B)_{\mu' \nu'} = \Lambda_{\mu'}^\mu \Lambda_{\nu'}^\nu (A \wedge B)_{\mu...

Homework Statement In the given figure, a wedge of mass 2m is lying at rest on a horizontal surface. The wedge has a cavity which is the portion of a sphere of radius R. A small sphere of mass m is released from the top edge of the cavity to slide down. All surfaces are smooth.Prove the maximum...

I would be very grateful for help with deriving the following equation... "A smooth fixed plane is inclined at 30 degrees to the horizontal. A wedge of mass M and angle 30 degrees is held on the surface so that its upper face is horizontal, and a particle of mass m rests on this face. The...

im stuck on question 8. the equation i got for the wedge is .6R -.5S=ma r stands for relative force of the particle s stands for relative force of the wedge . i got the equation 4mg-R=5m(.6a) for the particle where a stands for acceleration of the wedge. does anyone know where to go from here...

Is there a set of relationships for the wedge product of basis vectors as there are for the dot product and the cross product? i.e. e1*e1 = 1 e1*e2 = 0 e1 x e2 = e3

Q4 A wedge of mass 11 kg is held on the ground with its base horizontal and smooth faces inclined at 30° and 45° respectively to the horizontal. A 5 kg mass on the face inclined at 30° is connected to a 7 kg mass on the other face by a light inextensible string which passes over a smooth light...

Homework Statement What is the relationship between " acceleration of block with respect to wedge" and "acceleration of wedge " ? Homework EquationsThe Attempt at a Solution If the wedge moves by x units , then the string gets loosened/shortened at three places . The top two are x units...

Suppose we are given this definition of the wedge product for two one-forms in the component notation: $$(A \wedge B)_{\mu\nu}=2A_{[\mu}B_{\nu]}=A_{\mu}B_{\nu}-A_{\nu}B_{\mu}$$ Now how can we show the switch from tensor products to wedge product below...

Homework Statement A block rests on a wedge inclined at angle ##\theta##. The coefficient of friction between the block and plane is ##\mu##. The wedge is given a horizontal acceleration ##a##. Assuming that ##\tan \theta > \mu##, find the minimum acceleration from the block to remain on the...

Homework Statement [/B]Mass m lies on a Weighing scale which is on Wagon M. the inclined surface is smooth, between m and M there is enough friction to prevent m from moving. 1) What does the weigh show? 2) What is the minimum coefficient of friction between m and M to prevent slipping? 3)...

↪ mentor note: thread moved to h/w forum so template is missing ↩ Hi, I have recently been learning relative acceleration and I have a bit of trouble with basics; In a problem with a smooth wedge on a smooth plane, a mass is gently placed on the wedge and I've been asked to find the...

My son and I were arguing about whether or not a particular noodle maker called a Spaetzle Maker is a lever. I say it is, and he says it isn't. Basically, one uses it to extrude raw noodle batter (eggs and semolina flour) over a pot of boiling water. It looks like a flat cheese grater with a...

Is the reason the block slides down the plane that the resultant of the normal force N and mg acts along the plane causing it to slide or is it because of the component of mg parallel to the plane acting on the box i.e. mgsin(theta)

In the adjoining figure if acceleration of M with respect to ground is a, then A) Acceleration of m with respect to M is a B) Acceleration of m with respect to ground is asin(α/2) C) Acceleration of m with respect to ground is a D) Acceleration of m with respect to ground is atan(α) The 2nd...

A block of mass m rests on a frictionless wedge that has an inclination of θ and mass M. Find the acceleration of the wedge M to the right such that the block m remains stationary relative to the wedge 1. Homework Statement a, \theta , M, mHomework EquationsThe Attempt at a Solution Draw a...

I am reading Barrett O'Neil's book: Elementary Differential Geometry ... I need help with some more issues/problems with the example on wedge products of differential forms in O'Neill's text on page 31 in Section 1.6 ..The example reads as follows: In my working of the example above ... trying...

I am reading Barrett O'Neil's book: Elementary Differential Geometry ... I need help with fully understanding the example on wedge products of differential forms in O'Neill's text on page 31 in Section 1.6 ..The example reads as follows: I do not follow the computations in this example ... can...

This isn't actually a problem. It is a doubt which I have about wedges according to Newton's Laws Consider a friction less wedge, of mass 'M', inclined at angle θ, placed on a smooth horizontal surface, on which a block of mass 'm' is placed. The block exerts some normal force perpendicular to...

Homework Statement A block of mass m is placed on a triangular block of mass M, which in turn is placed on a horizontal surface as shown. Assume frictionless surfaces. Find the speed of triangular block when the small block reaches the bottom end, Homework EquationsThe Attempt at a Solution...

Homework Statement A block of mass m is placed on a triangular block of mass M which in turn is placed on a horizontal surface. Assuming friction less surfaces find the velocity of the triangular block when the smaller block reaches the bottom end.The angle of inclination of the plane is...

