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 parti...
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 in eliptic orbit about the earth. At perigee (closest approach to the earth) it has an altitude of 1,100 km and at apogee (farthest distance from the earth) its altitude is 4,100 km. What are the satellite's energy E and angular momentum L? How fast is it traveling at perigee and at apogee? 4) A particle moves in a circle under the influence of an inverse cube law force. Show that the particle can also move with uniform radial velocity, either in or out (This is an example of neutral stability. Any slight perturbation to the circular arbit will start the particle moving radially, and it will continue to move uniformly ) Find 6 as a function of r for motion with uniform radial velocity v 5) Two non-interacting particles m, and m2 move towards each other with velocities v and v2. Their paths are offset by a distance b as shown in the sketch. Investigate the equivalent one body description of this system a) ua(t)-A cos(at + β) ,a # 0 6) Given the following expressions: b) ub (t)s B cos(at) + C sin(at), α * 0 . c) uc (t) = Ae-rt cos(at + β), γ # 0, α # 0 o.< > o 1) ü + 2αού + adu Given the following differential equations: Associate the differential equations with its solution. One solution can work for several differential equations and one differential equation may have several solutions. For each answer, specify the meaning of each constant A, B. C, a, β.y or how to determine it in a problem
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 in eliptic orbit about the earth. At perigee (closest approach to the earth) it has an altitude of 1,100 km and at apogee (farthest distance from the earth) its altitude is 4,100 km. What are the satellite's energy E and angular momentum L? How fast is it traveling at perigee and at apogee? 4) A particle moves in a circle under the influence of an inverse cube law force. Show that the particle can also move with uniform radial velocity, either in or out (This is an example of neutral stability. Any slight perturbation to the circular arbit will start the particle moving radially, and it will continue to move uniformly ) Find 6 as a function of r for motion with uniform radial velocity v 5) Two non-interacting particles m, and m2 move towards each other with velocities v and v2. Their paths are offset by a distance b as shown in the sketch. Investigate the equivalent one body description of this system a) ua(t)-A cos(at + β) ,a # 0 6) Given the following expressions: b) ub (t)s B cos(at) + C sin(at), α * 0 . c) uc (t) = Ae-rt cos(at + β), γ # 0, α # 0 o. o 1) ü + 2αού + adu Given the following differential equations: Associate the differential equations with its solution. One solution can work for several differential equations and one differential equation may have several solutions. For each answer, specify the meaning of each constant A, B. C, a, β.y or how to determine it in a problem