Center of mass Definition and 899 Threads

Homework Statement Given a homogenous rectangular surface, sides of length a and b=4*a, with a circular hole in x=a and y=a/2, find the center of mass. Homework Equations R=1/M*Ʃmi*ri , M= total mass, r= position vector area of a circle = pi*r2 , r being the radius The...

We all know the proof, from Newtonian mechanics, that the motion of the center of mass of a system of particles can be found by treating the center of mass as a particle with all the external forces acting on it. I want to prove the same think, but within the framework of Lagrangian mechanics...

Hello! I'm here again, now with a new exercise! :biggrin: Homework Statement A block of mass m is at rest over this wedge (it's a triangle) of mass M that is at rest over a table. There is no friction. The point P of the block has a height h from the table. Then the block starts to move. What's...

Homework Statement a toy which have a shape of tank (military vehicle) has a platform of 192mm long, 140mm wide, weight of 2075grams. The canon is 239mm long, 50mm wide, and weight of 400grams. the canon is on top of the platform and being assembled 58mm from the front side of platform. where...

Homework Statement I'm trying to understand the equations given in my textbook (Principles of Physics, Ninth International Edition) for finding the center of mass. The equations are given below. They're used to find the x, y, and z components of the center of mass for objects. I'm trying to...

Hi. Just like in classical mechanics, I've read that in relativity, the velocity v of a particle just reverses after an elastic collision in the center of mass. I.e, if v is the velocity before the collison and v' is the velocity after, then v = -v'. I wondered how one goes about showing this...

Homework Statement A trailer with a mass of 900 kg with mass centre (centroid) at G is attached to a towing car at A. If the car and trailer reach a velocity of 60 km/h along a horizontal road in a distance of 30 m from rest with constant acceleration, compute the vertical component of...

Hi, this is a problem on center mass. Homework Statement A beam hangs straight down from a point O(O is placed at x=0 and y = 0, aka origo). The beam is attached to the point O. Beam has length L and mass M. The density of the beam is uniform, so the centermass of the beam is...

Calculus 3 project – any and all help is appreciated. We've just gone over center of mass with double integrals, so it's a bit peculiar to see this project feature only one integral. I went over that in calc 2 – and as a result, know how to calculate it that way. However (as you will see in...

Homework Statement 9) Three cubic boxes, each with side 0.1m, are stacked on top of one another. The lowest one is filled with gold bars and has mass 25kg; the middle one contains aluminum bars and has mass 10kg. The top one contains balsa wood and has mass 2kg. The height above the floor...

Homework Statement The z com of the entire ice cream cone, the base being an inverted right circular cone, the top a hemisphere. Equal density throughout. Must solve using integrals and density relationship. Homework Equations The z com of the top hemisphere (ice cream) is equal to 3/8 R...

Homework Statement Two objects are on a stick where one is stuck in place and the other one can slide. Both objects have the same mass and the stick has negligible mass. Homework Equations COM = \frac{m_1 x_1 + m_2x_2}{m_1+m_2} v_1 = t The Attempt at a Solution COM =...

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...

Problem: A symmetrical rowboat, mass M = 116 kg, length L = 6.89 m, points toward the shore. A man, mass m = 90 kg, stands in the back of the boat, distance d = 35.7 m from the shore. If the man now walks to the front of the boat, how far will he be from the shore? Here is what I did...

Homework Statement Find the center of mass of the solid figure similar to a cone pointing upward with slope = 1 Note: the density varies with z^2 and the edge has a slope of 1. From symmetry we see that both Xc and Yc are equal to zero. Find the center of mass in the z direction as a function...

Center of Mass Rowboat Question...Please Help! Can someone please help with below question? I really don't know where to begin... When empty, a 166 kg rowboat is symmetrical. A boy of mass 70.5 kg sits 2.1 m from the center of mass of the rowboat toward the front of the boat, and a girl of...

Homework Statement I have equations that are y1= 2sin(\frac{3}{2}x) and y2= \frac{1}{3}x the point where they intersect is called "a" (about x≈1.88). Find the center of mass where M is the total mass of the object.Homework Equations xcm= \frac{1}{M}∫x dM The Attempt at a Solution I found...

