Center of mass Definition and 916 Threads

I came across a particular result which bothered me, it stated that: Result: A person bending to 90 degrees at the waist with their back to a cliff will fall because their center of mass is past their feet. This statement perturbed me, because, when I applied it myself, I found that, while I...

A thin rectangular plate of uniform area density = 2.86 kg/m^2 has a length of 42.0 cm and a width of 23.0 cm. The lower left hand corner is located at the origin, (x,y)=(0,0) and the length is along the x-axis. There is a circular hole of radius 7.00 cm with center at (x,y)= (15.00, 9.50) cm...

Two blocks each of length L are piled near the end of the table. What is the maximum distance between the edge of the table and the edge of the outer block before the system topples? I understand that if the center of mass of the system must be to the left of the edge of the table for the...

I need to find the center of mass of a cone with point facing downwards, of height H and radius R. Since the density is constant throughout and because of axial symmetry the center must be somewhere on the z-axis. I know from convention that this is H/4 but i need to derive this. Rcm...

The triangle has uniform surface mass density of. The method that I've been taught involves some basic integration and substitution of dm for (Density X dA). And then substituting dA with one expression in terms of dy, and another in terms of dx. I don't really like the method I was...

An object rolls because of friction yea? So does that mean a torque is produced when the ball is given an initial push? I mean there is a force, and the force is perpendicular to the line which connects to the center of rotation, so this would be logical yea? But if there is a torque, then...

Why when we throw an extended object like a baseball bat will the center of mass follow the same parabolic path that we expect for a smaller obeject like ball, while the bat itself will rotate around this ceneter of mass? Why does center of mass behave like a simpler object? thank you

i don't understand how can the center of mass = (L/4, L/4) the hint is provided. based on the hint, i would write the answer is (L/2, L/2) :confused:

1. How is it that when high jumpers go over bars, their centers of mass pass underneath? 2. why must a hockey stick that is thrown rotating on ice stop rotating at exactly the same time as when the center of mass comes to rest?

it is said that the posiion vector of the cener of mass of a rigid body can be obtained by: r_{CM}= \frac{1}{M} \int r dm I'm not sure I understand this expression. What exactly is dm? and I thought it was the sumation of mass times distance divided by the total mass...

Hi, I was hoping to gather some feedback for one of my homework problems. Any help would be much appreciated. The problem is as follows: A mortar fires a shell of mass m at speed v_0. The shell explodes at the top of its trajectory as designed. However, rather than creating a shower of...

A 2.81 kg hollow cylinder with inner radius 0.29 m and outer radius 0.5 m rolls without slipping when it is pulled by a horizontal string with a force of 47.7 N, as shown in the diagram below. Its moment of inertia about the center of mass is .5m(r(out)^2 + r(in)^2). What is the...

A solid shere of mass M and radius R rolls without slipping down an inclined plane whose incline angle with the horizontal is 30 degrees. What is the acceleration of the sphere's center of mass? gsinX is the acceleration, so it would be g/2 right?

I am having the hardest time figuring out the center of mass of this problem. A sheet of metal is cut in the shape of a parabola (imagine that you have a parabola shape with the top being flat). The curved edge of the sheet is specified by the equation y=ax^2, and y ranges from 0 to b. Find...

I have been missing for class 3days and i was get lost because my daughter gets sick in the past weeks :cry: :( until todate. The problems i need everyone helps below are just a sample exam. I have contact my professor about my family problems and he was nice, gave me the sample exam which it's...

Greetz :) I recently found this problem and have made a few attempts at answering it but still have not found an answer i am 100% confident with, I would appreciate it if anyone who is keen to attempt it could give some advice and explanations for their reasoning in the solving of this...

On a frictionless table, a glob of clay of mass 0.740 kg strikes a bar of mass 1.740 kg perpendicularly at a point 0.140 m from the center of the bar and sticks to it. If the bar is 0.660 m long and the clay is moving at 9.600 m/s before the impact, what is the final speed of the center of mass...

