Wedge Definition and 267 Threads

There are two ways to assign a ##(n-1)##-dimensional distribution on the tangent bundle built over a differentiable manifold of dimension ##n##. Namely it can be assigned either via the wedge product of ##(n-1)## independent vector fields or via a covector field (1-form). Which is the...

So i have been solving problems of Newton's Laws of motion and this thing has been quite conflicting for me. I wont complicate my question. I just need one answer. What is the absolute value of normal force on a block of mass M on a wedge? I know it seems a pretty dull question but here me...

This question is from the book Kleppner and Kolenkow Q 3.8: ___________________________________ My attempt is posted here: ___________________________________ The value of a(minimum) that I'm getting is different from the official solution. The official solution is posted here...

Hello everyone, we have recently covered electrodynamics in differential forms. I managed to get familiar with most of the concepts, but one thing came just up where I can't figure out what's going wrong. I tried computing the 3-form ##dx^i \wedge dx^j \wedge dx^k## by hand. However, even after...

My textbook derives the condition for bright and dark fringes on an air wedge by assuming that the reflected and refracted rays have a path difference of pi. Hence the conditions for bright and dark fringes end up being the opposite of what is expected. However I did not really understand the...

An air wedge is illuminated with light and an interference pattern is produced. What will happen to the interference pattern when the air wedge is filled with water? The answer given at the back of the book is that the fringe spacing of the interference pattern will increase, however my...

I have seen a few posts on this subject before, but none have really answered my question. For clarity, I will refer to the 1st example as a wedge, and the second as a ramp (although both are of course inclined planes). With both examples that I outline below, we will assume no friction, and a...

Is my answer correct? And if not, why?

So, when the mass reached the peak, its horizontal velocity will be the same as the wedge's. Using conservation of momentum : $$ mu = 2mv$$ $$v = \frac u 2$$ With v is the final velocity for both objects. Now, what we need is the acceleration of the wedge, which we can find by using Newton's...

My solution for part b) (i.e. minimum acceleration) in case it's needed: https://ibb.co/D8CCQMM I'm confused about part c. 1) Since the block will travel up the incline if a > a_max, acos(theta) is up the incline. But based on my attached FBD diagram, acos(theta) should be down the incline...

I have drawn a fbd and the logic I think is that at rest the block moves down the wedge but when a force P is applied vertical force becomes zero and the horizontal force ##F_N\sin \beta## = P?

Intuitively, the Rindler wedge is timelike in Minkowski coordinates and an object crossing the horizon enters a spacelike region. This seems at odds with my understanding of the light cone where the 2 regions are reversed. I think this may be related to the signature of the metric but I'm not...

Let ##\omega## be 2-form and ##\tau## 1-form on ##R^3## If X,Y,Z are vector fields on a manifold,find a formula for ##(\omega\bigwedge\tau)(X,Y,Z)## in terms of the values of ##\omega## and ##\tau ## on the vector fields X,Y,Z. I have known how to deal with only one vector field.But there are...

I think on top of the wedge the KE of both the wedge and block will be same but this fact doesn't take me anywhere. The base length of the wedge is not given. Maybe that would have helped.

Clearly if ##F = 0## and ##\tan\theta > \mu_s##, then using the above equations for ##f_s## and ##n##, we get ##f_s > \mu_s n## so the block will slip. However, it seems that as long as the force ##F## is directed to the right with a certain minimum magnitude, namely ##\frac{\tan\theta -...

So assume we have a wedge traveling at a constant V horizontally, that is braced so it CANNOT move vertically. Ignore air and friction. See picture. It hits a stationary tennis ball and due to the angle, there is a net force on the ball as shown. The energy should come from the kinetic...

A block slides on a frictionless wedge which rests on a smooth horizontal plane. There are two constraints in this system. One that the wedge can only move horizontally and another that the block must remain in contact with the wedge. We want to find the virtual displacements for the two block...

So I’m having trouble with relative motion with moving inclines and I literally can’t find any help online and my prof does a lot of these problems. This is one of my homework problems, can anyone help me with it please.

Hi, I have a question regarding oblique shockwaves. Question: How can we determine what the wedge angle is for the shockwave in a situation? Context: This problem here shows an oblique shock wave on the trailing edge of the body and it simply states that the wedge angle is 6 degrees. Why is...

The entire mass of the wedge is ##(M+m)## therefore ##F=(M+m)a##. The forces acting on the small mass are its downward weight ##mg## and the normal force with the contact of the wedge therefore I got that ##N=mg\cos\theta##. Similarly the horizontal component is ##N=ma\sin\theta## therefore...

Hi, just wondering how I would calculate the volume of this wedge? see photo attached

if the tiny block moves downward by an amount x, the wedge should also move forward by the same amount x as they are connected by the same string whose length has to remain constant, (by differentiating it wrt time we get speed) hence I concluded that v1 = v2, but my book says otherwise what is...

We have a wedge whose surface is ##\theta## from the horizontal surface. After a block is placed on its frictionless slant surface, the wedge starts to accelerate due to a force F. What is the normal force acting upon the block? I have been trying to solve it but I got no clue. Could someone...

For question b, the official solution sets up a non-inertial coordinate on the block and writes out the following two equations: $$\begin{cases} \begin{align*} f\cos(\theta)+N\sin(\theta)-mg=0 \qquad \hat\jmath \\ N\cos(\theta)+f\sin(\theta)=ma \qquad\quad\;\;\, \hat\imath \end{align*}...

https://www.physicsforums.com/attachments/264405

Hello to all. I am new at PF. I am very happy to be here now that I know you. I am at the middle of a UTM (universal tensile machine) design. My machine is going to be a simple testing machine in which I only intent to measure the ultimate tensile strenght. That been said, I want to be as clear...

