Two astronauts (Fig. P10.67), 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 momentum 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? Figure P10.67 Problems 67 and 68.
Two astronauts (Fig. P10.67), 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 momentum 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? Figure P10.67 Problems 67 and 68.
Two astronauts (Fig. P10.67), 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 momentum 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?
Figure P10.67 Problems 67 and 68.
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.
Consider the circuit shown in the figure below. (Let R = 12.0 (2.)
25.0 V
10.0
www
10.0 Ω
b
www
5.00 Ω
w
R
5.00 Ω
i
(a) Find the current in the 12.0-0 resistor.
1.95
×
This is the total current through the battery. Does all of this go through R? A
(b) Find the potential difference between points a and b.
1.72
×
How does the potential difference between points a and b relate to the current through resistor R? V
3.90 ... CP A rocket designed to place small payloads into orbit
is carried to an altitude of 12.0 km above sea level by a converted
airliner. When the airliner is flying in a straight line at a constant
speed of 850 km/h, the rocket is dropped. After the drop, the air-
liner maintains the same altitude and speed and continues to fly in
a straight line. The rocket falls for a brief time, after which its
rocket motor turns on. Once its rocket motor is on, the combined
effects of thrust and gravity give the rocket a constant acceleration
of magnitude 3.00g directed at an angle of 30.0° above the hori-
zontal. For reasons of safety, the rocket should be at least 1.00 km
in front of the airliner when it climbs through the airliner's alti-
tude. Your job is to determine the minimum time that the rocket
must fall before its engine starts. You can ignore air resistance.
Your answer should include (i) a diagram showing the flight paths
of both the rocket and the airliner, labeled at several…
1. In an industrial fabrication process, a fluid, with density p = 800 kg/m and specific heat capacity
c = 5000 J/kg-C°, emerges from a tank at a temperature, T, = 400 °C. The fluid then enters a metal pipe with inner radius a = 2.0 cm and outer radius b = 3.0 cm and thermal conductivity k = 180 W/m•C°.
Outside the pipe the temperature is fixed at Tout = 15 °C.
If the fluid flows at speed v = 8.0 m/s and the length of the pipe is L = 25 m, what is the temperature
of the fluid at the end of the pipe? (Answer: 83 °C)
please I need to show All work problems step by step
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