System of particles Definition and 49 Threads

Why is the center of mass acceleration zero? Did I do anything wrong?

So i was able to solve the angular velocity part but i don't know how to find the velocity of centre of mass . For the first part i simply conserved momentum about COM because if i consider the particles as a part of the same system as rod the collision are internal forces . I am mainly...

We know that if we take two particles and assume no external force is applied then by Newtons third law total momentum gets conserved after collision. If we take three particles and there is collision between them and no external force then the momentum is again conserved for each pair like in...

Hello guys, I’m studying Newton’s Mechanics at the first year of engineering, and I would like to ask one question about torque. In my book I found this statement ‘’ Given a system of particles, it’s always possible to determine a pair of forces which torque is indipedent from the pole chosen...

I think it is quite simple as an exercise, following the two relevant equations, but at the beginning I find myself stuck in going to identify the lagrangian for a relativistic system of non-interacting particles. For a free relativistic particle I know that lagrangian is...

Since there are no external forces, the angular momentum (##L##) and linear momentum (##P##) are conserved. Let's call the left rod ##A## and the right one ##B##. If all the balls were fixed, I'd write ##L_0=L_f## ##L_A+L_B=(I_A+I_B)\omega_f## From this equation I can find the final angular...

Suppose we have a system of particles being acted upon by a single external force ##\mathbf{F}^{e}##. Each individual particle feels a force of ##\mathbf{f}_i = \mathbf{f}_{i}^{int} + \mathbf{f}_{i}^{e}## such that ##\sum_i \mathbf{f}_{i}^{e} = \mathbf{F}^{e}##, and ##\mathbf{f}_{i}^{int}## are...

I have known and used this theorem for a long time solving problems ("Calculate the CM of the some given shape"). I took the theorem to be "obvious" and didn't know it could be proved (and that indeed it was a theorem at all). I can make no attempt at the proof. Any help would be welcome.

I have a project to make the solar system. I am trying to start from somwhere. On the notes it says that we need to start by creating a System of Particles Two-body simulation (Circular motion) Implement Gravitational acceleration Each particle (planet) could have its own field. I.e. Each...

Let, we want to calculate the P.E(potential energy) of a system containing 3particles p1,p2,p3.the point of observation is P.so now we should add up the P.E at P due to p1,p2,p3 to get the net potential energy of the system,but why we take the P.E of particles due to each other into count...

Hi! I want to start solving problems from the text 'Orbital Mechanics for Engineering students' by Curtis 2nd edition. Is this the right place to post? Homework Statement 2.1 Two particles of identical mass m are acted on only by the gravitational force of one upon the other. If the distance d...

I have heard it said that in classical physics that if one knows all the particles of a systems momentums and positions, that the evolution of the system can be completely known. I would imagine this also would have to include the nature of all the forces acting on the particle. Also, for...

Question: A) Derive the work - energy theorem for one particle. B) Check whether it is applicable for a system of particles and a rigid bodyWork - energy theorem for one particle system, total sum of work done by individual forces = work done by total force To show the above equality, let's...

Dear Experts, Trying to analyze the work done by internal forces in a very simple two particle system which is attracted to each other with a constant force, i performed calculations based on two frame of references, 1.The center or mass frame of reference and 2. Frame of reference of one of the...

Homework Statement A system has three non-degenerate energy levels with energies 0, ε, and 2ε. a) Calculate the entropy of the system if the three levels are populated by two distinguishable particles such that the total energy is U=2ε. b) Calculate the entropy of the system if the three...

Homework Statement A bead of mass m kept at the top of a smooth hemispherical wedge of mass M and radius R is gently pushed towards right.As a result,the wedge slides due left.Find the magnitude of velocity of bead relative to the wedge. Homework Equations $$MV=m(v\cos(\theta)-V)$$ and...

In classical field theory, the field, φ, is usually constructed from a very large number of coupled harmonic oscillators. Let's say our φ consists of just electrons. What does φ best represent physically, a very large number of electrons or can it represent just a few electrons? Which is the...