Homework Statement An Object A of mass M falls in a vertical plane under gravity. While it is in air, it breaks into two fragments, one having mass M/3 and the other having a mass of 2M/3. The center of mass of the broken fragments taken together shifts compared to that of the object A...

Homework Statement A 58 kg woman and an 78 kg man stand 8.00 m apart on frictionless ice. How far from the woman is their CM? 4.6 m If each holds one end of a rope, and the man pulls on the rope so that he moves 2.6 m, how far from the woman will he be now? Use two significant figures in...

Is kinetic energy of center of mass of a system is equal to KE of of system?? Does Kinetic energy(KE) of center of mass is equal to kinetic energy of system? I think no... Example take two identical particle moving with velocity v and -v. kinetic energy is mv^2 but KE of center of mass is...

A piece of wire of uniform cross section is bent in the shape shown above (for picture: http://tinypic.com/r/23tjr45/5). What are the coordinates of the center of mass? Relevant equations: Was I supposed to integrate the wire on all 4 sides? I wasn't sure exactly what to do at this point.The...

Homework Statement Four particles are in a 2-D plane with masses, x- and y- positions, and x- and y- velocities as given in the table below: M X Y Vx Vy 1 8.9kg -2.6m -4.8m 3.2m/s -3.9m/s 2 7.9kg -3.4m 3.6m...

I'll start off by saying I have ZERO scientific background. I'm very interested in having a general working knowledge of physics and such, but I'm more concerned with creative applications for writing at the moment. Ever seen a movie with way too many scientific impossibilities? Yeah, I'd like...

When calculating the gravitational field from the earth, why can we make the assumption that all of the mass of the Earth is 'averaged' at the the geometrical center? If we imagine the Earth as a bunch of pieces, and then calculate the sum of forces from each of these pieces, would it not be...

Hi all, I've been digging around in Google as well as searching under physics forum for a while now but I still can't find the answer to my question. If there is already an answer then I'm sorry for wasting the server bandwith and database harddrive usage I learned the formulation for...

Is the center of mass a concrete point on a body or an abstraction? As far as I can see the internal forces all add to zero in the center of mass. But if you imagine that a body made up of n particles with a single particle located exactly in the coordinates of the center of mass, I can't see...

Hi, ((sorry my english is limited.)) Can anyone explain the answer of this problem? https://www.physicsforums.com/showthread.php?t=193986 .

Hey, so I'm new to Physics Forums as a registered member, but I've been checking this site out for what seems likes years. Homework Statement Locate the center of the mass of the Earth-moon system with respect to the center of the Earth, and then find the orbital velocity of the Earth...

Hello all, I'm confused with the center of mass concept. Regard the following problem, we have a spring with negligible mass joined to two masses m1 and m2 (m1=m2) on a table without friction force. At t=0 a thrust Vo (initial velocity) is given to m2 with direction perpendicular to the...

A solid half-cylinder of radius 1 meters and length of 5 meters lies under 50 meters of water at the bottom of a lake. The cylinder is made of a material of constant density d. 1. Find the center of mass. I said that the COM will be in the center because there is a constant density. 2...

Homework Statement Four masses are connected by 17.4 cm long, massless, rigid rods. If massA=105.0 g, massB=231.0 g, massC=204.0 g, and massD=248.0 g, what are the coordinates of the center of mass if the origin is located at mass A? See attached picture. Homework Equations Xc.m = \sumΔm x...

Hey all! I always use this principle when I do exercises, but today I found out, that I can't explain why it's valid. What I'm talking about is that when you apply a torque to a free object it will always start to rotate around it's center of mass rather than just an arbitrary point. Why is...

Six problems due Monday, and I have no idea what I'm doing on either of these. Problem 1: Homework Statement A group of people has a total mass of 1500kg and are standing on one end of a 20,000kg boat. They walk 6.5m to the other end of the boat. How much does the boat move? The water...

Lets say I have n number of masses, x1, x2, x3,...,xn. How do I find the center of mass of the group of masses? I'm not really sure how to do this, but does it have something to do with having a test mass and finding the direction of the force and different points around the group of masses...

