Center of mass Definition and 900 Threads

Homework Statement Given: g=9.8 m/ss Given: A uniform flexible chain whose mass is 7 kg and length is 5 m. Given: A small frictionless pulley whose circumference is negligible compared to the length of the chain. Problem: Initially the chain is hung over the pulley with nearly equal...

To determine the location of the center of mass of a car, the car is driven over a scale. When the front wheels are over the scale, the weight recorded by the scale is 5.70 x 103 N. When the rear wheels are over the scale, the scale reads 6.30 x 103 N. The distance between the front and rear...

Homework Statement A block of mass M = 15 kg moves with velocity V and explodes at the origin into two pieces of masses m1 = 10 kg and m2 = 5 kg. The piece m1 moves in the positive direction of y-axis with speed v1 = 4.5 m/s, whereas the other piece m2 moves in the positive direction of...

Homework Statement What is the center of mass a hollow 2D right triangle having legs of length A and B. The sides of the triangle are also extremely thin. Assume uniform density. Homework Equations \overline{x}=∫xmdx/∫mdx The Attempt at a Solution...

A solid hemisphere of radius r given by: x2+y2+z2= r2, z ≥ 0 Suppose the density of the hemisphere is the constant δ. The coordinates of the center of mass (a,b,c) are given by: a=(∭ xδdV) / (∭ δdV) b=(∭ yδdV) / (∭ δdV) c=(∭ zδdV) / (∭ δdV) Find a, b ,c ** So far what i...

I tried this problem but only managed to somewhat understand Part A. But that answer is wrong as well, so can someone guide me through steps of finding the answer: Thank you. To keep the calculations fairly simple, but still reasonable, we shall model a human leg that is 0.92 m long (measured...

Consider a system of several point-masses separated by large distances and moving with relativistic speeds in relation to one another. GR says that gravitational waves travel at the speed of light. SR says that simultaneity often does not exist for such point-masses. Question: Is it possible...

In this problem we will examine the collision between a baseball (the cowhide) and a bat (the ash). We assume a one-dimensional problem. That is, the bat hits the ball squarely, so that the ball reverses its direction after the collision. We also assume that the ball hits the bat at the center...

Homework Statement I'm building a hovercraft, and I'm familiar with how to calculate center of mass--however, there's something that will be sitting on the surface of the hovercraft that's throwing me off. I just can't seem to get it to work. I'm just trying to find what the mass would be at...

Let vectors vec{A}=(0,0,-3), vec{B}=(2,0,0), and vec{C}=(0,1,1). Calculate the following, expressing your answers as ordered triples (three comma-separated numbers). Calculate A x C. For this part, remember that only perpendicular components contribute to the cross-product. The vector C has...

Question: Determine the location of the center of mass of a "L" whose thin vertical and horizontal members have the same length L and the same mass M. Use the formal definition to find the x and y coordinates, and check your result by doing the calculation with respect to two different...

[FONT="Century Gothic"][SIZE="1"]Homework Statement A big olive (m = 0.051 kg) lies at the origin of an xy coordinate system, and a big Brazil nut (M = 0.56 kg) lies at the point (0.81, 3.0) m. At t = 0, a force Fo = (2.6 + 1.7) N begins to act on the olive, and a force Fn = (-4.4 -3.4) N...

Homework Statement A baseball player holds a 36-ounce bat (weight = 10.0 Newton) with one hand at the point O. The bat is in equilibrium. The weight of the bat acts along a line 60 centimeters to the right of O. What is the torque exerted on the center of mass of the bat by the player...

1. Ball 1, ball 2, and ball 3 have masses 1 kg, 2 kg, and 3 kg respectively, and are initially arranged at x = 5 m, x = 10 m, and x = 15 m respectively (see picture). y = 5 m for all three balls. Now suppose that a net force of 1 N is applied to ball 1 in the +y direction and a net force of 2 N...

1. Ball 1, ball 2, and ball 3 have masses 1 kg, 2 kg, and 3 kg respectively, and are initially arranged at x = 5 m, x = 10 m, and x = 15 m respectively (see picture). y = 5 m for all three balls. Now suppose that a net force of 1 N is applied to ball 1 in the +y direction and a net force of 2 N...

Homework Statement Consider the Sun and the Earth as a 'system' of two 'particles'. The center of mass of this system lies a distance L from the center of the Sun. Find L and compare it to the radius of the Sun. The center of mass of the Earth-Sun system lies? A. inside the radius of the...

Homework Statement A man decides to boat out on the lake for a relaxing day of fishing. At one point during the day, he finds himself facing the shore. He judges that he is a distance Dinit = 35 ft from the shore. The man has a mass of Mman = 190 lbs, and the boat a mass of Mboat = 270 lbs. The...

Homework Statement A puck with a mass of 0.08 kg and a radius of 0.04 m slides along an air table at a speed of 1.5 m/s. It makes a glancing collision with a second puck at rest having a radius of 0.06 m and a mass of 0.12 kg such that their rims just touch. Because their rims are coated...

Homework Statement In Fig. 9-39, three uniform thin rods, each of length L = 28 cm, form an inverted U. The vertical rods each have a mass of 12 g; the horizontal rod has a mass of 31 g. What are (a) the x coordinate and (b) the y coordinate of the system's center of mass? (Give your answer in...

