# True vs. Apparent weight question

In summary, to find the astronaut's true weight, you need to use Newton's 2nd law and the equation Fn - Fg = ma, where Fn is the apparent weight, Fg is the true weight, and a is the acceleration of the system. The normal force is equal to the apparent weight, not the true weight. Using these equations and the given values for acceleration and the mass of the Earth, you can solve for the astronaut's true weight.

## Homework Statement

An astronaut in a rocket has an apparent weight of 1.35x103N [down]. If the acceleration of a rocket is 14.7 m/s2 [up] near Earth's surface, what is the astronaut's true weight? The acceleration due to gravity on Earth's surface is about 9.81 m/s2 [down].
Mass of Earth is 5.97x1024, not sure if that's needed or not.

## Homework Equations

Fnet = ma
Fg = Gm1m2 / r2
g = Gm(source) / r2
g = Fg / m(test)

## The Attempt at a Solution

I'm confused about what I should be solving for (I think it should be Fg), if the apparent weight is the normal force shouldn't it be directed up? I'm also confused about which acceleration to use and where, also which formula to use. So I'm pretty lost! Any help would be greatly appreciated :)

Yes the normal force is directed up on the astronaut and is equal to the so-called apparent weight. Just use Newton's 2nd law and your first and last equation after first determining the other force besides the normal force acting on the astronaut. No need to use the middle 2 equations since g is already given.

## Homework Statement

An astronaut in a rocket has an apparent weight of 1.35x103N [down]. If the acceleration of a rocket is 14.7 m/s2 [up] near Earth's surface, what is the astronaut's true weight? The acceleration due to gravity on Earth's surface is about 9.81 m/s2 [down].
Mass of Earth is 5.97x1024, not sure if that's needed or not.

## Homework Equations

Fnet = ma
Fg = Gm1m2 / r2
g = Gm(source) / r2
g = Fg / m(test)

## The Attempt at a Solution

I'm confused about what I should be solving for (I think it should be Fg), if the apparent weight is the normal force shouldn't it be directed up? I'm also confused about which acceleration to use and where, also which formula to use. So I'm pretty lost! Any help would be greatly appreciated :)
Have you drawn a free body diagram, or do you think you have advanced beyond the point where you need to use free body diagrams?

PhanthomJay said:
Yes the normal force is directed up on the astronaut and is equal to the so-called apparent weight. Just use Newton's 2nd law and your first and last equation after first determining the other force besides the normal force acting on the astronaut. No need to use the middle 2 equations since g is already given.
I'm still a bit confused, I solved for the mass using Fg = (mass)(gravity) :
1.35x103N = (mass)(9.81m/s2)
mass = 137.614 kg

But then after I plugged it into my formula Fn - Fg = ma I got a true weight of -672 N. I'm not sure where I went wrong.

Chestermiller said:
Have you drawn a free body diagram, or do you think you have advanced beyond the point where you need to use free body diagrams?
I have drawn the free body diagram, and I have come up with the equation Fn - Fg = ma. However when I plug in the mass that I found (if that's even the right mass) I get a negative answer.

How much is the system accelerating by?

You have mistakenly confused apparent weight with true weight. Fg is true weight, Fn is apparent weight. Your equation is correct, but you need to make the proper substitutions. The normal force is not equal to mg.

Sho Kano said:
How much is the system accelerating by?
14.7 m/s2 up.

PhanthomJay said:
You have mistakenly confused apparent weight with true weight. Fg is true weight, Fn is apparent weight. Your equation is correct, but you need to make the proper substitutions. The normal force is not equal to mg.
Oh I see! I know why that is wrong, but I'm still not sure about how to find the mass of the astronaut correctly. I think I need that first to answer the question.