Is it possible for an entangled system of particles to be disentangled at a distance, without making them interact directly with each other?

Homework Statement Landau&Lifshitz Vol. Mechanics, p101 Q1 Find the moment of inertia of a collinear set of molecules Homework Equations I=sum m_i*(r_i^2) The Attempt at a Solution r_i= r_i'-r_cm where r_cm=sum m_i*r_i/sum m_i I=sum m_i r_i^2 I= 1/M sum m_i m_j (r_i' - r_cm)^2 I=1/M sum m_i...

inertial frame is one in which isolated particle has constant velocity but is there actually any "isolated particle " ? how then can frame be defined as or not being inertial ? or is it that - for a system in which acceleration due to external forces is equal for all members , the frame of...

Homework Statement Ok, so in this system, there are two point particles of mass M connected by massless levers of length L. The pair of masses pivots about the upper point and rotates about the axis at an angular frequency ω. The lower mass is constrained to slide on the vertical axis. The...

Question: "Write the quantum state for the following system of particles distributed over evenly spaced energy levels" The diagram (couldn't upload so hope its not too rough): 5 ---------------------- 4 ---------------------- 3 --------------X------- 2 ------X---X------X---- 1...

I am following along with Goldstien's Classical Mechanics Book and I am on page 11. The text is breaking down the total potential energy of a system into two parts: the external conservative forces and the internal conservative forces. My question pertains to the internal forces. Writing the...

Take a closed system of particles. Each has it's own mass, but that's really about it for the sakes of this argument. Now suppose there is some standard force law that applies between particles, whatever it may be. (In general it will depend only on the separation between particles and thus be...

Homework Statement Define Force in a system of particles about point P Homework Equations The Attempt at a Solution I know force can be explained but not defined. However, i don't think you can just say the force is a push or a pull in a "system of particles about point P". Can...

I thought objects with kinetic energy have to be moving... And moving objects have momentum... So how is it that something with kinetic energy can have no momentum? Could you give me specific examples of such cases? Thank you so much! :)

Homework Statement Four particles are in a 2-D plane with masses, x- and y- positions, and x- and y- velocities as given in the table below: M X Y Vx Vy 1 8.9kg -2.6m -4.8m 3.2m/s -3.9m/s 2 7.9kg -3.4m 3.6m...

1. Homework Statement Two particles of masses m1=8 kg and m2=5 kg are connected to the two ends of a light inextensible string which passes over a fixed smooth pulley. Initially each of the two particles are held at a position which is 5 m above a horizontal ground. The objects are then...

Homework Statement A particle is to move in an xy plane, clockwise around the origin as seen from the positive side of the z axis. In unit-vector notation, what torque acts on the particle at time t = 9.5 s if the magnitude of its angular momentum about the origin is (a) 8.0 kg·m2/s, (b)...

Homework Statement In figure (a), a 5.4 kg dog stands on a 16 kg flatboat at distance D = 6.1 m from the shore. It walks 2.1 m along the boat toward shore and then stops. Assuming no friction between the boat and the water, find how far the dog is then from the shore. Homework...

At time t = 0, a ball is struck at ground level and sent over level ground. The figure below gives the magnitude p of the ball's momentum versus time t during the flight. (p1 = 7.0 kg·m/s and the vertical axis is marked in increments of 0.5 kg·m/s.) At what initial angle above the horizontal is...

Homework Statement Find the centre of gravity of this system of particles Homework Equations attached image showing diagram http://www.zshare.net/image/7209360586277b98/ The Attempt at a Solution Taking moments about a, 4*0+6*30 = 184 then not sure Any help is greatly appreciated Thanks...

I am very much confused with this statements "The forces of action and reaction never cancels out each other , but the internal forces on a system of particles cancel out in pairs " I think i know the reason for the first statement.i.e,The forces of action and reaction are acting on different...

Homework Statement A 2100 kg truck traveling north at 41 km/h turns east and accelerates to 51 km/h. (a) What is the change in the truck's kinetic energy? What are the (b) magnitude and (c) direction of the change in its momentum? Homework Equations currently using delta P = mvf - mvi...

