Effective g
Calculate the effective value of g, the acceleration of gravity at a point 310.0 km above the earth surface.
8.91 m/s^2
The height (310.0 km) above the earth surface is typically where the space shuttle flies. From your last calculation you find that gravity at 310.0 km is close to the gravity on the earth's surface. This means that the weight (mass times gravity) of the astronaut is not zero. Choose the correct/incorrect statements below.
Incorrect: The astronauts in the shuttle appears "NOT weightless" because the spaceship moves in one direction (around the Earth) whereas the astronaut is pressing its floor along a different direction (towards the Earth).
Correct: The astronauts in the shuttle appears "weightless" because both the spaceship and the astronauts share the same acceleration.
Incorrect: The astronauts in the shuttle appears "weightless" because the centrifugal force exerted on the spaceship compensates its weight.
Concepts
From part (a), the acceleration due to gravity at an altitude of 310.0 km above the earth surface is 8.91 m/s2. This is 90.9 % that of g on the surface of earth and is not negligible. When a shuttle is in orbit, it is traveling at a high speed. Gravity pulls the shuttle and the astronauts toward earth so that they are free-falling toward earth but in a circular path so that they never hit earth!
Two things are required, (1) free-fall and the (2) high tangential speed of the shuttle and the astronauts. If you just say, free-fall, the shuttle and the astronauts will sooner or later goes splat as they hit the surface of the Earth!
8.91 m/s^2
The height (310.0 km) above the earth surface is typically where the space shuttle flies. From your last calculation you find that gravity at 310.0 km is close to the gravity on the earth's surface. This means that the weight (mass times gravity) of the astronaut is not zero. Choose the correct/incorrect statements below.
Incorrect: The astronauts in the shuttle appears "NOT weightless" because the spaceship moves in one direction (around the Earth) whereas the astronaut is pressing its floor along a different direction (towards the Earth).
Correct: The astronauts in the shuttle appears "weightless" because both the spaceship and the astronauts share the same acceleration.
Incorrect: The astronauts in the shuttle appears "weightless" because the centrifugal force exerted on the spaceship compensates its weight.
Concepts
From part (a), the acceleration due to gravity at an altitude of 310.0 km above the earth surface is 8.91 m/s2. This is 90.9 % that of g on the surface of earth and is not negligible. When a shuttle is in orbit, it is traveling at a high speed. Gravity pulls the shuttle and the astronauts toward earth so that they are free-falling toward earth but in a circular path so that they never hit earth!
Two things are required, (1) free-fall and the (2) high tangential speed of the shuttle and the astronauts. If you just say, free-fall, the shuttle and the astronauts will sooner or later goes splat as they hit the surface of the Earth!