# 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.

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.
Good. Now plug in ##F_g=mg## and solve for ##F_n##

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.
Yes that is correct. F_n is given. F_g is mg. Solve for m using your equation that you determined from your free body diagram and Newton 2, substituting in the given value for a. Then solve for F_g.

## What is the difference between true weight and apparent weight?

True weight is the actual weight of an object, which is a measure of the force of gravity acting on it. Apparent weight, on the other hand, is the perceived weight of an object, which takes into account not just the force of gravity but also any other forces acting on the object, such as buoyancy or drag.

## How is apparent weight different from weight?

Apparent weight is different from weight in that it takes into account other forces acting on an object, while weight is solely a measure of the force of gravity. For example, a person standing on a scale in an elevator may have a different apparent weight depending on whether the elevator is accelerating upwards or downwards, even though their true weight remains the same.

## What factors can affect the apparent weight of an object?

The apparent weight of an object can be affected by a variety of factors, including the object's mass, the force of gravity acting on it, the presence of other forces such as buoyancy or drag, and the reference frame in which the object is being measured. For example, an object may have a different apparent weight when measured on Earth versus on the moon due to the difference in gravity.

## How do you calculate apparent weight?

To calculate apparent weight, you need to take into account the object's true weight (determined by its mass and the force of gravity), as well as any other forces acting on the object. The equation for apparent weight is: Apparent weight = True weight - Other forces. This can be applied to situations such as an object in free fall or an object in a fluid, where other forces may be present.

## Why is it important to understand the difference between true weight and apparent weight?

It is important to understand the difference between true weight and apparent weight because it can affect the accuracy of measurements and calculations. In some situations, such as in physics experiments or engineering designs, it is crucial to have an accurate understanding of the forces acting on an object. By understanding the concept of apparent weight, scientists and engineers can make more precise and informed decisions. Additionally, understanding apparent weight can also help in understanding the behavior of objects in different environments, such as in space or underwater.

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