Centre of mass Definition and 219 Threads

Homework Statement Find the velocity of the centre of mass of two photons with different energies (they happen to be approaching). Homework Equations E = hf p(photon) = E/C E=gamma(mc^2) The Attempt at a Solution I have calculated the energy of the two photons in the centre of mass...

Homework Statement A high-energy photon γ1 of energy 261 GeV collides with an infrared photon γ2 of energy 1eV to produce an electron-positron pair via the reaction γ1 + γ2 → e- + e+ The Attempt at a Solution Conservation of momentum: p1 - p2 = (0.5)pe...

1. A stationary pulley carries a rope,one end of which supports a ladder with a man and the other a counter weight mass M.The man of mass 'm' climbs up a distance "L" wrt the ladder and then stops.The displacement of CM of the system is? Homework Equations How do i approach this question...

Homework Statement A symmetric block of mass M1 with a groove of hemisphere shape of radius R rests on a smooth horizontal surface in contact with the wall as shown in the figure. A small block of mass m2 slides without friction from the initial position .Find the maximum velocity of the block...

Homework Statement Three identical balls are connected by light inextensible strings with each other as shown and rest over a smooth horizontal table .At the moment t=0,ball B is imparted a velocity.Calculate the velocity of A when it collides with ball C. Homework Equations The Attempt at a...

http://examsolutions.co.uk/a-level-maths-papers/Edexcel/Mechanics/Mechanics-M2/2010-June/paper.php Question 3) part a) I got the answer to be 2.5 which is correct part b) I don't really get how to do this, I understand as a new particle is being added which is the same mass of the...

The diagram shows a pendant in the shape of a sector of a circle with center A. The radius is 4 cm and the angle at A is 0.4 radians. Three small holes of radius 0.1 cm, 0.2cm and 0.3 cm are cut away. The diameters of the holes lie along the axis of symmetry and their centers are 1, 2 and 3 cm...

Homework Statement The question is posted here: http://galileo.phys.virginia.edu/classes/252/mass_and_energy.html I'm not too convinced by their explanation of 'compensation of shift in centre of mass' The Attempt at a Solution What I understand is this: 1)Box of mass M moves distance d...

Homework Statement A pulley fixed to a rigid support carries a rope whose one end is tied to a ladder with a man and the other end to a counterweight of mass M. The man of mass m climbs up a distance h with respect to the ladder and then stops. If the mass of the rope and the friction in the...

I know that for a system of particles, the x, y and z coordinates of the centre of mass are given by (\frac{1}{M} \sum_{i = 1}^{n} m_i x_i, \frac{1}{M} \sum_{i = 1}^{n} m_i y_i,\frac{1}{M} \sum_{i = 1}^{n} m_i z_i). For a solid body, we can treat this like a continuous distribution of matter...

Homework Statement The question is attached in the picture. I did part (a) without much problems.. But I have no clue what part (b) is about at all! Even the solutions don't make much sense to me. The Attempt at a Solution I tried to work out how the diagram would look like...

Homework Statement The question is attached in the first picture. The Attempt at a Solution The method they used makes perfect sense, but I can't see what's wrong with my method. Their method 1. Find individual centre of mass of each semi-circle by Pappus's 2nd theorem 2. Sum up...

a triangle ABC with AB=BC=2a and AC=2a rt(2) is drawn on a uniform lamina. A semi-circle is drawn on BC as diameter,on the opposite side of BC from A and the area enclosed by the triangle and the semi-circle is cut out. The resulting lamina is suspended freely from B,show that AB makes an angle...

If a large, stable floating object is placed in the ocean, free floating, and the tides and currents act on that object causing it to rotate, will it always rotate about its center of mass?

Homework Statement 2 equal masses 'm' are attached to a spring of spring constant 'K' and unstretched length 'L'. The system is rotating about its centre of with an angular velocity 'w'. The linear velocity 'v' of m is comparable to that of speed of light 'c'. Find a relation between the...