Homework Statement I've just started with center of mass, and instead of the method in the book, I tried solving the center of mass for a solid hemisphere using angle as a variable, but the answer didn't match. A small disk of mass "dm" is taken, which subtends an angle "dθ" at the center.The...

Homework Statement 1. Find of the center of mass of the image below. 2. A human head weighs 8lbs, a human torso weighs 20lbs, and a human's hips and legs weighs 20lb. The headis 10m long, the torso is 25m long, and the hips and legs are 35m long. Find the center of mass of the body...

Why is it that for instance the Earth and the moon orbit their common center of mass? I mean surely the moon feels a gravitational force as though the mass of the Earth were concentrated at its center? If yes, what is that then makes it orbit around their center of mass rather than this point. I...

Homework Statement Find the center of mass of figure , of uniform density Homework Equations X = m1 x1 + m2 x2 + ... / m1 + m2 ... The Attempt at a Solution i broke the figure in 4 rectangles and got individual center of masses my answers comes out to be (13b/8 , 5b/2)...

Homework Statement I've just started with center of mass, and instead of the method in the book, I tried solving the center of mass for a solid hemisphere using angle as a variable, but the answer didn't match. A small disk of mass "dm" is taken, which subtends an angle "dθ" at the center.The...

Homework Statement Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D is bounded by the parabola x=y2 and the line y = x - 2; ρ(x, y)=3Homework Equations m=\int\intD ρ(x, y) dA The Attempt at a Solution Basically I just need help...

Homework Statement 1. Homework Statement On a frictionless table, a glob of clay of mass 0.72 kg strikes a bar of mass 1.34 kg perpendicularly at a point 0.23 m from the center of the bar and sticks to it. If the bar is 1.22 m long and the clay is moving at 8.3 m/s before striking the...

Homework Statement Given that I have a system with a rod of diameter 1 1/2 inches with a length of 17 in and a weight of 10 1/3 oz and a rod with a diameter of 3 inches with a length of 17 in and a weight of 20 2/3 oz. The two rods are butted together at one end almost looking like a bottle...

Given the picture in the attachment of two rods touching with them each being 17 inches long and one weighing double the weight of the other, would it make sense that the center of mass is 2/3 of the way down the picture from the thinner end? Or, am I going about this idea the wrong way?

I am currently trying to find the center of mass of two rods. One rod is 20 2/3 oz and is 17 inches long with a diameter of 3. The other rod is 10 1/3 oz and 17 inches long with a diameter of 1 1/2 The bigger rod is touching the smaller one if they were both standing up. It looks almost like a...

Homework Statement The upper side of a uniform plate of thickness w is given by a function y(x) = 4a+x^2/a. Length of this plate on the x-axis is a . Find x coord of the center of mass of this object, with respect to the origin O . Take density of the plate as p The Attempt at a Solution...

Homework Statement Find teh center of mass of a thin infinite refion in the first quadrant bounded by the coordinate axes and the curve y=e-2x, if ρ(density)= xy Homework Equations The Attempt at a Solution I set M= ∫∫ xy dydx where y goes from 0 to y=e-2x, and x goes from 0 to...

Homework Statement Let m1, m2 and m3, the mass of 3 particles and v12, v23, v13 their respective relative velocities. a) Show that the total kinetic energy of the system in relation to the center of mass is: ( m1m2v12^2 + m2m3v23^2 + m1m3v13^2 ) / (m1+m2+m3) b) generalize this result...

Suppose I give you a curve f(x) = \sin^2 (x) + ln(x) And suppose I tell you to rotate this curve about the x axis, we get disks. Now, I ask you, what is the center of mass of this object? Now immediately, you could say that \bar{y} = 0 because it is symmetric about the x-axis. I don't...

Homework Statement Find the center of mass of a triangle with two equal sides of length a. The triangle's third side is length b and it has a uniform mass of M. Homework Equations R = \frac{1}{M} \int dm \vec{r} dm = \frac{M}{A} A = \frac{1}{2}base*height The Attempt at a Solution...

Homework Statement Hey all. Below is the question and picture related to it. "Three uniform metre sticks each of mass M are attached together as follows: Stick 1 lies along the y-axis from y = 0 to y = 1.0m. Stick 2 lies along the x-axis from x = 0 to x = 1.0m. Stick 3 makes an angle of 60...