Central force Definition and 95 Threads

Homework Statement A particle moves in the central force field \overrightarrow{F}=-kr^{n}\hat{r} , where k is a constant, and r is the distance from the origin. For what values of n closed stable orbits are possible? Homework Equations The Attempt at a Solution I thought for...

Homework Statement The problem involves two particles of masses m and M; initially, m is at r=∞ and has a velocity v=v_o. The path of m is deflected, ie pulled towards M due to its gravitational pull. Question: Find the mass M (in terms of the quantities given) at a distance d where the...

Homework Statement In the study of motion in a Central-Force Field in radial coordinates it is defined an effective potential energy which depends only on the radius r: in particular there is a term 'centrifugal' because the relative force (-grad) has a centrifugal versus. What is the...

[b]1. A particle of mass m and angular moment L moves in a central force V=(1/2)kr^2 (k>0). Find the period of revolution for the circular movement and the period of small radial oscillations around the stable cicular orbit. Homework Equations The Attempt at a Solution Well I tried...

I have a problem and can’t seem to work it out! Ok, here goes: X/|X|^3 = grad U(X) which, when integrated gives U(X)= -1/|X| But I can’t seem to integrate to get the correct answer. Also, if U(X)= -1/(|X|^v ) where v is a constant, then what is grad U(X) now? Thanks for...

Homework Statement A particle of mass m moves from infinity along a straight line that, if continued, would allow it to pass a distance b/Sqrt[2} from a point P . If the particle is attracted toward P with a force which is: \frac{-k}{mr^5} radially inwards. If the angular momentum is...

Homework Statement Sketch the elliptical and hyperbolic orbits two objects make around each other if their masses are equal. Next to each, sketch the equivalent one-body orbit. Homework Equations The Attempt at a Solution For the elliptical orbit, I just drew two ellipses that...

Homework Statement A particle of mass m is subject to a repulsive central force Am/r^{3} (A is a constant). At a large distance from the center of force, the particle has speed v_{0} and its impact parameter is b. Use conservation of energy and angular momentum to show that the closest m comes...

Homework Statement Some students have just drawn my attention to the problem of particle motion under central force where the x and y coordinates are specified as functions of time, such as x(t) = A [ kt – cos(βt) ] y(t) = B [ 1 – sin(βt) ], (here A, B, β and k are constants)...

The problem Given Newton's law of gravitational attraction, that the force a body exerts on a particle in space is directed towards the body and has a magnitude proportional to the inverse square of the distance to the body, show that the force field is described by the 1-form...

Homework Statement a body of mass 1kg moves under the influence of a central force with potential energy question V(r)= -exp(-3r/2)/5r2 .it is found to move under a circular orbit of radius 2 m Homework Equations find the total energy and the angular momentum The Attempt at a Solution

Homework Statement Homework Equations on image The Attempt at a Solution The first thing I did was use the second equation to get Theta dot = L/mr2 Which I then subbed into the first equation to eliminate Theta dot. Now I need everything in terms of r, and this is...

I'm trying to understand Central Force problems and Scattering (from a central force) but the website of my course (I'm studying Analytical Mechanics) doesn't offer very good matterial on the subject. Can anyone suggest good papers about it, accompanied by problems and their solutions? Thanks.

Hello, sorry for my English:D Homework Statement I am trying to find motion equations for a mass moving around a big mass (ex. planet around sun), assumption is that the mass in middle is static (so this can be reduced to moving of mass around central force in middle of cartesian system), and...

Homework Statement 1. Homework Statement A particle of mass m moves under action of a repulsive central force Fr=Cr-3 with constant C greater than 0. At a very large distance from the centre of the force, the partcle has kinetic energy K and its impact parameter is b. Use conservation of...

Homework Statement A particle of mass m moves under action of a repulsive central force Fr=Cr-3 with constant C greater than 0. At a very large distance from the centre of the force, the partcle has kinetic energy K and its impact parameter is b. Use conservation of energy and angular...

4. For a wide range of orbital radii, stars in the Galaxy (including our sun) move in nearly circular orbits with a speed v0 »220 km/s which is independent of the orbit's radius. Find the force law and the form of the potential energy function for a star moving through the Galaxy (it is not an...

Homework Statement Consider the motion of a particle in the central force F(r) = -kr. Solve for the particle's location as a function of time, r(t) and theta(t).Homework Equations The Attempt at a Solution E = 1/2 m r'^2 + \frac{L^2}{2mr^2} + U(r) I know U(r) = 1/2 k r^2 \frac{dr}{dt} =...

Homework Statement a particle of mass m is attracted to the origin by a force F=-k/r^2 find the time t for the mass to reach the origin Homework Equations \DeltaU= U-U0 = \int\textbf{F}(r) dr The Attempt at a Solution I found \DeltaU by \DeltaU= U-U0 = \intF(r) dr and by...

Homework Statement A particle moving in a plane is attracted towards a point (fixed) by a force zr^-5. The particle is projected from an apse at distance a with speed SQRT(z/(2a^4)). Show that the orbit is r=acos(theta) Using the Orbit Eq: d^2 u/dC^2 + u = za^-5/(hu)^2 h = angular...

If you are given a central force field and an initial velocity of a particle in this field, how would you go about finding the orbit of the particle in polar coordinates? Thanks for you help and time.

