2. A mass moves along the r-axis subject to an attractive force 17c2mx/2 and a retarding...
A particle of mass m moves in one dimension along the positive x axis. It is acted on by a constant force directed toward the origin with magnitude B, and an inverse-square law repulsive force with magnitude A/x^2. Find the potential energy function, U(x). Sketch the energy diagram for the system when the maximum kinetic energy is K_0 = 1/2 mv_0^2 Find the equilibrium position, x_0.
Please show what basic mechanical equations are used or explain how to derive the equation. Not just looking for the answer. c 60 kg/s is subject to a A damped harmonic oscillator with m - 10 kg, k 250 N/m, and driving force given by Fo cos ot, where Fo 48 N. (a) What value of ω results in steady-state oscillations with maximum amplitude? Under th condition:
2. The equations of motion for a system of reduced mass moving subject to a force derivable from a spherically symmetric potential U(r) are AF –102) = (2+0 + rē) = 0 . (3) Using the second of these equations, show that the angular momentum L r 8 is a constant of the motion (b) Then use the first of these equations to derive the equation for radial motion in the form dU L i=- What is the significance of...
A particle of mass m is subject to a damping force equal to -bv, and also a driving force equal to Fa coswat, but there is no spring force. Find a solution for x(t) by guessing one of the form x(t) = A cos watB sinwat. If you write your solution for x(t) in the form of C cos(wat- ), what are C and ø? (This problem is a special case of the one we did in Lecture 20, but...
A 4 kg particle moves along an x axis, being propelled by a variable force directed along that axis. Its position is given by x = 1 m + (6 m/s)t + ct2 - (4 m/s3)t3 with x in meters and t in seconds.The factor c is a constant. At t = 4 s the force on the particle has a magnitude of 32 N and is in the negative direction of the axis. What is c?
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...
Please show all work. A particle moves along the x-axis. A second particle is located at the coordinate (0,3). It is known the force that one particle exerts on the other is given by where .G is a positive constant . r represents the distance between the particles m1, m2 refer to positive constants about the particles (mass). The direction of the force is directly from one particle to the other. . (0,3) (x,0) (A)For a given position of a...
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...
Please help solve the following question with steps. Thank you! 3. Suppose that an object moves along the helix r(t) - (2 cos t, 2 sin t, L.) , 2π subject to the force field F-(-y, x, z). Determine the work 0-t done. 3. Suppose that an object moves along the helix r(t) - (2 cos t, 2 sin t, L.) , 2π subject to the force field F-(-y, x, z). Determine the work 0-t done.
Acceleration in polar coordinates is required 1. A particle of unit mass moves along a trajectory , 2r) θ E (03), and θ E ( a coal, -a cose r(8)--, expressed in plane polar coordinates. The angle 6(t) changes with time according to the equation θ wt. Here a, are positive constants independent of time. (a) [10 marks) Compute the transverse acceleration of the particle (b) [10 marks) Find the force acting on a particle and express it in terms...