Lamina Definition and 42 Threads

Could I please ask for help with the following: ABCD is a uniform square metal plate of side 3m. Points E and F are taken on AB and BC respectively such that BE = BF = x m and the portion BEF is removed. 1) Find the distance of the centroid of the remainder from AD 2) Show that the remainder...

taking origin at the centre of the square. ##d\phi = \vec E.\vec{da}## $$d\phi = \frac {kqa}{(x^2 + y^2 + a^2)^{3/2}} da$$ $$\phi = \int_{-a/2}^{a/2}\int_{-a/2}^{a/2}\frac{kqa}{(x^2+y^2+a^2)^{3/2}}(dx)(dy)$$ on evaluating this double integral i get $$\phi = (q/\pi{\varepsilon}_0...

Could I please ask for help with the following: A lamina ABCD is in the form of a trapezium in which DC is parallel to AB, AB = 2a, CD = a and AD = h and the angle BAD is 90 degrees. Find the position of the centre of gravity of the lamina from the edges AD and AB. The lamina is placed...

Could I please ask for help with the following question: A lamina is in the shape of an equilateral triangle ABC, and D, E, F are the midpoints of BC, CA, AB respectively. Forces of magnitude 4N, 8N, 4N, 3N, 3N act along AB, BC, CA, BE, CF respectively, the direction of each force being...

When the lamina rotates about A, FA must act on B (because it is the farthest away) perpendicular to AB (so that all of FA contributes to rotation). Same argument is valid for rotation of lamina about B as well. Having noted that, I tried two approaches: Approach 1- If I assume that the...

Hi, In one of the standard calculus textbooks, source #1, the formula for y-coordinate of center of gravity for a homogeneous lamina is given as follows. In another book of formulas, source #2, the formula is given without the factor "1/2" as is shown below. Personally, I believe that source...

I feel there is a really obvious flaw in my logic but i can't pin it down So i have to find the thrust on the lamina which is basically force of bauyancy F(bouyancy)= Vρg Now volume of the triangular lamina is its rea into its hieght. v = Ah hence F = Ahρgsome information i feel i didnt take...

Hello everyone, nice to be here. I am going to calculate the young modulus of 3 layers of carbon fiber laminar composite For example: 1st: 12K plain wave carbon fiber in 0 degree 2nd:3K till wave carbon fiber in 45deg 3rd:12K plain wave carbon fiber in 0 degree How can I approach to calculate...

Homework Statement find the moment of inertia about the origin for the lamina which the surface of sphere (x^2) + (y^2) +(z^2) = 9 . z>2 . Given that density is a constant . Here's my wroking The ans is 16pi (k) , but my ans is different , is my ans wrong ? If so , which part is wrong ? I...

Homework Statement A plate is in the form of half disc of radius a and placed at positive y-axis. Given that the density of plate is directly proportional to the distance of the straight edge of the plate . Find the mass Homework EquationsThe Attempt at a Solution $$\int_{0}^\pi \int_{0}^a\...

Homework Statement Homework Equations m = ∫∫sρ(x,y,z)dS The Attempt at a Solution I used polar coordinates for this (is that necessary here)? I found zx and zy, took the cross product of those, and found it to be √(2). So dS = √2 dA. √2 ∫02pi∫25r2drdθ = 78pi√2

Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D = {(x, y) | 0 ≤ x ≤ 1, −1 ≤ y ≤ 1}; ρ(x, y) = 7xy2 I got my mass to be 7/3 but I'm not sure how to go about finding the center of mass

Homework Statement A lamina has constant density \rho and takes the shape of a disk with center the origin and radius R. Use Newton's Law of Gravitation to show that the magnitude of the force of attraction that the lamina exerts on a body of mass m located at the point (0,0,d) on the positive...

Homework Statement A lamina is bounded by the x-axis, the y-axis, and the curve ##y = 4 -x^2.## Determine the centroid position ##(\bar{x},\bar{y})## of the lamina. Homework Equations ## A = \int_a^b (f(x) - g(x)) dx ## (Area) ##\bar{x} = \frac{1}{A}\int_a^b x(f(x) - g(x)) dx ## ##\bar{y}...

Homework Statement Find the x-coordinate of the center of mass of the lamina that occupies the region cut from the first quadrant by the lines x = 6 and y = 1 if the density function is p(x,y) = x + y + 1 Homework Equations Mass = ∫∫spdσ X Coordinate of center of Mass = Myz/M Myz = ∫∫sxpdσ...

Homework Statement I have a laminate subject to 3 forces and 3 moments: Nx = normal force resultant in the x direction (N/m) Ny = normal force resultant in the y direction (N/m) Nxy = shear force resultant (N/m) Mx = Bending moment resultant in the x direction (Nm/m) My = Bending moment...

Homework Statement Find the center of mass of a planar lamina, in the form of a triangle with vertices (0,0),(0,a),(a,a), if ρ=k Homework Equations m = ∫∫f dA xbar = My/m ybar = Mx/m The Attempt at a Solution mass = ka²/2 Mx = ∫∫yk dy dx My = ∫∫xk dy dx...

Homework Statement I have a practical coming up and I have to research the method and calculations. I will be given an irregular lamina that I need to use as a compound pendulum in an experiment to determine the gravitational acceleration, g, as well as the moment of inertia (Io) of the...

A lamina comprises a uniform rectangular card ABCD where AB = 10 cm and BC = 12 cm with a circle of radius 3 cm cut out. The centre of the circle is 7 cm from AB and 4 cm from AD. How would I find the centre of mass for this lamina? I know to find the centre of mass for a uniform lamina we...