How can I get the central force law by using orthogonal transformation of position vector, x=Ar where A is an orthogonal matrix and r is a position vector? Thanks!

Homework Statement \int dr \left[\alpha + \frac{\beta}{r^2}\right]^{-1/2} How can I get started on this? Thanks.

Homework Statement 1a) Verify that the kinetic energy of two particles can be written as the kinetic energy of a single 'reduced mass' particle with velocity r'equal to their difference. 1b) In the center-o-mass frame, show that theta is the same for r1 as for r, whereas the polar angle for...

If F denotes the central force and is given as the inverse of the square distance F=-k/r^2. where k>0. How can i show that F the path of the partilce under that force is a conic? What i can see is that it is the second law of Kepler. And when i try to compare F with the former equation of...

Problem A particle moves in a force field described by F(r)=-\frac{k}{r^{2}}e^{-\frac{r}{a}} where k and a are positive. Write the equations of motion and reduce them to the equivalent one-dimensional problem. Use the effective potential to discuss the qualitative nature of the orbits...

Homework Statement A particle moves under the action of a central force in a spiral orbit given by r=a*theta. Show that the force is f(r) = (-L^2/mr^3)*[1 + (a^2)/(r^2)] Homework Equations The Attempt at a Solution I know how to do the problem, but I keep ending up with a...

Homework Statement http://img147.imageshack.us/img147/7830/scan0001ym3.png The Attempt at a Solution A) i think force of Tension give them necessary centripetal force directed toward the center of the cylinder. C) Centripetal Force Plz help me

Homework Statement http://img147.imageshack.us/img147/7830/scan0001ym3.png The Attempt at a Solution A) i think force of Tension give them necessary centripetal force directed toward the center of the cylinder. C) Centripetal Force Plz help me

Homework Statement Central force F=-ar/(r^3) & Central potential energy,U=-(a/r) (not U_eff) Find the nature of orbits if (i)a>0 and (ii)a<0 Homework Equations The Attempt at a Solution If we remember the attractive central force E=E(r) diagram,i.e.the one showing the graph of...

Homework Statement Homework Equations The Attempt at a Solution Please check if I am correct: The following are Central force: a.Action and reaction forces between two bodies b.Van der Waal's force between two molecules c.dipolar force between two small magnets d.Force...

We know a two body problem may be analysed as an equivalent one body problem.Why a three/more body problem cannot be reduced to a one-body problem? I think in that case we do not find an equivalent reduced mass... Anyone can say something?

General form of a central force is F(r)=F(r) (r^) [Note that This form of central force satisfies L=rxp=0 as well] But the isotropic or centro-symmetric form is F(r)=F(r) (r^) I found in a book that the second form of a central force is conservative.OK,this can be proved easily.What...

Homework Statement A particle moves in a circular orbit under the action of a force f(r)=-(k/r^2).If k is suddenly reduced to half its value, what would be the nature of the orbit? Homework Equations e=sqrt[1+(2*L^2*E)/(mk^2)] The Attempt at a Solution My attempt: Clearly,the...

Homework Statement A particle of unit mass is projected with a velocity v-(sub 0), at right angle to the radius vector at a distance 'a' from the origin of a center of attractive force given by: f(r)= -k*(4/(r^3)+ (a^2)/(r^5)). If (v-(sub 0))^2 = (9*k)/(2*(a^2)) find the polar equation of...

hello, i am having problems with this question "If a force on an object is always directed along a line from the object to a given point, and the magnitude of the force depends only on the distance of the object from the point, the force is said to be a central force. Show that any central...

In the Bohr model of the hydrogen atom, the speed of the electron is approximately 1.96e+6 m/s. Find the central force acting on the electron as it revolves in a circular orbit of radius 4.8e-11 m. Answer in units of N.

If anyone could help me with this problem I would be very grateful, its been annoying me for a day or two now! Its one of those exam questions that lead you through a derivation, giving you blanks to fill in. Although these are designed to make the derivation easier, sometimes it makes a...

A planet of mass m follows an elliptic path around the Sun with a semi-major axis a and an eccentricity e, using the polar form for the radial position of the planet with respect to the sun: a) Find both the radial component of the velocity Vr and the angular component of the velocity V theta...

An extra-solar planet moes in an elliptic orbit around a star of mass M. The max distance between the planet and the star is known to be r2 = 8r1 where r1 is the min distance between the planet and the star. a) What is the eccentricity of the planet's orbit? b) What is the period of the...

The orbit of a particle in a central field is known to obey the following relationship: r = A/(1+sin(theta)) a) determine the form of the central force F(r) that is responsible for this motion. b) What is the distance of closest approach between the particle and the point that acts as the...

Hi we just studied motion under central force. we got the following question... is this possible trajectory(see attachment) under central force and force source is outside the loop? (my answer is that it is possible if force source is repulsive) whatever the answer is how can i explain it...

For what form of a central force is the motion of a body exactly circular?

A particle of mass m is subjected to a repulsive force k/r^5, where k is a constant. Initially it is at a very large distance from the force center O and has a velocity of magnitude such that, if it were directed along a path through the center of the force, the closest distance of approach...

Why electrons do a circumferential motion under the magnetic force and planets do a elliptical motion under the gravity? I don't understand this because the magnetic force and the gravity are all central force. Can anyone tell me what's the difference between them, in words, mathematics or in...