Homework Statement alley club-ax consists of a symmetrical 8 kg stone attached to the end of a uniform 2.5 kg stick that is 98 cm long. How far is the center of mass from the angle end of the club-ax? Homework Equations Xcm = (sum) x*m / m The Attempt at a Solution I don't know...

Is it because less force (from, say, potential objects that could tip the object) is required to exert the same amount of torque on objects with higher center of mass?

1. A pellet gun fires ten 2.0 g pellets per second with a speed of 500 m/s. The pellets are stopped by a rigid wall. What are (a) the magnitude of the momentum of each pellet, (b) the kinetic energy of each pellet, and (c) the magnitude of the average force on the wall from the stream of...

Is it different from the center of mass? My book says yes but doesn't answer the question.

Homework Statement If x is the height of the remaining soda at any time in a can of soda, find x (in terems of M, H, and m) when the center of mass is the lowest. {{The soda is draining out of the bottom of the can}} Also, the Can and soda have uniform density. So the can is set up so...

Homework Statement A rod of length 24.5 cm has linear density (mass-per-length) given by the following equation, where x is the distance from one end. λ = 50.0 g/m + 20.5x g/m2 (a) What is its mass? (b) How far from the x = 0 end is its center of mass? Homework Equations...

Urgent ! Center of mass and relevant stuffs Homework Statement A vertical spring of constant k is attached at the bottom to a platform of mass mp, and at the top to a massless cup. The platform rests on a scale. A ball of mass mb is placed in the cup. What is the reading on the sacle when...

Homework Statement A baseball bat of length L has a peculiar linear density given by \lambda = \lambda0 * (1+X2/L2) Find the x coordinate of the center of mass in terms of L Homework Equations Mxcm= mr The Attempt at a Solution So I use integration The integrand I have is x*\lambda dx...

Homework Statement A box with its center of mass off-center as indicated by the dot is placed on an inclined plane. In which orientation does the box tip over? Homework Equations Teacher didn't even mention anything related to this The Attempt at a Solution Since the CM was at...

Hey guys, does anyone know a good website teaching center of mass? I need to know how to find the center of mass of objects like spheres, cubes etc. and also do problems such as "a man is standing on a boat and moves from one side to the other, how far does the boat move." Stuff like that...

Homework Statement To determine the location of the center of mass of a car, the car is driven over a scale. When the front wheels are over the scale, the weight recorded by the scale is 5.05 x 103 N. When the rear wheels are over the scale, the scale reads 6.20 x 103 N. The distance between...

1. A right circulat cone of constant density (5kg per m^3) is 4 meters from the base to the tip. the diameter of the base is 6 m. find each of the following using inergrals A) Find the volume and mass of the cone B) find the center of mass of the cone C) find the moment of inertia of the...

Homework Statement From an inertial reference frame S, the vector position of a particle of mass m1 = 1kg is given by r1(t)=(txhat - t^2yhat)m. The vector position of a particle m2=2m1 is given by r2=(t)=(txhat +t^3yhat)m Assume t=1second Find the position, the velocity and the...

If you guys would be kind enough to show me if my attempt to problems posted are correct or incorrect. Homework Statement A uniform 3.0 kg cylinder of radius 0.15 m is suspended by two strings wrapped around it, as shown in the figure below. As the cylinder descends, the strings unwind from...

Homework Statement I am very fuzzy about how to find the center of mass of an object and, similarly, the moment of inertia for an object using integrals. Here are the formulas as I remember them. Center of mass: (1/M) \int \vec{r} dm Moment of Inertia: \int R^{2} dm What I was...

A uniform spherical shell of mass 9.00 with diameter 54.0 has four small masses of mass 2.00 attached to its outer surface and equally spaced around it. This combination is spinning about an axis running through the center of the sphere and two of the small masses What friction torque is...

Homework Statement Find the mass and center of mass of the solid bounded by the planes x=0, y=0, z=0, x+y+z=1; density\delta(x,y,z)=y Homework Equations M=\int\int_D\int\delta dV M_{yz}\int\int_D\int x \delta dV;M_{xz}\int\int_D\int y \delta dV;M_{xy}\int\int_D\int z \delta dV...

Before begining, I would like to point out I did look at the following thread previous to this one, and thus have a few questions about that thread and it's application to this one: https://www.physicsforums.com/showthread.php?t=143536 Homework Statement The problem...

Homework Statement A pendulum consists of a uniform disk with radius r=0.100m and mass 0.500 kg attached to the end of a uniform rod with length L=0.500 m and m 0.250 kg. It pivots at the other end of the rod. a) Calculate the rotational inertia of the pendulum about the pivot point. b) What...

Homework Statement 3 identical rectangular blocks on frictionless surface have equal magnitudes of force and in the same direction are exerted on them. The CoM is the same for all the blocks and in the center of the rectangle. For block 1, the force is exerted to the left of the CoM, and...

Homework Statement http://img201.imageshack.us/img201/2135/21592808vx2.th.jpg http://g.imageshack.us/thpix.php In class you learned that when a person walks, their centre of mass must be positioned directly above the foot their weight is resting on. The figure shows the anatomy of the...

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=...

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...