Here is the problem: A region is defined as being bounded by the parabola x = y^2 and the line y = x - 2. The density of this region is \delta = 3x. a) Find the center of mass. b) Find the moment of inertia about the y-axis. c) Find the radius of gyration about the y-axis...

Two balls of masses m1 and m2 are moving along x-axis w/ velocities, v1>v2>0. After transforming from the lab frame to the center-of-mass frame, what are the velocities of m1, v1com, and mass m2, v2com? Vcom is the center of mass velocity for the system of both balls. The choices are...

A cone of height h and base radius r has density equal to distance from its base. Find it's center of mass. How do I write a function for the density? Is it p=h-z? And what are the limits of r if I want to do this in cylindrical coordinates? Thanks in adv.

question is http://home.earthlink.net/~urban-xrisis/clip003.jpg I'm guessing that the center of mass has to be in the edge. I'm not sure how to set it up so that I can find the most distance. any ideas?

Been trying this one using: x1m1 = x2m2 I guess I just maybe am not using the right mass or length for center of mass.. Here's the question: A 0.19 kg meter stick balances at its center. If a necklace is suspended from one end of the stick, the balance point moves 16.3 cm toward that...

I feel silly for ask you for help on this simple center of mass problem but i got wrong answers... 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...

a solid sphere of mass M and radius R rolls without slipping down an incluned plane whose incline angle with the horizontal is 30 degrees. That is the acceleration f the sphere's center of mass? not sure how to attack this problem. Any equations and leads would be appreciated.

I'm having a difficult time with this question, and I'm sure it's easy. The question is, find the center of mass of the three-mass system. Specify relative to the left-hand 1.00kg mass. Mass1 = 1kg Distance = 0m? Mass2 = 1.5kg Distance = .50m Mass3 = 1.1kg Distance = .75m I'm...

A thin rectangular plate of uniform areal density 2.96 kg/m2 has length 42.0 cm and width 26.0 cm. The lower left hand corner is located at the origin, (x,y)= (0,0) and the length is along the x-axis. There is a circular hole of radius 5.50 cm with center at (x,y)=(15.00,11.00) cm in the plate...

A uniform plate of height 1.59 m is cut in the form of a parabolic section. The lower boundary of the plate is defined by: y=0.65x^2. Find the distance from the rounded tip of the plate to the center of mass. i tried to do this usin calculus and got the answer Ycm=1.01 which was wrong and...

Any hints on how to approach this problem? A lamina occupies the part of the disk x^2 + y^2 <= 1 in the first quadrant. Find the center of mass if the density at any point is proportional to the square of its distance from the origin

Hello everyone. I'm burning my head at this one, maybe someone could offer some insight? Here's the deal: imagine two masses, m1 and m2, united by a massless spring, of length l (relaxed). m1 | | _ > spring, at length l (relaxed) | ___m2____ ground The system has...

What is the equation to find the velocity of the center of mass? since... x_{CofM}=\frac{m_1x_1+m_2x_2}{M_{total}} then... v_{CofM}=\frac{d(m_1x_1+m_2x_2)}{dt(M_{total})} this means... if p=momentum v_{CofM}=\frac{p}{M_{total}} is this correct?

A uniform square plate L = 5.9 m on a side as a square section d = 2.5 m cut out of one side. What is the center of mass of the remaining plate? Use a coordinate system with origin (0, 0) at the center of the plate. The answer must be given in components. X = ? Y = ?. From the...

A little confused, could someone explain what it means when it is said that "the point in a body or a system of bodies, at which the total mass of the body or system may be regarded as concentrated".(definition of Center of mass) What does it mean concentrated? I'm trying to understand the...

Part of my problem for physics is finding how far a person can move along a floating board. The board is not acted on by any outside forces so the center of mass before the person starts moving and the center of mass afterwards stays the same. Their is no air friction on the board. The Person...

Would anyone be able to give me a hint for this question? Do I take the integral? I have possible answers but I am unsure. A rod of length 30.0 cm has a linear density given by: D = 50.0g/m + 20.0xg/m^2 where x is the distance from one end measured in meters. a. What is the mass of...

