Center of mass Definition and 900 Threads

Homework Statement Or any coordinates really. In the normal Cartesian plane, the center of mass is defined from the x, y , and z distance as follows \bar{x} = \frac{1}{Area(R)}\iint_R x dA \bar{y} = \frac{1}{Area(R)}\iint_R y dA \bar{z} = \frac{1}{Area(R)}\iint_R z dA Now is there one for...

Homework Statement A metal rod is 50cm long. Its linear density at the point x cm from the left end is given by the equation p(x)=1/(100-x) gm/cm. Find the mass and center of mass for the rod. Homework Equations mass = \int p(x)dx center of mass = moment / mass The Attempt at a...

Center of mass of ... I just don't know where to post this...feel free to move it. Assuming our universe is the 3-dimensional surface of a 4-dimensional sphere, my question is: where is the center of mass of the universe ? Nowhere, everywhere, is it in the center of the sphere ? There's no...

Homework Statement During the weight-in of a truck it's been determined that the load of the weight acting on the front axis and back axis are 18 [kN] and 12 [kN] correspondingly, when the truck is empty as shown in the diagram. The max load allowed on every axis is 40.Calculate the size of...

Homework Statement Find the center of mass of the solid of uniform density bounded by the graphs of the equations: Wedge: x^2+y^2=a^2. z=cy(c>0), y>=0, z>=0 Homework Equations Mx=int(y*p(x,y) dA) dA=area of integration, dydx/dxdy The Attempt at a Solution I set up all the...

The concept of "Center of Mass" is mentioned often in QM literature. I saw one blurb stating that a diatomic molecule could be represented as a SHO vibrating about the "center of mass" between the two atoms. But is there a precise definition of center of mass in QM based solely on the state...

Homework Statement Find the mass and center of mass of a wire in the shape of the helix x=t, y=\cos{t}, z = \sin{t}, 0 \le t \le 2 \pi, if the density at any point is equal to the square of the distance from the origin. Homework Equations Arc length formula: ds =...

Homework Statement What is the x and y coordinates of the center of mass for the uniform steel plate shown in the figure ? Homework Equations x=1/M \sum x dm The Attempt at a Solution I am not really sure how to being this one. Mass isn't given so I am not sure where to start. I...

1. a club ax that consists of a symmetrical 9 kg stone is attached to the end of a uniform 2.5 kg stick. stick is 80 cm long, stone is 18 cm. how far is the center of mass from the handle end of the club-ax? Homework Equations [b]3. i for the life of me not know how to go about...

Homework Statement Two identical 0.19 kg blocks (labeled 1 and 2) are initially at rest on a nearly frictionless surface, connected by an unstretched spring, as shown in the upper diagram, where x2 = 0.05 m. Then a constant force of 8 N to the right is applied to block 2, and at a later time...

Homework Statement Two point-like masses have common center of mass located at (xc=2.1cm, yc=4.3cm). Mass M1=49kg is at (x1=65cm, y1). Mass M2=7.5kg is at (x2, y2=(-85)cm). A third mass M3 is placed at (x3=(-15.3)cm, y3=9.4cm). What is the mass of M3 if the x-coordinate of the center of mass...

Homework Statement Pluto's diameter is approximately 2370km , and the diameter of its satellite Charon is 1250km . Although the distance varies, they are often about 1.93×104km apart, center-to-center. Assuming that both Pluto and Charon have the same composition and hence the same average...

Homework Statement we are looking at two stars in the eridani system, eri B and eri C. the period of the system is 247.9 years. the system's measured trigonometric parallax is 0.201 arcseconds and the tru angular extent to the semimajor axis of the reduced mass is 6.89". the ratio of...

Homework Statement Find the centroid (center of mass) of the region in the first quadrant bounded by y=x, y=3x, x=n (>0) Homework Equations The Attempt at a Solution No idea how to start the question, since I have to get the area of the region but the graph does not intersect...

Homework Statement A 1540-kg truck has a wheel base of 3.13 m (this is the distance between the front and rear axles). The center of mass of the truck is 1.29 M behind the front axle. (a) What is the force exerted by the ground on each of the front wheels? (b) What is the force exerted by...

Homework Statement This is a very simple problem to state, yet I've not found any answers on PF or anywhere else online. So let's say we have a simple rigid body like a rod. We apply an external force Fext for a fixed time dt to the rod in two different ways: (1) directly on the center of...