Homework Statement One particle, mass m1, is fired vertically upwards with an initial velocity v0 from the ground (height y = 0). At the same time (t = 0), another particle, mass m2, is released from rest at a height y = h, directly above the first, where h > 0. The particles are then in...

Homework Statement The exercise asks you to calculate the magnitude of the magnetic field (\vec{B}=B\hat{z}), knowing that the U shaped conductor is initially parallel to Oyz plane and then rotated around the y-axis to a stable position defined by θ (angle) with the vertical axis (z). The U...

Homework Statement Why is the attachment true? (It's from my notes) Homework Equations General centre of mass equations The Attempt at a Solution Really not sure how the lecturer did this. It's quoted as if it's obvious but I don't see it at all, this has been annoying me for a...

Homework Statement A non uniform rod of length L=1m and linear mass density: λ(x)=λo(1-(x/2L)) with λo=1Kg/m. It is supported at it's midpoint and initially tips over so that it's left end lies on the ground. Part a: Find the position of the centre of mass along the rod when it is in it's...

I've just found out that in the centre of mass frame, the angle of deflection in a collision is different from in the lab frame. I vaguely understand why: if the frame you viewed the particles in was also moving but only horizontally it would make their horizontal movement appear to decrease...

Hi,today my teacher said that there is a little bit different between centre of mass and centre of gravity. But he said there is no different between them in my level(teenager) What is the different between them and why we can ignore the differences?

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 3 800 kg/m3. The monument is 15.7 m high and 64.8 m wide at its base and is everywhere 3.60 m thick...

Homework Statement Two balls with masses m1 and m2 moving on a horizontal table in the same direction but at different speeds collide elastically. Obtain expressions for the position and motion of the centre of mass in terms of the separate positions and motions of the two balls before...

Homework Statement Find the centre of mass of the 2-dimensional plate which occupies the region inside the circle x^2+y^2=2x, but outside x^2+y^2=1, and for which the density is proportional to its distance from the origin. Homework Equations Centre of mass for x coordinate: 1/m ∫∫ x ρ(x,y)...

How do you calculate the centroid of the earth-moon system? Is it this exact point that the moon-earth system orbits? Is it an elliptical or circular orbit?

A uniform lamina ABCD is in the shape of a parallelogram and its mass per unit area is u. Axes Ox, Oy are chosen, with O the point on AB such that AO = 2/3AB. Points A, B, C and D have coordinates (-2a, O), (a, O), (2a, b) and (-a, b) respectively. Find the x and y coordinates of the centre...

What is moment of mass of system of particles? And how it relates centre of mass...?

hii.. this is shruti... i want to make an inverted linear pendulum of bi ped humanoid robo... can any 1 help me in calculating the centre of mass and centre of gravity... of a humanoid robot...

What does it mean for a body (or many bodies) to have the centre of mass at a certain point? How does the formula for finding the centre of mass find it? How can you describe the centre of mass with respect to the other particles of an object?

Hi all I am new here! can anyone tell me how can i rotate the object around it's center of mass and not the origin of Cartesian co-ordinates(0,0).. thanks in advance for help..

Homework Statement A 5m long uniform plank of mass 8kg is supported by two pillars at 0.5m and 3m from the left hand end. a 20kg child walks along the plank towards the right hand end. calculate 1. the position the child ia at when the plank begins to tip 2. the forces exerted by the...

Homework Statement The proposed maximum colliding beam energy, Ec, in the Large Hadron Collider is 7TeV per beam (proton-proton collisions). By a Lorenz transformation, show clearly that to produce the same centre of mass energy in a 'fixed target' interaction, the beam energy woulr have to...

Homework Statement A square of side 2R has a circular hole of radius R/2 removed from one quarter (see file attachment). The centre of the hole is located at (R/2, R/2) from the centre. Locate the centre of mass with respect to the centre of the square. Homework Equations The...

