How Is an Astronaut's Apparent Weight Calculated in Space?

AI Thread Summary
The discussion focuses on calculating the apparent weight of a 75 kg astronaut 2500 km from the Moon's center in two scenarios: moving at constant velocity and accelerating towards the Moon at 2.3 m/s². The relevant equations include gravitational force and weight calculations. The user initially struggled with the setup for the accelerating scenario, likening it to an elevator problem. Ultimately, the user resolved their confusion and successfully worked through the calculations. The thread highlights the importance of understanding gravitational effects and acceleration in determining apparent weight in space.
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Homework Statement


What is the apparent weight of a 75 kg astronaut 2500 km from the center of the Moon in a space vehicle (a) moving at constant velocity and (b) accelerating towards the moon at 2.3 m/s^2. State direction in each case.


Homework Equations



F=Gm1m2/r^2 and F=mg


The Attempt at a Solution



I solved part a and figure it out. Setting up b is what's giving me troubles. Should this be set up like an elevator/weightless problem or what? I'm uber confused.
 
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Disregard.. Figured it out.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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