Centre of mass Definition and 219 Threads

1. I have to work out the centre of mass energy of a beam collider of e-e+ each beam having an energy of 45.6Gev, That was no problem, i used the formula below and got The centre of mass = (2E)^2 = 91.2Gev. My problem arises when i apply this to a beam hitting a fixed target. The question...

Homework Statement To keep the calculations fairly simple, but still reasonable, we shall model a human leg that is 92.0m long (measured from the hip joint) by assuming that the upper leg and the lower leg (which includes the foot) have equal lengths and that each of them is uniform. For a...

I have a few questions that are driving me nuts. First: Calculate the centre of mass of the object shown below. Assume that the mass density is uniform. Place the origin, O, at the lower left. If the positive x-axis points to the right along the page, what is the x coordinate of the centre of...

1. A 280kg flatcar 21 m long is moving with a speed of 7.0 m/s along horizontal frictionless rails. A 85kg worker starts walking from one end of the car to the other in the direction of motion, with speed 1.5 m/s with respect to the car. In the time it takes for him to reach the other end, how...

Homework Statement From a uniform circular disc of radius 2 centimeter( its centre of mass is at 'O') , a circular portion of radius 1 cm is removed such that shift in centre of mass is maximum.The disc is now rotated about about 'O' perpendicular to the plane through an angle then the...

Hi, When a circular section object (cylinder, sphere of radius r) rolls down an inclined plane (at angle theta) it experiences both linear and angular acceleration due to gravity. I have read multiple times that: mg sin(theta) - friction = m a where friction = Torque/r From there on...

Homework Statement A child crouches on a swing. She is held AT REST, at 30 degrees to the vertical. The distance from her centre of mass (CM) while crouching to the suspension point is 3 m. The swing is released. When she reaches the lowest point, she SUDDENLY stands up. Her CM is now 2.6m...

Please help me in derivation of the cetre of mass of truncated sphere

Homework Statement "Alley club-ax consists of a symmetrical 8 kg stone that is 18cm long, and is attached to the end of a uniform 2.5 kg stick that is 98 cm long." Homework Equations cm = centre of mass x(cm) = x1m1 + m2x2 / (m1+m2) The Attempt at a Solution m1=8 m2=2.5 x1=9...

Homework Statement A carpenter's square has the shape of an "L," as shown at the right. Find the coordinates of its center of mass, assuming it to be made of uniform, material. (Hint: divide the L-shape into two rectangles.) Homework Equations MaXa+MbXb/(Ma + Mb) The...

Hi How would I show that the centre of mass of two point particles, one of mass m1 and the other m2, when released from rest from infinite simultaneously, stays in the same place? I feel this is a very simple question, I just can't seem to get it right. Everything I've tried still involves...

Homework Statement derivation of the centre of mass of the truncated sphere Homework Equations The Attempt at a Solution i tried to solve it with triple integrals but i failed to figure ut the integral limits

Homework Statement A uniform square metal plate of side 10 cm has a square of side 4cm cut away from one corner. (a) Find the position of the centre of mass of the remaining plate. It is now placed on a rough inclined plane as shown in the diagram. The place is inclined to the horizontal at...

Homework Statement an isosceles with base=a, height=h. It has uniform density and negligible thickness. Homework Equations determine it's centre of mass by integration,using more than one orientation The Attempt at a Solution It is a two-dimensional continuous structure. Let the...

Is there anyway of breaking up the parts of an a round spherical bottomed cone into a regular cone and a hemisphere? I can find the CM of a cone with its tip on the origin, and a hemisphere with its flat bottom in the x-y plane. Can I break the round bottomed cone up into these 2 parts? How...

Homework Statement Three uniform rods, each of length L = 22cm, form an inverted U. The vertical rods each have a mass of 14g; the horizontal rod has a mass of 42g. What are (a) the x coordinate and (b) the y coordinate of the system's centre of mass? Homework Equations x(com) = 1/M...

