Two astronauts (Fig. P8.80), each haring a mass of 75.0 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.00 m/s. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum and (b) the rotational energy of the system. By pulling on the rope, the astronauts shorten the distance between them to 5.00 m. (c) What is the new angular momentum of the system? (d) What are their new’ speeds? (e) What is the new rotational energy of the system? (f) How much work is done by the astronauts in shortening the rope? Figure P8.80 Problems 80 and 81
Two astronauts (Fig. P8.80), each haring a mass of 75.0 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.00 m/s. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum and (b) the rotational energy of the system. By pulling on the rope, the astronauts shorten the distance between them to 5.00 m. (c) What is the new angular momentum of the system? (d) What are their new’ speeds? (e) What is the new rotational energy of the system? (f) How much work is done by the astronauts in shortening the rope? Figure P8.80 Problems 80 and 81
Solution Summary: The author explains the formula to calculate the angular momentum of the astronauts.
Two astronauts (Fig. P8.80), each haring a mass of 75.0 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.00 m/s. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum and (b) the rotational energy of the system. By pulling on the rope, the astronauts shorten the distance between them to 5.00 m. (c) What is the new angular momentum of the system? (d) What are their new’ speeds? (e) What is the new rotational energy of the system? (f) How much work is done by the astronauts in shortening the rope?
Figure P8.80 Problems 80 and 81
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
Answers with -1.828, -1.31 or 939.3 are not correct.
Three slits, each separated from its neighbor by d = 0.06 mm, are illuminated by a coherent light source of
wavelength 550 nm. The slits are extremely narrow. A screen is located L = 2.5 m from the slits. The
intensity on the centerline is 0.05 W. Consider a location on the screen x = 1.72 cm from the centerline.
a) Draw the phasors, according to the phasor model for the addition of harmonic waves, appropriate for this
location.
b) From the phasor diagram, calculate the intensity of light at this location.
A Jamin interferometer is a device for measuring or for comparing the indices of refraction of gases. A beam
of monochromatic light is split into two parts, each of which is directed along the axis of a separate cylindrical
tube before being recombined into a single beam that is viewed through a telescope. Suppose we are given the
following,
•
Length of each tube is L = 0.4 m.
• λ= 598 nm.
Both tubes are initially evacuated, and constructive interference is observed in the center of the field of view. As
air is slowly let into one of the tubes, the central field of view changes dark and back to bright a total of 198
times.
(a) What is the index of refraction for air?
(b) If the fringes can be counted to ±0.25 fringe, where one fringe is equivalent to one complete cycle of
intensity variation at the center of the field of view, to what accuracy can the index of refraction of air be
determined by this experiment?
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