- #1
Abu
- 39
- 16
Homework Statement
What is the apparent weight of a 70-kg astronaut 3800 km from the center of the Earth's Moon in a space vehicle when
a) Moving at a constant velocity
b) Accelerating toward the Moon at 2.9 m/s^2?
State direction in each case
Homework Equations
wt = m(g+a)
wt = m(g-a)
Fgr = GmM/r^2
The Attempt at a Solution
So for a) I first found the acceleration due to gravity at that point, which is
g = GM/r^2
The mass of the moon is 7.36x10^22
g = 6.67x10^-11 (7.36x10^22)/3800000
g = 0.33 m/s
At a constant velocity, the weight is simply mg. So, 70x0.33 = 23.7 Newtons
For b however, I am not entirely sure. This is what I was thinking when I was trying to solve the problem:
Since you are accelerating at 2.9m/s^2 towards the moon, I will use wt = m(g-a) because I was taught that when going against the force of gravity, the wt = m(g+a) is used, and vice versa.
I get the following answer:
wt = 70(0.33 - 2.9)
= -179.9 Newtons
Now I have a couple of problems. I am not sure what direction these values for a) and b) are pointed towards and if a negative apparent weight is even possible (or if that answer is even correct in the first place).
Thank you very much for your patience.