Center of mass Definition and 916 Threads

Homework Statement A sledgehammer with a mass of 2.60kg is connected to a frictionless pivot at the tip of its handle. The distance from the pivot to the center of mass is rcm=0.610m, and the moment of inertia about the center of mass is Icm=0.04kg*m2. If the hammer is released from rest at...

Homework Statement Three cubes, of side L1, L2, and L3, are placed next to one another (in contact) with their centers along a straight line as shown in the figure. What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material and L1=...

[b]1. A cubical box has been constructed from a uniform metal plate of neglible thickness. The box is open at the top and has an edge length L=40cm. Find (a)the x coordinate (b) the y coordinate and (c) z coordinate of the center of mass of the box. (part a and b I have solved. I need help...

In Fig. 9-39, three uniform thin rods, each of length L = 49 cm, form an inverted U. The vertical rods each have a mass of 14 g; the horizontal rod has a mass of 33 g. What are (a) the x coordinate and (b) the y coordinate of the system's center of mass? (Give your answer in cm)...

A stone is dropped at t = 0. A second stone, with twice the mass of the first, is dropped from the same point at t = 500 ms. (a) How far below the release point is the center of mass of the two stones at t = 850 ms? (Neither stone has yet reached the ground.) (b) How fast is the center...

Homework Statement If a particle of mass 5.6 kg is moving east at 10 m/s and a particle of mass 17 kg is moving west at 10 m/s, what is the speed of the center of mass of the pair? Homework Equations Not sure how it would relate, but to find the center of mass = (m1x1 + m2x2)/(m1+m2)...

Homework Statement The figure shows the dimensions of a composite slab; a fraction of the slab is made of aluminum (density = 2.70 g/cm3) and other part is made of iron (density = 7.85 g/cm3). They are not equal as indicated in the figure, but have x1 = 7.5 cm and x2 = 14.5 cm. As measured...

Tipping something given its center of mass? My LAST homework problem! Homework Statement A rectangular block of mass 3.0 kg is at rest on a table. Its height (in its current position) is 0.7 m, but because its composition varies vertically, its center of mass is at a height of 0.40 meters...

Homework Statement a. The Hermes experiment is a fixed target experiment. The HERA accelerator creates circulating beams of electrons of energy 27 GeV; these are repeatedly crashed into a target of protons which are at rest. What is the center of mass energy of the electron-proton...

Hi, I have just been pondering the problem of electron - positron annihilation into a single photon in the CM frame. I was stuck at a discrepancy - that in the center of mass frame, the total momentum of the particles was zero, but the energy is the sum of the energies of the original...

Hello, As I'm seeing the center of mass at university, many questions came to me but I could solve most of them. However I'm not sure about some points. Say you have the system a human on ice. (without air. And consider the ice to be frictionless with the human). I could hardly understand...

Hi! I'm very curious to know how the Center of mass, that I know from Math is relevant for the physics' subjects. I know already how it affects stars, but I'm interested to know how it is being used in electricity, magnetism, mechanics and other stuff on EARTH :-p Therefore, I refer to...

Homework Statement A club-axe consists of a symmetrical 11.0 kg stone attached to the end of a uniform 2.9 kg stick, as shown in the figure. The length of the handle is L1 = 93.0 cm and the length of the stone is L2 = 10.0 cm. How far is the center of mass from the handle end of the...

Homework Statement Center of Mass of a hemisphere http://www.goiit.com/templates/default/images/chapters/center_mass/image064.gif http://www.goiit.com/templates/default/images/chapters/center_mass/image068.gif Why is volume of elemental disc = Rd\theta (cos \theta) (\pi R^{2}cos^{2}...

Homework Statement http://docs.google.com/Doc?id=d277r7r_60c2235gfg Homework Equations M(Rcm)=\int(rdm) The Attempt at a Solution Okay, so I've figured out that I have to integrate the radii by the mass element dm, which in this case would be p, because that's the mass/unit area? I think...

Homework Statement Consider a system of two particles, with masses m1 and m2. What is the ratio of their kinetic energies, T1=T2, in the center-of-mass frame? The Attempt at a Solution I do not really understand the question because center of mass frame was not taught in my class. From...

