An attractive central force exerted on a particle of mass m causes the particle to travel in a bound orbit. The orbit is elliptical with semi-major axis a and the force has magnitude Cm/r^{2} , where C is a constant and r is the orbit radius. If the particle's speed is v = (C/2a)^{0.5} when it is farthest from the source of the force, what is its speed when it is nearest the force source?
An attractive central force exerted on a particle of mass m causes the particle to travel...
A particle of mass m is subject to a central force which is attractive but independent of distance: Fr)Fo. (a) Sketch the effective potential Uer), and show that only bounded, stable orbits are (b) For this force, find the equivalent of Kepler's Third Law for circular orbits. In other (c) Discuss whether perturbed circular orbits are closed or open, and justify your answer (d) Set up the differential equation for the general orbital trajectory r(e). (It does not have possible...
The 0.5 kg particle shown travels at a speed of 3 mps around the surface of the stationary drum. All surfaces are assumed to be frictionless. Find the (a) normal force exerted by the mass particle on the surface of the drum (b) radius of the horizontal path of the particle.
2. Two bodies with reduced masses m, and m, interact via the central force F--ks. a. The effective single particle of reduced mass u has an elliptical orbit whose energy is an increment AE above the minimum energy Vmin for a closed orbit. Find the angular momentum and pericenter radius rmin as a function of AE and Vmin- b. An impulsive force is applied to the effective particle at its pericenter, reducing the angular velocity to a factor k times...
The particle of mass m is released when the spring of stiffness K is compressed by a, and travels without friction around the vertical loop ABCD of radius r. Determine the force exerted by the loop on the particle at point B. Gravity acceleration is g. The particle of mass m is released when the spring of stiffness k is compressed by a, and travels without friction around the vertical loop ABCD of radius r. Determine the force exerted by...
The figure gives the acceleration of a 4.0 kg particle as an applied force moves it from rest along an x axis from x = 0 to x = 9.0 m. The scale of the figure's vertical axis is set by a_s = 10.0 m/s^2. How much work has the force done on the particle when the particle reaches (a) x = 4.0 m, (b) x = 7.0 m, and (c) x = 9.0 m? What is the particle's speed...
Mahiindra cole Centrale Tutorial Sheet-3 Central forces/SHM PHYSICS-101 Date 150220 1) Let a particle be subject to an attractive central force of the form n where r is the distance between the particle and the centre of the force. Find fn), if all circular orbits are to have identical areal velocities, A 2) For what values of n are circular orbits stable with the potential energy un-Ai where A > 0? 3) A satellite of mass m 2,000 kg is...
Problem 1: A charged particle of mass m,=-10-30.kg and charge 9,=-1.602-10-'9.C enters a region of magnetic field of uniform magnetic field with a speed of v, = 2.1.10^." along the y-axis. The region of magnetic field exits above y=10.0 cm and is otherwise unform in x, y, and z. While in the magnetic field the particle is observed to have an orbit bending to the right with radius R, =5.0.cm. (A) Draw a picture for this problem. (B) Find the...
3.2 Electric Field of a Charged Particle The four properties of the electric field of a charged particle are captured by the vector field where the particle has charges and the source-to-target radial vector field and its associated unit vector field are defined as Psr (x,y) = (x - 1s)i + (- ) Pris(z,y) STIFT IFs (2.y) and k = 8.99 x 10°N C/ mºis Coulomb's constant. Question 3.3) Consider a 2 C source particle, located at the position (1,3)...
A. An α-particle has a charge of +2e and a mass of 6.64 × 10-27 kg. It is accelerated from rest through a potential difference that has a value of 1.67 × 106 V and then enters a uniform magnetic field whose magnitude is 2.49 T. The α-particle moves perpendicular to the magnetic field at all times. What is (a) the speed of the α-particle, (b) the magnitude of the magnetic force on it, and (c) the radius of its...
A small particle of mass m is at rest on a horizontal circular platform that is free to rotate about a vertical axis through its center. The particle is located at a radius r from the axis, as shown in the figure above. The platform begins to rotate with constant angular acceleration α . Because of friction between the particle and the platform, the particle remains at rest with respect to the platform. When the platform has reached angular speed...