Hi there, I can't get my head round how to do the math for this problem. I'm sure it's not as hard as I think... Homework Statement Show that the CoM of a uniform solid hemisphere of radius r lies at a distance (3/8)r from the centre of the flat face. You may find it convenient to regard the...

Can anyone tell me that if centre of mass and load centre of gravity of a heavy vehicle doesn't concide,what vl be its effect on vehicles acceleration?

Homework Statement A woman and a man support a non-uniform plank, AB of mass 10kg and length 4m. The woman holds the plank 1m from A and the man holds the plank at B. The vertical reaction provided by the woman is 56N find; A) the vertical reaction force provided my the man b) The position at...

Homework Statement Ok, there's a cylindrical mug of mass m. When full of water it has a mass 4m. Assuming the base of the mug has no mass, how full is the water in the mug when the centre of mass is the closest to the base? (as a proportion of the height of the mug I'm guessing) The...

Homework Statement A 270 kg flatcar 20 m long is moving with a speed of 5.0 m/s along horizontal frictionless rails. A 90 kg worker starts walking from one end of the car to the other in the direction of motion, with speed 3.0 m/s with respect to the car. Homework Equations MVcm = m1v1...

Consider a free floating spacecraft in space sufficiently far from any gravitational or other external forces. The spacecraft is equipped with attitude control thrusters. The thrusters fail and fire randomly and intermittently but symmetrically about the craft's centre of mass i.e. the craft...

Hi. I'm not sure how to picture it on the x-y-axis. I found this in the textbook: If i have a plate bounce by 0<= x <=2 and 0<= y <= 3. and the density is constant. I'm looking for two integrals that corresponding to stirps in the x-direction and y-direction. let say the density is...

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

SOLVED Homework Statement A plate of of Mass m contains an ice cube of mass M and side L. Find the shift in centre of mass when th ice melts. (Gravity absent) The Attempt at a Solution I think that the centre of mass will come down by ML/2(M+m) But my book gives it zero. why? What has gravity...

Hello. Could someone possibly help me with this question? 1. The problem: The attatchment depicts a truck which has a centre of mass C. • The truck is front wheel drive. • The geometrical position of C is defined. • The coefficient of friction between the tyres and the road is μ. •...

Homework Statement the centre of mass for a 2D car is 1.125m towards the rear wheels from the front wheels, there is then 1.675m to the rear wheels. If a load with a centre of mass 0.4m from the rear wheels towards the back of the car is added how heavy does this load need to be to move the...

Homework Statement A uniform plate of mass m is suspended in the way shown. determine immediately after the connection at B has been released ;: A) angular aceleration of plate B) acceleration of its centre of mass Homework Equations before b is detached t1 + t2 = mg (Linear equillibrium) t1...

Two identical balls, each with velocity v, strike each other at right angles to each other. They stick together. Ignoring friction, (a) describe the motion of the combined ball after the collision and (b) describe the motion of the centre of mass of the two balls before and after the collision...

I'm not sure this is the right place to post this question but here goes: In feynman vol.1 39-9 there is a situation where two molecules are about to collide in a CM frame, the frame has velocity Vcm and the two molecules have respective velocities v1 and v2, then there is no correlation...

consider a symmetrical solid body. we say its centre of mass is at its geometric centre. that is, for uniform density we've taken mass to vary exactly as volume. now when the same body is taken from a place of gravitational field A to gravitational field B. say from the Earth to jupiter, this...

hi, Can anyone please help me to find the centre of mass of an object in a 3D co-ordinate system. Thanks in advance

Considering a infinite unbound universe in 4 spatial dimensions, could the cosmic expansion be explained if we consider all matter in the universe to be accelerating towards its centre of mass due to its grav pull

Homework Statement A person of mass M is standing at one end of a board of mass m and length l. The board rests upon frictionless ice surface, and its mass is uniformly distributed along its length. The person now walks to the center of the board and stops. In terms of the given quantities...

