A space station is constructed in the shape of a hollow ring of mass 5.00 × 10 4 kg. Members of the crew walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius r = 100 m. At rest when constructed, the ring is set rotating about its axis so that the people inside experience an effective free-fall acceleration equal to g . (See Fig. P10.52.) The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring. (a) What angular momentum does the space station acquire? (b) For what time interval must the rockets be fired if each exerts a thrust of 125 N? Figure P10.52 Problems 52 and 54.
A space station is constructed in the shape of a hollow ring of mass 5.00 × 10 4 kg. Members of the crew walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius r = 100 m. At rest when constructed, the ring is set rotating about its axis so that the people inside experience an effective free-fall acceleration equal to g . (See Fig. P10.52.) The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring. (a) What angular momentum does the space station acquire? (b) For what time interval must the rockets be fired if each exerts a thrust of 125 N? Figure P10.52 Problems 52 and 54.
Solution Summary: The author analyzes how the angular momentum acquired by the space station is equal to the acceleration due to gravity.
A space station is constructed in the shape of a hollow ring of mass 5.00 × 104 kg. Members of the crew walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius r = 100 m. At rest when constructed, the ring is set rotating about its axis so that the people inside experience an effective free-fall acceleration equal to g. (See Fig. P10.52.) The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring. (a) What angular momentum does the space station acquire? (b) For what time interval must the rockets be fired if each exerts a thrust of 125 N?
Figure P10.52 Problems 52 and 54.
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.
You're on an interplanetary mission, in an orbit around the Sun. Suppose you make a maneuver that brings your perihelion in closer to the Sun but leaves your aphelion unchanged. Then you must have
Question 2 options:
sped up at perihelion
sped up at aphelion
slowed down at perihelion
slowed down at aphelion
The force of the quadriceps (Fq) and force of the patellar tendon (Fp) is identical (i.e., 1000 N each). In the figure below angle in blue is Θ and the in green is half Θ (i.e., Θ/2). A) Calculate the patellar reaction force (i.e., R resultant vector is the sum of the horizontal component of the quadriceps and patellar tendon force) at the following joint angles: you need to provide a diagram showing the vector and its components for each part. a1) Θ = 160 degrees, a2) Θ = 90 degrees. NOTE: USE ONLY TRIGNOMETRIC FUNCTIONS (SIN/TAN/COS, NO LAW OF COSINES, NO COMPLICATED ALGEBRAIC EQUATIONS OR ANYTHING ELSE, ETC. Question A has 2 parts!
The force of the quadriceps (Fq) and force of the patellar tendon (Fp) is identical (i.e., 1000 N each). In the figure below angle in blue is Θ and the in green is half Θ (i.e., Θ/2). A) Calculate the patellar reaction force (i.e., R resultant vector is the sum of the horizontal component of the quadriceps and patellar tendon force) at the following joint angles: you need to provide a diagram showing the vector and its components for each part. a1) Θ = 160 degrees, a2) Θ = 90 degrees. NOTE: USE DO NOT USE LAW OF COSINES, NO COMPLICATED ALGEBRAIC EQUATIONS OR ANYTHING ELSE, ETC. Question A has 2 parts!
Chapter 10 Solutions
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