Homework Statement Square lamina (of side a) of uniform density. Find I about a diagonal. Homework Equations I = ∫ dm*l^2 The Attempt at a Solution So I drew a square and its diagonal and I imagine a differential mass drawn somewhere on the lamina. The distance squared to that...

An industrial tool is made from alaminar material occupyingthe region between thestraight lines y =2, y=1 2x and y =3−x. The density of thematerial varies and is given by thefunction σ(1 + x), where x is the horizontal distancefrom the y-axis and σ is aconstant. The mass of the...

Homework Statement The boundary of a lamina consists of the semicircles y=\sqrt{1-x^{2}} and y=\sqrt{4-x^{2}} together with the portions of the x-axis that join them. Find the centre of mass of the lamina if the density at any point is proportion to its distance from the origin. Homework...

Suppose the density of any point on a semicircular lamina {(x, y) : x >= 0,$$ x^2 + y^2$$ <= r^2 is proportional to its distance from the origin. Compute the centre of mass. I am trying to figure out what is the density function for this case.

Homework Statement Consider a lamina (two dimensional plate) with edges given by the lines y = sqrt(x) and y = -x + 2x^(2), for which the density is given by P(x; y) = x. (a) Define the domain of the lamina as the union of a Type 1 region and a Type 2 regions. b) Calculate the mass. Just...

a square lamina is made of 4 uniform thin rods each of which was a moment of inertia Ml^2 /12 about an axis perpendicular to their length and passing through their centres. My way of understanding it is the following : the two rods to whom the axis of rotation is perpendicular and passes...

Homework Statement Find the center of mass of the lamina which occupies if the density at any point is proportional to the distance from the origin. 36 <= x^2+y^2 <= 81, y >= 0 Homework Equations The Attempt at a Solution Rewrote it in polars to get 6<r<9. The x is clearly 0 as...

Homework Statement The question asks me to find the coordinates of the centroid of a uniform lamina enclosed by curve y=1-x^2. X axis and Y axis are in the 1st quadrant. Can you please tell me how to work out the limit for this equation?

http://img20.imageshack.us/img20/9443/ssssnm.png parallel and perpendicular axis theorem for moment of inertias So i solved the Moment of inertia for the large square through the perpendicular axis through a, (1/3)*M*(l^2), where l is 4a/2=2a, using the perpendicular theorem, Ixx+Iyy=Izz, we...

Hi, one of my vac work questions is: A lamina has density d(x,y) = x^2 + y^2 and is defined by -2<x<2 ; -3<y<3. Calculate the moment of inertia about an axis perpendicular to the lamina through the point (1,1). I'm confident that I find Ix which is equal to the double integral of the...

hi, I'm stuck and I can't seem to find a simple solution to questions regarding how to find the centre of mass of a lamina. for example: A uniform lamina with mass/unit area 0.12grams/cm2 consists of a square of side 80cm, with one corner at the origin O(0, 0) and other corners at B(80, 0)...

The boundary of a lamina consists of the semicircles y=\sqrt{1-x^2} and y=\sqrt{4-x^2} together with the portions of the x-axis that join them. Find the center of mass of the lamina if the density at any point is proportional to its distance from the origin. I drew a graph that looks like...

Homework Statement Consider a lamina rotating freely (no torques) about a point O of the lamina. Use Euler's equations to show that the component of \omega in the plane of the lamina has constant magnitude. [Hint: Use the reults of Problems 10.23 and 10.30. According to Problem 10.30, if...

Ok I have an electric fence behind my house. And next to it is a small building that has a lamina roof. I would like to electrify this roof using the current from my fence. Does anyone know of a way to make this work right. From what I know there has to be a ground output for the...

Homework Statement A lamina of unit density consists of the region between the two curves y=\sqrt{4-x^2} and y=1-4x^2 and the x axis. Find it's moment of inertia about the x-axis. Homework Equations This is the correct answer: 2\left \{ \int_{0}^{2}\int_{0}^{\sqrt{4-x^2}}}y^2 dy dx...

Homework Statement Calculate the depth below the water surface of the centre of pressure of the water pressure acting on the submerged triangular lamina, height 3m, base 2m and located at a depth of 1m below the surface.Homework Equations not entirely sureThe Attempt at a Solution I found the...

Homework Statement can anyone please send me the link to calculate the moment of inertia of cuboid,rectangular and triangular lamina ??(along with figure) Homework Equations The Attempt at a Solution

Homework Statement Calculate the moment of inertia of a uniform triangular lamina of mass m in the shape of an isosceles triangle with base 2b and height h, about its axis of symmetry. The Attempt at a Solution I've tried various things for this and never get the correct answer...

Find the mass and center of mass of "lamina" ? Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer...

A lamina occupies the part of the disk x^2+y^2=<25 in the first quadrant and the density at each point is given by the function \ro (x,y)=3(x^2+y^2) i am to find the mass, so this is what i did: \int _0 ^{ \frac{\pi}{ 2}} \int _0 ^{5}(3 r) r dr d \theta i evauated this and got pi/2...

Hi, I'm not sure if this mechanics question should be in the Maths forum or the physics forum :confused: Nevertheless, I apologise first if I have posted in the wrong area :frown: I was wondering if anyone could help me with the following question. A lamina moves in its own O(x,y)...

Can someone please explain to me how to start off this question? A uniform semicircular lamina has mass M. A is the midpoint of the diameter and B is on the circumference at the other end of the axis of symetry. A particle of mass m is attached to the lamina at B. The centre of mass of the...

Where is the centre of mass of a semicircular lamina which is uniform? I know it is somewhere along the line of symestry, but where excactly?:confused: