Apparent weight of a body with upward acceleration

[TH02]

Homework Statement

What is the apparent weight during take-off of an astronaut whose actual weight is 750N if the resultant upward acceleration is 5g?

Relevant Equations

F=ma
Weight = mg

I initially attempted to get the answer by multiplying the mass by 50, as I assumed if the upward acceleration was 5g then the weight could be found by just multiplying the mass by the acceleration of 50ms^-2. However that resulted in an answer of 3750 which was far below the correct answer of 4500. After much trial and error I only got the correct answer when I multiplied the mass of 75kg by an acceleration of 60ms^-2, however I do not understand why this works.

 

[PeroK]

Homework Statement:: What is the apparent weight during take-off of an astronaut whose actual weight is 750N if the resultant upward acceleration is 5g?
Relevant Equations:: F=ma
Weight = mg

I initially attempted to get the answer by multiplying the mass by 50, as I assumed if the upward acceleration was 5g then the weight could be found by just multiplying the mass by the acceleration of 50ms^-2. However that resulted in an answer of 3750 which was far below the correct answer of 4500. After much trial and error I only got the correct answer when I multiplied the mass of 75kg by an acceleration of 60ms^-2, however I do not understand why this works.

What's the weight if the upward acceleration is zero?

 

[TH02]

What's the weight if the upward acceleration is zero?

Wouldn't it just be 750N?

 

[PeroK]

Wouldn't it just be 750N?

Yes. And what if the upward acceleration is $1g$?

 

[TH02]

Yes. And what if the upward acceleration is $1g$?

75N?

 

[PeroK]

75N?

How do you get that?

 

[TH02]

How do you get that?

My thinking was if I have a gravitational field strength of 10ms^-2 acting downwards and I also have an upwards acceleration of 1g (I think this is 10ms^2 in this context) acting in the opposite direction, they would cancel out? I have a feeling I'm making a big mistake here

 

[PeroK]

My thinking was if I have a gravitational field strength of 10ms^-2 acting downwards and I also have an upwards acceleration of 1g (I think this is 10ms^2 in this context) acting in the opposite direction, they would cancel out? I have a feeling I'm making a big mistake here

You should be thinking in terms of forces. When there is more than one force, you must add them together to get the unbalanced force (*). See the Khan academy page. You should also learn about free body diagrams if you haven't already.

(*) Note that force is a vector quantity.

 

[TH02]

You should be thinking in terms of forces. When there is more than one force, you must add them together to get the unbalanced force (*). See the Khan academy page. You should also learn about free body diagrams if you haven't already.

(*) Note that force is a vector quantity.

Thank you, I'll have a look

 

[Chestermiller]

Have you drawn a free body diagram of the astronaut showing the forces acting on him, or do you think you have advanced beyond the need to do that?

 

[TH02]

Have you drawn a free body diagram of the astronaut showing the forces acting on him, or do you think you have advanced beyond the need to do that?

I drew a free body diagram but I'm not sure if I did it correctly

 

[Chestermiller]

I drew a free body diagram but I'm not sure if I did it correctly

Let’s see it and the associated force balance equation.

 

[TH02]

Let’s see it and the associated force balance equation.

Let’s see it and the associated force balance equation.

I'm not sure what you mean by force balance equation
But here is a rough free body diagram

 

[PeroK]

I'm not sure what you mean by force balance equation
But here is a rough free body diagram
View attachment 265763

That clearly shows a downward force and an upward acceleration!

However, perhaps the real question in this case is what is weight anyway?

 

[Chestermiller]

I don’t see a. gravitational force acting on him, and I don’t see an upward force from the seat he is in.

 

[TH02]

That clearly shows a downward force and an upward acceleration!

However, perhaps the real question in this case is what is weight anyway?

Isn't weight the force acting on the mass of a body due to the gravitational attraction of the earth?

I don’t see a. gravitational force acting on him, and I don’t see an upward force from the seat he is in.

Ah yes, maybe I should step back for a moment and learn how to properly do FBD's

 

[PeroK]

Isn't weight the force acting on the mass of a body due to the gravitational attraction of the earth?

Yes, then I guess the question is what is the apparent weight you are asked to calculate?

 

[TH02]

Yes, then I guess the question is what is the apparent weight you are asked to calculate?

I'm not quite sure, would it be a sum of the true weight and the force caused by the body's mass and acceleration?

 

[PeroK]

I'm not quite sure, would it be a sum of the true weight and the force caused by the body's mass and acceleration?

Note that acceleration does not cause a force. An unbalanced force causes acceleration.

In this case I would take apparent weight to be the force between the astronaut and the seat she is sitting in.

 

[Chestermiller]

F-mg = ma

 

[Chestermiller]

Isn't weight the force acting on the mass of a body due to the gravitational attraction of the earth?Ah yes, maybe I should step back for a moment and learn how to properly do FBD's

Obviously

 

[TH02]

I've figured out how to do the FBD's and I think I've got it now, thanks for the help and sorry for being a bit thick
$F-mg=ma$
$F=mg+ma$
$F=m(g+a)$
$F=75(10+50)=4500N$

 

[haruspex]

I've figured out how to do the FBD's and I think I've got it now, thanks for the help and sorry for being a bit thick
$F-mg=ma$
$F=mg+ma$
$F=m(g+a)$
$F=75(10+50)=4500N$

Yes, but you did not need to assume a value for g.
If the upward acceleration is 5g then the apparent weight is 6 times the rest weight.