Particle motion Definition and 62 Threads

For part (c) my understanding is that in this case for the particle to cross the origin it must have at least as much kinetic energy as there is potential energy at ##U(0) = A##. Given the potential energy and kinetic energy at any position x=a is equal to ## U(a) = \frac {ka^2} {2} +...

I have attempted but I don’t get anywhere.

The equation of motion can be integrated w.r.t. ##t## since ##\frac{d}{dt} (\mathbf{r} \times \mathbf{B}) = \dot{\mathbf{r}} \times \mathbf{B} + \mathbf{0}## $$\int (q\dot{\mathbf{r}} \times \mathbf{B} + m\mathbf{g}) dt = \int m\ddot{\mathbf{r}}(t) dt$$ $$\frac{q}{m} \mathbf{r} \times \mathbf{B}...

The particle is moving under a force field with the potential energy equation described above. I find it logical that Newton's Laws can be used as in the question itself it is stated that the velocity is quite small and we could approximate its subsequent motion via the notions of Classical...

I have question, how can I solve problem of particle in rigid box when one of the wall gets completely destroyed? At time t = 0 the right wall of box gets completely destroyed, left wall is still here( ψ(0) = 0 ), also at t = 0 we know that particle is in ground state. How can I search for...

We all know that the state of matter can be changed by increasing temperature or by applying pressure. And, all of these, in some way lead to a change in the particles' speed. The speed of the particle decides the state of matter. So, if we were to throw an object at very high speeds, like 50%...

Hello, I haven't been able to find the answer to this anywhere. When calculating the energy gained by a particle that is accelerated across the gap of two cavities (e.g. Dees in a cyclotron, or charged cylindrical cavities of a linear accelerator), does one need to take into account the size of...

Hello all, I want to say thank you in advance for any and all advice on my question. My classical mechanics textbook (Marion Thornton) has been taking me through motion for a particle with retarding forces. The example it keeps giving is: m dv/dt = -kmv which can be solved for: v = v0e-kt...

Homework Statement A particle moves along a circle in a region of uniform magnetic field of magnitude B=4.0 mT. The particle is either a proton or an electron. It experiences a magnetic force of magnitude 3.2x1015 N. What are (a) the charge of the particle? (b) The particle speed? (c) The...

Homework Statement A particle moves in a straight line with the acceleration shown in the figure. Knowing that it starts from the origin with ##v_0 = -14ft/s##, plot the v-t and x-t curves for 0 < t < 15 s and determine (a) the maximum value of the velocity of the particle, (b) the maximum...

Homework Statement 11.10 The acceleration of a particle is directly proposional to the time t. At t = 0, the velocity of the particle is v = 16 in./s. Knowing that v = 15 in./s and that x = 20 in. when t = 1 s, determine the velocity, the position, and the total distance traveled when t = 7s...

We consider a monoatomic gas in a closed box. A textbook says : Since the assumption is that the particles move in random directions, the average value of velocity squared along each direction must be same. Why the assumption is that the particles move in random directions implies that the...

Homework Statement Two parallel plates located at a distance "L" from each other they maintain a potential difference "V" because of a battery (as shown in the picture). Through a small hole, made in bottom plate, electrons get into system (with mass "m" and charge "-e"), with velocity "v" and...

Homework Statement [/B] Hi everyone! So I've got this similar problem as I posted yesterday, but this one is slightly different due to the presence of gravity: A particle in gravitational field ##~~g## starts traveling upward (positive direction) along the y-axis from ##~~y=0## with the...

Homework Statement Pytel Dynamics Problem 13.4 13.4 The particle passespoint O at the speed of 2.4 m/s. Between O and B, the speed changes at the rate of 2.2√v m/s2, where v is the speed in m/s. Determine the magnitude of the acceleration when the particle is (a) just to the left of pont A...

A particle moves in a vertical plane from rest under the influence of gravity and a force perpendicular to and proportional to its velocity. Obtain the equation of the trajectory, and identify the curve.

Hi all, Just a clarification to ask about: if a have an electron (all by its lonesome) in its ground state, it will have non-zero kinetic energy (zero-point energy), even at absolute zero. This should mean the particle (oscillating field excitation in QFT) is always moving. Now, to be clear...