Homework Statement In the arrangement shown in fig 1.24, the masses of the bar, m, and of the wedge, M, and also the wedge angle, ##\alpha##, are known. The masses of the thread and pulley are negligible, and friction is absent. Find the acceleration of the wedge M. The Attempt at a...

Homework Statement [/B] For the situation shown in the diagram, the block of mass m remains in place on the sloping front of the accelerating wedge, even though that sloping front is frictionless. Given these values, M = 20.0 kg, m = 4.00 kg, and theta= 34.0, calculate the net force acting on...

Homework Statement A block of mass m is kept on a smooth wedge of angle α and mass M which is in turn kept on a smooth floor. When the system is released from rest, calculate the force exerted by block on the wedge. Homework Equations None. The Attempt at a Solution Let the block a have a...

Homework Statement [/B] In the attached picture, the rope is being pulled by a constant force T. All the surfaces are smooth. The pulley and the rope are massless and frictionless. Find the acceleration of the wedge.(use g=10ms-2) Homework EquationsThe Attempt at a Solution The normal force...

Part (a) is easy to do by setting up a triple integral, but for part (b), I was a bit confused by the diagram provided by the solutions manual: Why is the spherical wedge (shaded) graphed on the z-y axis? In the most general case, shouldn't the two lines that form angle $\phi_1$ and $\phi_2$...

Homework Statement A man is standing on a small wedge that is sliding down a frictionless large wedge (base on the ground - horizontal) with angle 60. I don't have a picture so I'll just say that the surface of the smaller wedge is parallel to the ground. It has a weighing machine on it and the...

Homework Statement A greasy spud is launched off of the top of an infinitely large frictionless wedge. The angle that the wedge slopes down at is 30 degrees. Find the launch angle that maximizes the horizontal range of the spud.Homework Equations [/B] x = x0 + vxt + (1/2)at2 The Attempt at a...

how the wedge is connected with highlighted string?

Homework Statement A small block with mass m is moving towards a stationary slope with velocity v, angle θ and height h, suppose all surfaces are frictionless. Suppose the slope has mass M and it is able to move freely on the ground, what is the minimum initial speed for the block to be able...

Homework Statement :There is a wedge of mass kept on smooth surface. M and block of mass m is sliding in the depression of the wedge.And there is wall in left of the wedge.At which instant velocity of the wedge will be maximum?(surface of contact between wedge and block is smooth) [/B]...

Homework Statement :block slides on smooth triangular wedge kept on smooth floor.Find velocity of wedge when block reaches bottom. (image is attached) Homework Equations :Let the velocity of the triangular wedge be V.And v be the velocity of block m. [/B] applying conservation of linear...

Hi, I am studying Sean Carroll's "Lecture notes on General Relativity". In the second chapter he identifies the volume element d^nx on an n-dimensional manifold with dx^0\wedge\ldots\wedge dx^{n-1}. He then claims that this wedge product should be interpreted as a coordinate dependent object...

Suppose we want to find the constraint equation relating the acceleration of a block on a wedge to the acceleration of the wedge (see attached images). We can write: $$h - y = (x - X) \tan{\theta}$$ What if ##X## was measured to the centre of mass of the wedge for instance? Wouldn't the correct...

I want to learn clifford and grassmannian algebras. I need to be taken from mostly a beginners point, and from a place of matrices only in general terms, and years since use. ANybody up for it? I am a software developer, so not at the bottom of any learning curve.

I guess the title really says it all. I'm reading "space-time algebra" by David Hestenes, and he explains the properties of the wedge product (area of parallelogram, antisymmetric, etc.) and it sounds just like the cross product to me. He then says clearly however that this is not to be...

Homework Statement Given: The friction between the block with mass 11kg and the wedge with mass 22kg is 0.48. The surface between the wedge with mass 22kg and the horizontal plane is smooth (without friction). The [A][/g] = 9.8m/[/2]. A Block is released on the incline plane (top side of...

Homework Statement Given: The friction between the block with mass 6 kg and the wedge with mass 18 kg is 0.27 . The surface between the wedge with mass 18 kg and the horizontal plane is smooth (without friction). The acceleration of gravity is 9.8 m/s^ 2. A block is released on the inclined...

Homework Statement The crate shown is held against wedge B by a spring. The spring is 96.0% of its original uncompressed lengthl=2.75m, and the spring constant is given ask=1650N/m. The coefficient of static friction at all contacting surfaces is μs=0.150. The mass of the crate is m=22.0kg ...

Hi, kind of stuck with how to calculate frictional forces in a particular problem: I am modeling yarn using mass spring system, zero dimensional nodes. Question is, what to do when a yarn can get stuck between a wedge? How to calculate friction force vector, surface reaction and so? Since a...