A constant horizontal force F of magnitude 12 N is applied to a uniform solid cylinder by fishing line wrapped around the cylinder. The mass of the cylinder is 10 kg, its radius is 0.1 m, and the cylinder rolls smoothly on the horizontal surface. (a) What is the magnitude of the acceleration of...

Hello everyone. Take an object in you hands. Throw it in the air. While launching it, your hands will push on the object in different points of it. The object will ALWAYs rotate, free in the air, about an axis that passes for the center of mass. Does anybody know why? I found that in that...

Homework Statement Prove the magnitude R of the position vector \vec{R} for the center of mass from an arbitrary point of origin is given by the equation M^{2}R^{2} = M\sum{m_{i}r^{2}_{i} - \frac{1}{2}\sum{m_{i}m_{j}r_{ij}^{2} Homework Equations \vec{R} = \frac{1}{M}...

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...

Homework Statement Find the center of mass of a semi-circular plate of radius r Find the volume when the plate (above) is rotated around a line along its straight sideHomework Equations 2(pi) integral of r dr The Attempt at a Solution I honestly don't know how to do centroids. :-( I'd like...

Consider two identical billiard balls – one with velocity v and the other stationary. They collide with each other. (a) Describe the motion of the two balls after the collision. (b) Describe the motion of the centre of mass of the two balls before the collision. (c) Describe the motion of the...

Hi all, I need some help on a couple questions: 1) Find the moment of inertia about the x-axis of a thin plate of constant density 1 (density = 1) bounded by the circle x^2 + y^2 = 4. Then use your result to find Iy and Io for the plate. Here's how I was thinking to set it up: Since the...

Centroid ("center of mass") of cardioid... revisited This is actually a variation of the https://www.physicsforums.com/showthread.php?t=119622". As it happens, the cardioid I'm working with is identical to jbusc's: r = 1 + \cos(\theta) and \delta \equiv 1 The task is to find the...

Homework Statement Show that the center of mass of a uniform semicircular disk of radius R is at a point 4R/(3(pi)) from the center of the circle. Homework Equations Total mass Center of mass = M rcm = m1r1 + m2r2 + ...The Attempt at a Solution I do not know how to apply integration to this...

[SOLVED] center of mass in which direction would the center of mass of the body migrate if the arms were raised overhead? what about if the person had a bilateral amputation of his legs?

Homework Statement I have to find the center of mass of any vehicle. Homework Equations These are what I have to make. The Attempt at a Solution Here is what I have thought. I have two solutions :- 1. To find the mass of all the major components and their centers and then...

[SOLVED] Thin rod suspended freely on end and dropped. KE and Center of Mass Homework Statement A thin rod of length 0.75 m and mass 0.39 kg is suspended freely from one end. It is pulled to one side and then allowed to swing like a pendulum, passing through its lowest position with angular...

Homework Statement A rod of length 38.5 cm has linear density (mass-per-length) given by the following equation, where x is the distance from one end. λ=50.0g/m+16.5g/m^2 a. What is its mass in g? b. How far from the x=0 end is its center of mass in m? Homework Equations The...

[SOLVED] Need to find center of mass of a rod Homework Statement Where is the center of mass of a uniform, L-shaped iron rod of sides X = 0.8 m and Y = 0.5 m, respectively? Take the corner to be at (x,y) = (0,0), with the X and Y sides along those axes, respectively. (Assume that the rod is...

[SOLVED] Finding Center of mass Homework Statement Three cubes, of side 0, 20, and 30, are placed next to one another (in contact) with their centers along a straight line as shown in the figure. What is the position, along this line, of the CM of this system? Assume the cubes are made of...

Two paramedics, Bob and Charlie, carry a 200 lb patient on an 8-foot-long stretcher. Bob holds the front end of the stretcher and Charlie holds the back end. The patient lies closer to the front end of the stretcher, so his center of gravity is 3 feet from Bob's hands and 5 feet from Charlie's...

Integration Center of Mass Problem --Really frustrated Homework Statement An 800 g steel plate has the shape of the isosceles triangle shown in the figure. What are the x and y coordinates of the center of mass? Homework Equations The Attempt at a Solution I am getting...