Homework Statement A barbell is 1.5 m long. Three weights, each of mass 20 kg, are hung on the left, and two weights of the same mass are hung on the right. The width of each weight is 4 cm and the outside edge of each group of weights is placed 4 cm from the ends. Where is the center of...

The sigma notation of the center of mass is xcom = 1/M * SIGMA mixi. I understand this because you are just taking a "weighted average" of sorts to find the correct x-value. My difficulty in understanding arises when this is expressed in integral form i.e. xcom=1/M * INT xdm. First of all...

Hi, I was wondering about an issue that we just started in my physics class: we learned that center of mass (CM) and center of gravity (CG) coincide in an object as long as the force of gravity is uniform over that object. So, for something near the Earth's surface we can say that CM and CG...

Homework Statement an isosceles triangle with mass m and constant density is placed on an xy plane with base on the y axis. its height ranges from (0,-b/2) to (0,b/2) and its height is (a,0) Find its center of mass. I know that its density is equal 2m/ab. The Attempt at a Solution...

Homework Statement A square plate with edge a cm and areal density kr g/cm^2, where r is the distance (in centimetres) from P to one of the diagnals of the square. Find the mass. The Attempt at a Solution I know my diagram is wrong, and I know what the correct one looks like. However, I...

So we're about to start learning the center of mass without calculus. I already know the formula= you consider each mass times the respective distance from a chosen distance, divided by the total mass. You do that for the X and Y in 2D. Is that all I need for COM without calculus?

Homework Statement Semi circle of Radius R given. Find center of mass using polar coordinates, not double integrals. Homework Equations .5 intergral(r^2dpheta) (1/M) integral y dm r=R The Attempt at a Solution .5(2/piR^2) integral(R^3sinpheta do pheta) from 0 to pi, when I evaluate it I...

Hey all, small question, a mass is distributed along a rod by the function M(X)= bx - a(x^2). The length of the rod is 3b/4a. What is the center of mass. Ive tried working it out by using integrals to find the the total mass, and then divide it by 2, and then try to find out the x for that...

We have four squares that make up one big square. Square A is located at the top right corner, square B at the top left corner, square C at the bottom left corner, and square D at the bottom right corner. All these squares have equal masses, and the length of each square is 80 cm. What is the...

Homework Statement A man of mass 84.4 Kg is in the back of a boat of mass 425 kg which is moving without friction on ice with velocity 4.16 m/s. the man moves from the back to the top of the boat with velocity 2.08 m/s traveling for 18.2m. How much distance does the boat travel while the man...

Homework Statement is there any intuition of why the center of mass formula is what it is? in high school the teacher says is is what it is and that's that or something like that but is there any logic behind it? Homework Equations The Attempt at a Solution

Hello, I have a question about the angular momentum about the center of mass. I am using Goldstein's Classical Mechanics. In the formula, it is stated that angular momentum about the center of mass (L) = R x Mv + SUM-->i of (r'i x p'i) With R being the center of mass vector, M being the...

RCOM is a vector from an inertial frame to the point called the center of mass. The system behaves as if all the mass is concentrated at the center of mass and all the external forces act at that point. so \frac{d^{2}}{dt^{2}}\overrightarrow{R}{}_{COM}=\frac{\sum...

Homework Statement I'm trying to find the center of mass of the region (x²+y²)² =2xy in the first quadrant, but I got stuck. The Attempt at a Solution What I did is make the substitution x = r cos(t), y = r sin(t), which gives the equation r^{4}=2r²cos(t) sin(t), so r² = sin(2t)...

Homework Statement A square uniform raft, 18m by 18m of mass 6200kg is used as a ferry boat. if three cars each of mass 1350 kg occupy the NE, SE, and SW corners, determine the Centre of mass of the loaded ferryboat relative to the centre of the raft Homework Equations Center of mass...

Homework Statement How can I find the center of mass of a right triangle, of height h, length a, and mass m, without using calculus? Homework Equations The Attempt at a Solution I just need a hint on how to start please

Homework Statement Two people are carrying a 2 m long couch with a mass of M=20kg level with the horizontal by lifting it from it ends. The center of mass of the couch is 1 m from each end. While it is being carried, another person with a mass m of 60 kg sits on the couch 0.5 m from one end...