The problem is a dog weighing 10lb is standing on a flatboat so that he is 20ft from the shore. He walks 8 ft on the boat toward shoare and then halts. The boat weighs 40 lb, and one can assume there is no friction between it and the water. How far is the dog from the shore at the end of this...

Although this seems simple, I don't think I'm reading the problem right. Currently we are studying center of mass such as the velocity and position of the center of mass. The problem is a shell is fired from a gun with a muzzle velocity of 1500ft/s at an angle of 60 degrees with the...

I don't know how to treat a center of mass corrections. Suppose to have a Slater determinant of N single-particle wavefunctions. If I make a traslation to center of mass of system, this is mean to move all particle in the following way: R_i ---> R_i - (sum_j {R_j}/N) But how have I to...

Hey guys. this is my first time posting. can anyone tell me how to calculate the Y component of center of mass of a right triangle?? Major help would be appreciated :-D please email me at fakedoublebassdrummer@yahoo.com

Hey guys. this is my first time posting. can anyone tell me how to calculate the Y component of center of mass of a right triangle?? Major help would be appreciated :-D please email me at [email address deleted]

Hey guys, this is my first thread here. I'm just looking for a hint or two (no answer please). A sphere of styrofoam has radius R. A cavity of radius R/2 centered a distance R/2 directly above the center of the sphere is hollowed out and filled with a solid material of density five times...

A right cyllindrical can with mass M, height H, and uniform density is initially filled with soda of mass m. We punch small holes in the top and bottom to drain the soda; we then consider the height of the center of mass of the can and any soda within it. If x is the height of the remaining soda...

A thin 8.0 kg wheel of radius 28 cm is weighted to one side by a 5 kg weight, small in size, placed 10 cm from the center of the wheel. (a) Calculate the position of the center of mass of the weighted wheel. choosing the 8.0kg wheel to be on the origin, my cm is (8.0*0+5*0.1)/(8+5)...

A man of mass 83.8 kg stands on top of a uniform ladder whose mass is 11 kg and whose length is 8.7 meters. Find the distance (in meters) from the base of the ladder to the center of mass. Here's what I did: X(center of mass) = (83.8*8.7) + (11*0) / (83.8+11) = 7.69meters but the...

A thin 6.0 kg wheel of radius 30 cm is weighted to one side by a 2.0 kg weight, small in size, placed 24 cm from the center of the wheel. Calculate the position of the center of mass of the weighted wheel. Here's what I have so far. I set the origin as the center of the wheel. Center of...

PRoblem: A 4.00-kg block is traveling to the right at 5.50 m/s, and a second 4.00-kg block is traveling to the left at 4.00 m/s. Find the total kinetic energy of the two blocks in this reference frame. I did this by adding the two kinetic energies from the equation K =p^2/2m. It then asks...

With the engines off, a spaceship is coasting at a velocity of +250 m/s through outer space. The ship carries rockets that are mounted in firing tubes, the back ends of which are closed. It fires a rocket straight ahead at an enemy vessel. The mass of the rocket is 1200 kg, and the mass of the...

With the engines off, a spaceship is coasting at a velocity of +250 m/s through outer space. The ship carries rockets that are mounted in firing tubes, the back ends of which are closed. It fires a rocket straight ahead at an enemy vessel. The mass of the rocket is 1200 kg, and the mass of the...

A uniform thin wire is bent into a semicircle of radius r. Determine the coordinates of its center of mass with respect to an origin of coordinates at the center of the "full" circle. (The semicircle is in the positive y plane.)

I know how to find the center of mass of a 2 dimensional object like a piece of plywood or something like that, but when it comes to 3-D objects I'm clueless. All I know is Mx=x1m1+x2m2+...xnmn here is my problem, i don't know if i should split the pyramid into 4ths or not. The Great...

Problem: The real problem is that apparently the professor explained this on monday and I didn't make it to the class. So really, any nudges in the right direction will be greatly appreciated.