[SOLVED] Springs, Normal Modes, and Center of Mass coordinates 1.) Problem The problem of the linear triatomic molecule can be reduced to one of two degrees of freedom by introducing coordinates y_{1} = x_{2} - x_{1}, y_{2} = x_{3} - x_{2}, and eliminating x_{2} by requiring that the center...

[SOLVED] Center of Mass of compound cylinder I have this problem. I have a cylinder filled with two liquids of different densities and not able to mix up (like oil and water). I have to fill the cilynder in such a way so that the center of mass will be located as low as possible. For example...

A 4.5 kg ball initially rest at the edge of a 2.5 m long, 1.5 m high frictionless table. A hard plastic cube of mass 0.65 kg slides across the table at a speed of 20m/s and strikes the ball to leave the table in the direction in which the cube was moving. At t= 1 sec , F = .5 x10^3 At t= 2...

Homework Statement A solid "rough" of constant density (\delta =1) is bounded below by the surface z=4y^2,above by the plane z=4, and one the ends by the planes x=1 and x=-1. Find the center of mass...Homework Equations _{M}xy =\int\int\int z \delta dV Mass = \int\int\int\deltadV then to find...

Homework Statement Find the center of mass of the collection of mass points in Figure P.12 and then find the moment of inertia of the system about an axis through the center of mass and parallel to the y-axis. Homework Equations Center of Mass Moment of Inertia The Attempt at a...

Homework Statement [/B] A loaded coal car with a mass of 120 metric tons traveling at 2 m/s collides and couples with an empty, stationary coal car with a mass of 8 metric tons. (1 metric ton = 103 kg) (c) What is the speed of the center of mass of the system of two cars throughout the...

Homework Statement A projectile is launched with speed v0 at an angle theta with respect to the horizontal. At the peak of its motion, it explodes into two pieces of equal mass, which continue to move in the original plane of motion. One piece strikes the ground a horizontal distance D further...

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 mass 68.8 kg sits 2.38 m from the center of mass of the rowboat toward the rear of the boat. Find x, distance from center mass of the...

[SOLVED] Center of Mass problem Homework Statement A 3.12 kg particle has the xy coordinates (-1.76 m, 0.652 m), and a 2.89 kg particle has the xy coordinates (0.380 m, -0.636 m). Both lie on a horizontal plane. At what (a)x and (b)y coordinates must you place a 3.74 kg particle such that the...

Hi all, We are now going to do a kind of experiment in which we use a plumb bob to identify the vertical direction. But I think, the pumb string will point to the center of mass, while we need the geometric center . I mean the COM of the Earth is diffent from the geometric center and it...

Homework Statement A cylin drical con crete sil o is 4m in diameter and 30m high. it consists of a 6000kg concreet base and a 38000kg concrete cylindrical concreete walls. locate the center of mass of the silo (A) when it's empty and (B) when it is two thrids full of silage whose density is...

Homework Statement While standing on a long board resting on a scaffold, a 70 kg painter paints the side of a house. If the mass of the board is 15 kg, how close to end can the painter stand without tipping the board over? http://img146.imageshack.us/my.php?image=physicssl9.jpg Homework...

Homework Statement A dog, weighing 11.1lb, is standing on a flatboat so that he is 20.0ft from the shore (to the left in Figure (a)). He walks 8.5ft on the boat toward shore and then halts. The boat weighs 40.4lb, and one can assume there is no friction between it and the water. How far is the...

Homework Statement A cubical box has been constructed from uniform metal plate of negligible thickness. The box is open at the top and has edge length L = 97 cm. Find (a) the x coordinate, (b) the y coordinate, and (c) the z coordinate of the center of mass of the box. Homework Equations...

I am looking for a way to find the center mass of an object whose area is enclosed by x^{2} and \sqrt{x} without computing the x and y seperately (a great deal of paperwork). So... M\overrightarrow{R_{cm}} = \int \overrightarrow{r} dm \sigma = \frac{M}{A} = \frac{dm}{dA} \sigma A...

Homework Statement (1) the torso, neck, and head (total mass = 42.3 kg) with a center of mass located on the y-axis at a point 0.423 m above the origin, (2) the upper legs (mass = 19.8 kg) with a center of mass located on the x-axis at a point 0.190 m to the right of the origin, and (3) the...

Can anyone give me an object where the center of mass and the center of gravity are in different locations?