- #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.