Homework Statement Consider a charged particle entering a region of uniform magnetic field B - for example the Earth's field. Determine it's subsequent motion when the y-axis is parallel with the magnetic field Homework Equations F=qv x B = ma vector components of velocity, acceleration, and...

Homework Statement This is new for me, so forgive me my clumsiness. I am working on the following problem: A particle p is moving with a velocity v1 = c (speed of light) towards an object q, which is moving in the same direction with the speed v2, where v1>v2. Now, v2 is a function of the...

Hi all, Some time ago I was reading about Anderson localization (posted a question about it was well) - this got me thinking about vacuum fluctuations. I think I have the wrong idea in my mind - so wanted to ask the great community here about it: Quantum (vacuum) fluctuations must have an...

Homework Statement A uniform cylindrical drum of mass M and radius a is free to rotate about its axis, which i is horizontal. An elastic cable of negligible mass and length l is wrapped around the drum and carries on its free end a mass m. The cable has elastic potential energy \tfrac12...

Homework Statement A particle moves so that its equation of motion in vector form given is given by ##\vec{R}=((sint^-1)/2+t/2√(1-t^2))\vec{i}+1/2t^2\vec{j}## , ##0≤t<1## a)Show that particle moves with a constant speed. b)Compute ##\vec{v}## and ##\vec{a}##,and verify that...

Homework Statement At time t=0, a particle is located at the point (1,2,3). It travels in a straight line to the point (4,1,4), has speed 2 at (1,2,3) and constant acceleration 3i-j+k. Find an equation for the position vector r(t) of the particle at time t. Homework Equations The...

Homework Statement A particle of mass m moves in a circle of radius R at a constant speed v. Assume: The motion begins from the point Q, which has coordinates (R, 0). Determine the angular momentum of the particle about point P, which has coordinates (−R, 0) as a function of time. The...

Homework Statement A block of ice starts from rest on an apartment building’s roof, which slopes at 41° below the horizontal. The block slides down the icy frictionless roof for 5.0 m and then leaves the edge, which is 12 m above the ground. a. How far from the building does the block strike...

Homework Statement Assume the Earth's magnetic field is almost homogeneous with direction along the z-axis, with a small inhomogeneous modification which make the field lines converge towards the z-axis. Also ignore relativistic and gravitational effects. . First assume the magnetic field, B...

Homework Statement The expectation value of motion of a particle over a time interval t-to is C(t,to) = <0|x(t)x(to)|0> (product of position operators in Heisenberg representation for ground state harmonic oscillator) Homework Equations Schrodinger picture: <ψ(t)|Ω|ψ(t)> =...

Homework Statement A charged particle of mass m = 6X10-8 kg, moving with constant velocity in the y-direction enters a region containing a constant magnetic field B = 2.8T aligned with the positive z-axis as shown. The particle enters the region at (x,y) = (0.58 m, 0) and leaves the region at...

Homework Statement see attachment for question wording. a) find acceleration b) find horizontal displacement c) find final velocity vx=4.0*10^6m/s ε=4.0*10^2 N/C Δdy=0.02m mass of electron = me = 9.11*10^-31kg charge of electron = qe = -1.6*10^-19 C Homework Equations suvat...

Hi I am trying to simulate N particles evaporating from an oven, after which they propagate and eventually hit a wall. it is all classically, no quantum behavior. So far my approach has been the following: I pick a random Gaussianly distribution number, which I say is the velocity of the...

Homework Statement a particle of mass m is contrained to lie on along a frictionless,horizontal plane subject to a force given by the expression F(x)=-kx. It is projected from x=0 to the right along the positive x direction with initial kinetic energy T(o)=1/2kA^2, k and A are positive...

hi all, I've been trying to work this problem out, \frac{dv}{dt}-A(B-v)^{1.6}=G A, B and G are constants and Matlab can't give me a solution either. I'm wondering if there is even a solution?

Homework Statement Moves at G(f)=t^2-4t+3 a. Find displacement at 2 sec b. Find average velocity at 4 sec c. Find instantaneous velocity at t=4 d. Find acceleration at t= 4Homework Equations Instantaneous rate of change DisplacementThe Attempt at a Solution f'= 2t-4 (So this would be the...