Homework Statement A chain hangs b'n two points in the vertical plane, find its centre of mass. I have no idea where to start. Homework Equations The Attempt at a Solution

Homework Statement Hi I am really stuck on this problem. It reads as such: A uniform triangular lamina is isocceles and has the line y= 4 as its axis of symmetry. One of the vertices of the triangle is the point (2,1). Given that the x-co-ordinate of the centre of mass of the lamina is -3...

Homework Statement Hey everyone, I'm studying for my physics and came across a question for the COM of a hemisphere. However, I was wondering what methods there are to find the COM of a hemispherical shell instead. Any insight would be very much appreciated! =) After much of tearing Google...

Homework Statement Two identical blocks of mass m are attached via a massless spring of spring constant k. The length of the spring in equilibrium is l. The system moves on a frictionless horizontal plane. With one block resting against a wall, the two blocks are pushed to- gether, so...

Homework Statement Refer to attachments, this question is insane. Homework Equations Yet to determine how to break down the fork and which equations to apply The Attempt at a Solution I have tried to break down the fork into rectangles and triangles, any suggestions about how to...

Homework Statement What is the Relation between center of mass and center of gravity, please compare with simple example. Bco'z i am very confused about it Homework Equations The Attempt at a Solution

Homework Statement I'm doing my lab and my TA didn't really explain how we obtain the centre of mass. Basically the lab is you have a ruler and you make it horizontal and measure the force along it using a scale (obviously in Newtons)... So you measure the distance of the force from the...

Homework Statement Prove that the magnitude R of the position vector for the centre of mass from an arbitrary origin is given by the equation M2R2 = M\summiri2 - (1/2)\summimjrij2 Homework Equations F = MR'' F = p' p = \summjrj' The Attempt at a Solution I'm not...

Homework Statement determine the position of the centre of mass of a flat sheet of metal of homogeneous density rho. The sheet lies within the area bounded by the equations y=x^4 and y=5 Homework Equations integral centre mass The Attempt at a Solution a slightly trivial question...

I am trying to find the centre of mass of a projectile nose. I profoundly suck at integration, but I have managed to work out area, and now I'm battling centre of mass. Am I doing this correctly? Is my final integral correct? x = \sqrt{r_{1}^{2} - y^{2}} - (r_{1} - s_{2}) \int{x \;\delta y} =...

hi, I'm stuck and I can't seem to find a simple solution to questions regarding how to find the centre of mass of a lamina. for example: A uniform lamina with mass/unit area 0.12grams/cm2 consists of a square of side 80cm, with one corner at the origin O(0, 0) and other corners at B(80, 0)...

Homework Statement Let Ω be a tank whose shape is that of the lower hemisphere of radius R. The tank with a muddy suspension whose density ρ is ρ(x,y,z):=e^-h(x,y,z), where h(x,y,z) is the height of (x,y,z) above the lowest point of the tank. Find the center of mass in the tank Homework...

Homework Statement Let Ω be a tank whose shape is that of the lower hemisphere of radius R. The tank with a muddy suspension whose density ρ is ρ(x,y,z):=e^-h(x,y,z), where h(x,y,z) is the height of (x,y,z) above the lowest point of the tank. Find the center of mass in the tankHomework...

for a system of particles why is centre of mass independent of the origin?

Urgent Help Needed- Finding the speed at the centre of mass? Please help me :( Hi, I was attempting to work through this question. Anyways, I was working from a graph, so the radius 2.5 cm, the two of them collided, it was an inelastic collision as the two objects did part ways, so how do I...

Urgent Help Needed- Finding the speed at the centre of mass? Please help me :( Hi, I was attempting to work through this question. Anyways, I was working from a graph, so the radius 2.5 cm, the two of them collided, it was an inelastic collision as the two objects did part ways, so how do I...

Hi, I was attempting to work through this question. Anyways, I was working from a graph, so the radius 2.5 cm, the two of them collided, it was an inelastic collision as the two objects did part ways, so how do I find the centre of gravity? I attempted to calculate it... but if someone could...