Homework Statement A shell is shot with an initial velocity 0 of 29 m/s, at an angle of θ0 = 56° with the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass. One fragment, whose speed immediately after the explosion is zero, falls vertically. How far...

Homework Statement Two particles move in opposite directions along a straight line. Particle 1 of mass m1 = 23 kg at x1 = 16 m moves with a speed v1 = 34 m/s (to the right), while the particle 2 of mass m2 = 64 kg at x2 = −25 m moves with a speed v2 = −43 m/s (to the left). Given...

Homework Statement The vector position of a 3.15 g particle moving in the xy plane varies in time according to the following equation. r1 = (3i+3j)t + 2jt^2 At the same time, the vector position of a 5.00 g particle varies according to the following equation. r2= 3i-2it^2 -6jt For...

HELP!System of particles problem Homework Statement A 10kg dog walks 3m on a 20kg boat towards shore. How much nearer the shore does the dog end up if the boat was initially at rest. The Attempt at a Solution I am not really sure how to approach this problem. I think that the dog is 3...

A shell is shot with initial velocity \vec{}v_{0} is 20ms^{-1} at an angle \vartheta = 60 degrees. At the top of the trajectory, the shell explodes into two fragments of equal mass. Fragment1 has a speed of 0 immediately after the explosion and falls vertically. How far from the gun does...

A system consists of three particles, each of mass 4.00 g, located at the corners of an equilateral triangle with sides of 36.0 cm. (a) Calculate the potential energy of the system. m = .004, d = .2078 UG = Gm1m2/R U_total = sum of U_i U_total = Gm1m2/R + Gm1m3/R + Gm2m3/R U_total =...

Homework Statement Two particles move in opposite directions along a straight line. Prticle 1 of mass m1 = 26kg at x1 = 23 m moves with a speed v1 = 43 m/s(to the right), while the particle 2 of mass m2 = 63 kg at x2= -22 m moves with a speed of -37 m/s(to the left). Given: Counter...

The Problem: A 4 kg dog stands on a 16 kg flatboat at distance 12 m from the shore. The dog walks 5 m along the boat toward the shore and then stops. Assuming no friction between the boat and the water, find how far the dog is then from the shore. The dog's displacement is towards the shore...

Hey, I am a little confused with this system 1/2 particles spin at t=0 |PSI(0)> = 1/sqrt(3) (|+>_1|+>_2 + |+>_1|->_2 + |->_1|->_2 the values of S_1z and S_2z are measured at t=0. Then I have to calculate the probability that the same value will be found for the two particles. Any...

NASA often uses the gravity of a planet to slingshot a probe on its way to a more distant planet. The interaction of the planet and the spacecraft is a collision in which the objects do not touch. How can the probe have its speed increased in this manner? This problem confuses me, I want...

Hello All, I have a question that i can't seem to get. If someone could help me get started on part a that would be great. So far i have tryed using P =m1v1 and can't seem to find any other equations that would help with the problem. Any help is great! Thank You Problem: A cart...

Iam having problems with this question i think my technique is right but i,ve made a mistake somewhere Particles of mass m and 2m respectively are connected by a light inextensible string. Initially, the particles lie at opposite edges of a smooth horizontal table with the string just taut...

I need some help on how to solve this question, I don't really know how to do this at all. A vessel at rest explodes, breaking into three pieces. Two pieces having equal mass, fly off perpendicular to one another with the same speed of 30 m/s. The third piece has three times the mass of each...

Hi. In trying to convince myself that the total potential energy of a system of two particles was just the potential energy of one particle computed while considering the other particle fixed, I imagined two identical particles a distance 2r apart and attracting each other, and concluded that...

Help An isolated system of two identical particles, each of mass m, is described by an energy function E = ½ m |v1|^2 + ½ m |v2|^2 + ½ k |x1 – x2|^2 How can I use conservation of energy to find the acceleration of each particle in terms of the position of the particle? I would be thankful...