I think that the only force acting on the wall is the normal force caused by Coriolis force, so it can be calculated this way: ##N=m2\dot r \dot \theta## But ##\dot r## is not constant, so how can I calculate it? Then, I can't calculate the acceleration either since I don't have the value of...

When the box travels a ## X## distance, the wedge travels ## \frac{X}{2}##. So ##a = 2A## Using the wedge as a non inertial frame: I didn't use (4). Using (2) on (3) and then on (1) I got: ##2mA=mgsin\alpha +mAcos\alpha + \frac{-mgcos\alpha sin\alpha +mAsin^2\alpha +MA}{2cos\beta -...

Length of wedge/width of wedge = mechanical advantage

As per (b) in the above image, or easily solved with t=rFsin(theta), the perpendicular force is 260N. When inputting that value into the equation for torque, the value for torque is 520Nm, as per t=2.00*300*sin60. Because the wedge prevents the door from moving, the torque on/at the doorknob...

There’s a rigid rod pushing on a wedge. Velocity of the rod is v, which is vertically downwards, and the wedge is sliding to the right as a result with a velocity u. There is zero friction on the surface of the wedge and the surface of the rod in contact with the wedge. According to wedge...

I have some difficulties trying to understand non-inertial frames. I have problems to notice the acceleration in these cases, from an inertial reference frame and from non inertial refrence frame. Consider the first case, if I'm on the wedge, I see that the block doesn't move so there's no...

I tried making the fbd of both blocks the block on the incline will have mgsin30 friction force, tension and centrepetal force's cos component similarly second block will have mg tension and friction where normal will be centrepetal force after solving my ans is not matching

Problem Statement: In the arrangement shown in the figure, a block of mass m=2kg lies on the wedge of mass M=8kg.Find the initial acceleration of the wedge. Assume pulleys and thread massless and surfaces smooth. Relevant Equations: FBDs

A small mass of ##m## starts sliding down a wedge which is having a stationary circular track on it. If ##M = 2m## and friction exists between the wedge and the horizontal surface. Draw the Frictional force vs Theta graph. How to draw the graph? Please HELP

Are there any specific condintions for air to act as a screen? I just did my air wedge experiment yesterday and was wondering if we were to do it on a bigger scale, how would we do it?

Answers- 1,3,4 My attempt, the wedge being massless, there shoul not be any force acting on as it will then have infinite acceleration, so by that i really can't think of how force is applied on pully.

Now, the net vertical impulse on the wedge should be zero. It's quite obvious from the figure that the ground will also exert an impulse of ##J cos 30°## on the wedge. But they've given the answer as ##J sin 30°##. They're wrong, right?

I am working through Tu's "An Introduction to Manifolds" and am trying to get an understanding of things with some simple examples. The definitions usually seem simple and understandable, but I want to make sure I can use them for an actual function. I've worked a few problems below that my...

In Loring W. Tu's book: "An Introduction to Manifolds" (Second Edition) ... Proposition 3.27 reads as follows: The above proposition gives the wedge product of k linear functions as a determinant ...Walschap in his book: "Multivariable Calculus and Differential Geometry" gives the definition of...

I am reading Loring W.Tu's book: "An Introduction to Manifolds" (Second Edition) ... I need help in order to fully understand Tu's Proposition 3.21 ... ... Proposition 3.21 reads as follows: In the above proof by Tu we read the following: " ... ... ... ##= \sum_{ \sigma_{ k + l } } (...

I am reading Loring W.Tu's book: "An Introduction to Manifolds" (Second Edition) ... I need help in order to fully understand Tu's section on the wedge product (Section 3.7 ... ) ... ... The start of Section 3.7 reads as follows: In the above text from Tu we read the following: " ... ... for...

Hi PF! Given a 2D plane, the following is a parameterization of a circular arc with contact angle ##\alpha## to the x-axis: $$\left\langle \frac{\sin s}{\sin\alpha},\frac{\cos s - \cos\alpha}{\sin\alpha} \right\rangle : s \in [-\alpha,\alpha]$$ However, I am trying to parameterize a circle...

Homework Statement This is more of a conceptual question, but say a block was set on top of an inclined plane, which was set on top of a frictionless level surface. Would the inclined plane move? Why or why not Homework Equations None The Attempt at a Solution My thought...

Hello, we defined the wedge-product as follows Alt is the Alternator and the argument of Alt is the Tensor poduct of one k-form and a l-form (in this order w and eta). Suppose we have the wedge product of a 0-form (a smooth function) and a l-form , so the following may result: $$\frac{1}{l!}...

This HW problem due date has already passed. I had no problem with part a, but struggled thinking about parts b and c. I saw the solutions for parts b and c, but still don't exactly get it. I'll state the questions below, and tell you my way of interpreting the solution now. Could you tell me...

Homework Statement See question number 1. Homework Equations Work Energy Theorem, work done by all the forces=change in K.E. The Attempt at a Solution I tried solving this question this way, please help me calculate the Work Done by spring here?? I will be thankful for any help!

I am currently working on designing a linear brake/lock for a completely different purpose but it will be based on the same principle as in a quick clamp shown below. Before building a prototype I do want to make some rough calculations to check dimensions, angles etc. etc. However, I am for...