Suppose that A is a positive constant. Find the center of mass of a thin plate covering the region bounded by y^2= 4Ax and the line x=A. Assume that mass density at (x,y) is proportional to x. y=sqrt(4Ax) K is what I am saying is proportional to x xbar=My/m ybar=MX/m Im not...

Homework Statement An American football game has been canceled because of bad weather in Cleveland, and two retired players are sliding like children on a frictionless ice-covered parking lot. William 'Refrigerator' Perry, mass 162 kg, is gliding to the right at 7.41 m/s, and Doug Flutie, mass...

Homework Statement A shell is shot with an initial velocity 0 of 23 m/s, at an angle of θ0 = 54° with the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass (Fig. 9-42). One fragment, whose speed immediately after the explosion is zero, falls...

Homework Statement Explorers in the jungle find an ancient monument in the shape of a large isosceles triangle . The monument is made from tens of thousands of small stone blocks of density 3 174 kg/m3. The monument is 17.6 m high and 69.4 m wide at its base and is everywhere 3.30 m thick...

Homework Statement The figure above is a simple model of a crane. The base has a mass of 2000kg, and the boom has a mass of 200kg. What is the maximum mass of the ball if the crane is not to tip over? Note, in order for the crane to be stable, its center of mass cannot be outside the...

This problem is driving me crazy! Homework Statement How far from the center of the Earth (in km) is the center of mass of the Earth + satellite system if the satellite has a mass of 2970 kg and is in orbit 42400 km above the surface of the Earth. The mass of the Earth is 5.98*10^24 and the...

Homework Statement I know traditionally the center of mass of a triangle is 2/3 the way down its height, but i believe it varies here due to the uneven mass distribution. Here i have to find the center of mass distance from Q http://img508.imageshack.us/f/scn0001p.jpg/ Here is an image...

A uniform flat plate of metal with dimensions 10x 12 is situated in a reference plane with its bottom left hand corner at (-2, -6) and its upper right hand corner at (8, 6). The plate has a circular hole cut out of it centered about (4,0) with a radius of 2. Find the x coordinate of the center...

What is the speed of the center of mass of the disk? A string is wrapped around a disk of mass m = 1.5 kg and radius R = 0.11 m. Starting from rest, you pull the string with a constant force F = 6 N along a nearly frictionless surface. At the instant when the center of the disk has moved a...

Homework Statement Three cubes, of side l, 2l, and 3lo, are placed next to one another (in contact) with their centers along a straight line and the l = 2lo cube in the center. What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform...

Homework Statement A dog with mass 11 kg stands still in a boat with mass 45 kg. the dog is 20 meters from the shore. It then walks 8 meters in the boat towards the shore. how far is the dog from the hore aftter this? Homework Equations center of mass equation The Attempt at a...

Homework Statement In the figure, a 60 cm length of uniform wire, of 60 g mass, is bent into a right triangle. The x- and y-coordinates of the center of mass, in cm, are closest to... I am going to explain the picture in my textbook. The origin is at (0,0). It goes up 10 cm and to the...

A system consists of three particles located at the corners of a right triangle as shown below. Mass 1 is 7.0 kg, mass 2 is 6.4 kg, and mass 3 is 9.9 kg. If the distances a equals 15.8 m and b equals 2.0 m, then what is the center of mass (in m) in the vertical direction? Y center of...

Three objects of different masses are located at the corners of the triangle shown in the picture. If distance a equals 4.21 m, b equals 1.55 m, and c equals 11.93 m, then what is the center of the mass (in m) of the system in the horizontal with respect to the origin? X center of...

Homework Statement A meter stick has constant thickness and width , but the material that the stick is constructed from is very strange ... it has a variable mass density that is given by, ρ(x) = 0.800(1 + 0.00250x) grams/cm3 where x is measured in cm. Find the center of mass of the meter...

Homework Statement ~ Homework Equations integration The Attempt at a Solution for a) i use linear density and calculate the mass of circumference and integrate it bottom to top. is it riight?any other methods? for b) i use surface density and calcuate the mass of disk and...

Homework Statement ~ Homework Equations integration The Attempt at a Solution a) i use surface density and calculate the mass of a disk and integrate it from bottom to top. Is it right? But the cone is hollow so i only need to use the mass of the circuference? b) use "negative...