Homework Statement A particle of mass 3.2kg is moving due west with a velocity of 6m/s. Another particle of mass 1.6kg is moving due north with a velocity of 5.0m/s. The two particles are interacting. After 2s the first particle is moving in the direction N 30° E with a velocity of 3m/s...

Homework Statement A particle moves in a straight line away from a fixed point O in the line, such that when its distance from O is x its speed v is given by v=k/x , for some constant k. (a) show that the particle has a retardation which is inversely proportional to x3 The answer is...

Homework Statement A baseball is thrown downward from a 12.5m tower with and initial speed of 4.5m/s. Determine the speed at which it hits the ground and the time of travel. s = 12.5m u = 4.5m/s a = g = 10m/s^2 Homework Equations Motion equations used s = ut + 0.5at^2 v^2 = u^2 +2as...

Consider that we have a macroscopic, electrically charged, point object tracing out a circular path in a uniform magnetic field in the usual way due to the Lorentz force. Now we very slowly raise the overall strength of the magnetic field (slow enough that on one orbit, the object sees the same...

Hi everyone For the past few months I have been learning about the nucleus and the nuclear shell model. The experimental evidence for a shell structure is overwhelming and easy to understand. It is also quite straight forward to obtain the correct shell closures (magic numbers) using a 3d...

A particle of mass m travels in a straight line and experiences a single force, F(t) , in the direction of motion that varies with time t. ( a ) Given that m = 6 kg and F( t ) = 6 sin t + 24 N, use Newton’s 2nd law to show that the acceleration, a m/s2 , of the particle is...

Homework Statement Hi guys. I'm stuck at a question that has to do with magnetism and I would really appreciate some help! The question is: "An electron and an alpha particle are in a magnetic field and moves in circles with the same tangential speed. Calculate the ratio between the number...

What is the meaning of floatin and flying and moveing freely in space?

Two bodies begin a free fall from rest from the same height. If one starts 1.0 s after the other, how long after the first body begins to fall will the two bodies be 10 m apart? x = x + vt +1/2at^2 I'm having trouble visualising a solution.

Im having trouble understanding that if i have an equation for the motion of a particle how can i find out that a constant force is being acted upon the particle? Any help would be appreciated thank you.

Homework Statement Consider a particle of mass m that carries a charge q. Suppose that the particle is under the influence of both an electric field E and a magnetic field B so that the particle's trajectory is described by the path x(t) for a\leqt\leqb. Then the total force acting on the...

Homework Statement A proton is moving through a vertical magnetic field. The (instantaneous) velocity of the proton is 8.5x105m/s horizontally in the north direction. The (instantaneous) acceleration produced by the magnetic force is 2.90x105m/s2 in the west direction. What is the magnitude...

Homework Statement Hey all. I have F(v) and I'm looking for x(t). F(v) = -bV2 I'm a physics undergrad student who hasn't done diff. equations in a while, so I'm very unsure of my work so far... but here it is. The Attempt at a Solution I write F=ma as F(v)=mdv/dt: -bV2=mdv/dt -m∫ dv/v2 =...

Do the electric lines of force necessarily depict the trajectory of a charged particle? Or do they depict the trajectory at all.

Hi, Can anybody help with the following: A point particle moves in a plane with trajectory given by r(t) = R [θ (t)]^3/2, where R is a constant. The angle θ in radians increases in time according to the equation θ (t) = 1/2 α t^2, where α is a constant whose numerical value is α = 1...

Homework Statement Find the one-dimensional particle motion in the trigonometric potential U(x) = V tan^2(a x) , V > 0 . Find the one-dimensional particle motion in the Morse potential U(x) = A(1-e^-ax)^2. Homework Equations well at the moment in class our lecturer derived: T =...

Homework Statement A particle P of mass m moves on the x-axis under the force field with potential energy V=V0(x/b)4, where V0 and b are positive constants. Show that any motion of P consists of a periodic oscillation with centre at the origin. Show further that, when oscillation has amplitude...