Solution: Here we are given a particle moving in an elliptical trajectory under the influence of a central force , which is directed towards the center of rotation O.
(a)
where is the linear momentum of the particle, which is defined as the momentum of translation, being a vector quantity in classical physics, equal to the product of the mass and the velocity of the center of mass. It is given as -
And its magnitude is given by
where is the angle between and .
(b) For a general case of motion:
(c)
where r_{1} and r_{2} are the apogee and perigee of the elliptical path and
So,
Since
(10 points) The particle P descr ibes an elliptic trajectory under the influence of the central force F (Figure 1-Center). (a) Define an angular momentum and denote all the relevant quantities (...
The equation of motion of a particle is described by: OM t-1+(2)1 Determine the equation of trajectory of the particle and plot it on an xy coordinate system. a) b) At which point the motion starts. c) Determine the velocity vector and the acceleration vector of the particle in function of t d) Determine the tangential acceleration, the normal acceleration, and the radius of curvature in function of t. Is this a central acceleration, why or why not? At what...
To apply the principle of angular impulse and momentum to describe a particle's motion. The moment of a force about a point O, fixed in an inertial coordinate system, MO, and the angular momentum about the same point, HO, are related as follows: ∑MO=H˙O where H˙O is the time derivative of the angular momentum, HO=r×mv. Integrating this equation with respect to time yields the following equation: ∑∫t2t1MO dt=(HO)2−(HO)1 This equation is the principle of angular impulse and momentum, and it...
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...
8.4 The Two-Dimensional Central-Force Problem The 2D harmonic oscillator is a 2D central force problem (as discussed in TZD Many physical systems involve a particle that moves under the influence of a central force; that is, a force that always points exactly toward, or away from, a force center O. In classical mechanics a famous example of a central force is the force of the sun on a planet. In atomic physics the most obvious example is the hydrogen atom,...
A particle P of mass m=1 moves on the x-axis under the force field F=36/(x^3) - 9/(x^2) (x>0). Show that each motion of P consists of either (i) a periodic oscillation between two extreme points, or (ii) an unbounded motion with one extreme point, depending on the value of the total energy. Regards
002 (part 1 of 3) 10.0 points An alpha particle (mass 6.64 x 1027 kg, Z - 2) approaches to within 1.29 x 10-14 m of a carbon nucleus (7-6). Find the maximum Coulomb force on the alpha particle. Answer in units of N 003 (part 2 of 3) 10.0 points Find the acceleration of alpha particle at this point. Answer in units of m/s. 004 (part 3 of 3) 10.0 points Find the potential energy of alpha particle at...
1. (a) Figur1 shows the forces acting on a particle that falls from rest under gravity and is subject to a retarding force proportional to its velocity, bv Figure 1 mg (0) Show that the velocity, v, as a function of time,t,can be written as 1-e m 151 (i) Determine an expression for the particle's terminal velocity. 2] 151 Find the position as a function of time. (b) The terminal velocity of the particle is 50 ms1. Find (c) (i)...
Multivariable Calculus help with the magnitude of angular momentum: My questions is exercise 4 but I have attached exercise 1 and other notes that I was provided 4 Exercise 4. In any mechanics problem where the mass m is constant, the position vector F sweeps out equal areas in equal times the magnitude of the angular momentum ILI is conserved (Note: be sure to prove "if and only if") (Note: don't try to use Exercise 2 in the proof of...
Please answer all parts of the questions and please try making them clear and easy to understand. CONCEPTUAL QUESTIONS: (Total Points 10, 1 points each question) 1- A plate is supported by a bal-and-socket joint at A, a roller joint at B, and a cable at C. How many unknown support reactions are there in this problem? 300 N 400 N i m A) Four forces and two moments B) Six forces C) Five forces D) Four forces and one...
45. The change in total output resulting from a 1-unit increase in the quantity of an input used, holding the quantities of all other inputs constant, is ______. (Points: 3) average cost average product marginal cost marginal product 46. When an additional unit of a variable input adds less to total product than the previous unit, the firm must be experiencing ______. (Points: 3) increasing returns diminishing marginal returns diminishing average returns both B and C 47. The marginal cost...