Board on Ice 1. A person of mass M is standing at one end of a board of mass m and length l. The board rests upon a frictionless ice surface and it's mass is uniformly distributed along its length. Calculate how far from the person, d, the centre of mass is of the system. The person then walks...

Hi, for the following problem http://tinyurl.com/249gz8 the answer is d What i have done is Centre of mass of velocity =(m1*v1+m2*v2)/(m1+m2) but I am not sure how does it leads to the result d... can anybody help on this?

If I cut a perfect circle into a square piece of tin, how will the centre of mass be affected? I am making the assumption that I know the dimensions of the square as well as the diameter of the circle being cut. Let's say that I also know the position of the centre of the circle relative to the...

If a force is applied at centre of mass the object will only translate and not rotate. Can anyone proove this mathematically?

consider a head on elastic collision of a bullet of rest mass M with a stationary target of rest mass m. prove that the post-collision gamma factor of the bullet cannot exceed (m^2+M^2)/(2mM) im given as a hint to prove that if P,P' are the pre and post 4 momentum of the bullet and Q,Q' are...

Homework Statement Prove that centre of mass is a unique point Homework Equations definition of CM The Attempt at a Solution I started with O as origin.G as CM and G' as assumed 2nd CM in the same sysyem of particles. OG=R=(1/M) sum(i) [m_i*r_i] OG'=R'=(1/M) sum(k)...

im actually bugged of finding a solution for d topic mentioned can any 1 pleasezzz help me

Hey here is a quick question. I have a question on an assignment that is asking me to define lift in an aircraft (done) and its relationship to the aircraft's centre of mass. I'm unsure how to do that second bit as lift acts through the centre of pressure...not the centre of mass (also known as...

Prove that the magnitude of R of the position vector for the centre of mass from an arbitrary origin is given by the equation: M^2R^2 = M\sum m_ir_i^2 - {1\over 2}\sum m_i m_j r_{ij}^2 Well the centre of mass is given by: \vec R = \frac{\sum m_i r_i}{M} But squaring this doesn't seem to...

A station wagon of mass 2000kg has a wheelbase (distance between front and rear axles) of 3.0m. Ordinarily 1100kg rests on the front wheels and 900kg on the rear wheels. A box of mass 200kg is now placed on the tailgate, 1.0m behind the rear axle. How much total weight now rests on the front...

Wondering if someone could help me get this answer. I don't get spherical coordinates at all. The volume of the region given in spherical coordinates by the inequalities 3 less than or equal to rho less than or equal to 5 0 less than or equal to phi less than or equal to pi/6 -pi/6 less...

hello , could anyone explain to me the difference between a.) the centre of mass b.) the centre of gravity much aprreciated =) Cheers

http://i3.tinypic.com/wmjdqh.jpg its question number 10 hi all i was wondering if you could help me with my centre off mass question sthanks the diagram shows a thing uniform sqaure of metal which has a corner folded over. Calculate the distance the centre of mass of ABCDEF is from A...

why is it that a wise cyclist carries his load in packs on his bicycle intead of on her back? this is a poor question because of an assumption it makes. i understand that by carrying the load on the bicycle instead of on his back the cyclist lowers the ecntre of mass so that it is harder for...

For a distributed mass, F = M dv/dt where F is the total external force, M the total mass, and v the velocity of the centre of mass. But take the case of a gyroscope, where the force acting on the centre of mass is gravity, assuming it is uniform over the body. The gyroscope doesn't topple...

Hi, I appreciate that we can calculate the x-coordinate of the centre of mass of a system of bodies like this: x = (m_{1}x_{1} + m_{2}x_{2} + m_{3}x_{3} + ... + m_{n}x_{n}) / M where M is the total mass. This could be rewritten as x = \frac {1} {M} \sum_{i=1}^n m_{i}x_{i} My next step...