Astronaut's Apparent Weight in Different Gravitational Fields

[sona1177]

Homework Statement

What is the apparent weight of a 730-N astronaut when her spaceship has an acceleration of magnitude 2.0g in the following two situations:

a) just above the surface of the Earth
b) far from any stars or planets

Homework Equations

Wapparent=m(g + a)

The Attempt at a Solution

=2mg=2 * 74.5 * 9.8=1460 N. I guess this would be the answer to part b, away from stars or planets. My book says a) 2200 N and b) 1500 N (accounting for significant figures). But how do I do part a? I don't see the difference between being just above the surface of the Earth and far from any stars or planets.

 

[Andrew Mason]

Homework Statement

What is the apparent weight of a 730-N astronaut when her spaceship has an acceleration of magnitude 2.0g in the following two situations:

a) just above the surface of the Earth
b) far from any stars or planets

Homework Equations

Wapparent=m(g + a)

The Attempt at a Solution

=2mg=2 * 74.5 * 9.8=1460 N. I guess this would be the answer to part b, away from stars or planets. My book says a) 2200 N and b) 1500 N (accounting for significant figures). But how do I do part a? I don't see the difference between being just above the surface of the Earth and far from any stars or planets.

Think of two situations: 1) when the astronaut is standing still, not accelerating; and 2) the case where he/she is accelerating at 2g.

Near the earth, in the first case (a = 0) the normal force (from the rocket thrust) must just equal the force of gravity, mg, in order to have 0 acceleration. In order to accelerate at 2g away from the earth, the force must be 2mg over the force required just to stand still.

If far from gravitational fields, the rocket does not have to provide any thrust in order to maintain 0 acceleration. So in order to accelerate at 2g the force just needs to be 2mg (ie 2mg over the force needed to maintain 0 acceleration).

AM