56. Two astronauts (Fig. P11.55), each having a mass M, are connected by a rope of length d having negligible mass. They are isolated in space, orbiting their center of mass at speeds v. Treating the astronauts as particles, calculate (a) the magnitude of the angular momen- tum of the tWo-astronaut system and (b) the rotational energy of the system. By pulling on the rope, one of the astronauts shortens the distance between them to d/2. (c) What is the new angular momentum of the system? (d) What are the astronauts' new speeds? (e) What is the new rotational energy of the system? (f) How much chemical potential energy in the body of the astronaut was converted to mechanical energy in the system when he shortened the rope?

56. Two astronauts (Fig. P11.55), each having a mass M, are connected by a rope of length d having negligible mass. They are isolated in space, orbiting their center of mass at speeds v. Treating the astronauts as particles, calculate (a) the magnitude of the angular momen- tum of the tWo-astronaut system and (b) the rotational energy of the system. By pulling on the rope, one of the astronauts shortens the distance between them to d/2. (c) What is the new angular momentum of the system? (d) What are the astronauts' new speeds? (e) What is the new rotational energy of the system? (f) How much chemical potential energy in the body of the astronaut was converted to mechanical energy in the system when he shortened the rope?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

Pulsars are astronomical objects that give off very regular pulses of radio waves with periods roughly between 1 ms and 1 s. A pulsar may form when a star of medium mass dies. Contemporary astronomers have measured the angular speed of a pulsar in the Crab Nebula as 1.89 x102rad/s and have found that the pulsar is slowing down such that its angular acceleration has a magnitude of 2.39 x10-9 rad/s2. What was the initial angular speed of the Crab Nebula ́s pulsar in 1054 when it was discovered? Assume a year has 365days.
A 750 g disk and a 760 g ring, both 15 cm in diameter, are rolling along a horizontal surface at 1.3 m/s when they encounter a 13 ∘ slope. How far up the slope does the disk travel before rolling back down? How far up the slope does the ring travel before rolling back down?
Two astronauts (figure), each having a mass of 76.0 kg, are connected by a d = 11.0-m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 5.50 m/s. CM d (a) Treating the astronauts as particles, calculate the magnitude of the angular momentum of the two-astronaut system. |kg · m²/s (b) Calculate the rotational energy of the system. kJ (c) By pulling on the rope, one astronaut shortens the distance between them to 5.00 m. What is the new angular momentum of the system? |kg · m²/s (d) What are the astronauts' new speeds? m/s (e) What is the new rotational energy of the system? kJ (f) How much chemical potential energy in the body of the astronaut was converted to mechanical energy in the system when he shortened the rope? kJ Need Help? Read It Master It
Two 4.80 kg balls are attached to the ends of a thin rod of length 40.0 cm and negligible mass. The rod is free to rotate in a vertical plane without friction about a horizontal axis through its center. With the rod initially horizontal (the figure), a 690 g wad of wet putty drops onto one of the balls, hitting it with a speed of 4.21 m/s and then sticking to it. (a) What is the angular speed of the system just after the putty wad hits? (b) What is the ratio of the kinetic energy of the system after the collision to that of the putty wad just before? (c) Through what angle (deg) will the system rotate before it momentarily stops? Putry wad Rotation axis (a) Number Units (b) Number Units (c) Number Units
A 1.40-kg particle moves in the xy plane with a velocity of v = (4.40 î – 3.30 ĵ) m/s. Determine the angular momentum of the particle about the origin when its position vector is ř = (1.50 î + 2.20 ĵ) m. k) kg · m2/s
A particle is at a position vector r = (x, y, z) = (1.0i, 2.0j, 3.0k) m. It is traveling with a velocity vector (-5.0, +2.8, -3.1) m/s. Its mass is 3.8 kg. What is its vector angular momentum about the origin.
Rotating Bracelet. Enrico owns a circular bracelet of mass m = 23 g and diameter d0 = 6.9 cm, which is made of n identical small beads each connected with massless springs of spring constant nk where k = 0.5 N/m. (a) Through some unknown superpower, Enrico manages to make this bracelet levitate and spin horizontally (i.e. axis of rotation is vertical) with an initial angular velocity of ω = 10 rad/s without touching it. This causes the bracelet to lengthen, increasing its diameter. Despite this, Enrico forces the bracelet to maintain a constant angular velocity. Enrico observes that the diameter of this bracelet initially varies, but after a long time, it settles at a constant value d. For large n, what value does d approach? (b) Enrico repeats what he did previously, but this time, the bracelet no longer maintains a constant angular velocity. Again, Enrico observes that the diameter of this bracelet initially varies, but after a long time, it settles at a constant value d. For large…
A 1.30-kg particle moves in the xy plane with a velocity of V = (4.30 i − 3.70 j) m/s. Determine the angular momentum of the particle about the origin when its position vector is r = (1.50 i + 2.20 j) m.
The figure shows a device that can be used to measure the speed of a bullet. The device consists of two rotating disks, separated by a distance of d = 0.872 m, and rotating with an angular speed of 101 rad/s. The bullet first passes through the left disk and then through the right disk. It is found that the angular displacement between the two bullet holes is = 0.268 rad. From these data, determine the speed of the bullet. Number IN Bullet Units Motor
A figure skater is spinning with an angular velocity of +11.9 rad/s. She then comes to a stop over a brief period of time. During this time, her angular displacement is +3.54 rad. Determine (a) her average angular acceleration and (b) the time during which she comes to rest. (a) Number Units (b) Number Units
A figure skater is spinning with an angular velocity of +18.8 rad/s. She then comes to a stop over a brief period of time. During this time, her angular displacement is +4.94 rad. Determine (a) her average angular acceleration and (b) the time during which she comes to rest. (a) Number Units (b) Number i Units Save for Later