How Does Water Affect the Net Force on a Submerged Stone?

[rudransh verma]

You cannot ramdomly assign g to be a vector in some expressions and a vector magnitude in others

I didn’t do that intentionally because I know it’s wrong.
So are my variations right in post#24?
Have I got the concept of vectors?

 

[Orodruin]

I didn’t do that intentionally because I know it’s wrong.
So are my variations right in post#24?
Have I got the concept of vectors?

No, as I have already said. Many of them have major notational issues. The first thing you need to do is to take care of those. Then you can start writing down equations.

 

[rudransh verma]

Many of them have major notational issues.

Like?
We can sort it out one by one.

 

[Orodruin]

Like?
We can sort it out one by one.

No. It cannot be sorted out without the notation being sorted out first.

 

[rudransh verma]

No. It cannot be sorted out without the notation being sorted out first.

Ok! Let’s sort out the notation.
By the way I wrote what each notation mean in each eqn. Where is the problem?

 

[Orodruin]

Ok! Let’s sort out the notation.
By the way I wrote what each notation mean in each eqn. Where is the problem?

You have been told the problem repeatedly. Please read through what has already been said.

 

[rudransh verma]

You have been told the problem repeatedly. Please read through what has already been said.

I think I have solved the problem. I have been mixing the scalar and vector versions. g, -g, -mg, Fn(normal force), -Fs(static friction) are not vectors and are used in 1D motion.
Whereas the vectors are defined when we need to describe motion in 2D or 3D motion.
$\vec F_s=F_s\hat i$ is correct if static friction is actually in positive direction. We can also write this like $F_s=F_s=\mu F_N$
$\vec F_s=-F_s\hat i$ is same as $-F_s=-\mu F_N$
We can use the scalar as well as vector form if the motion is 1D. Both will be correct.
I edited the post#24. Please verify it. I hope it’s right now.
In 1D motion we can just use signs to tell the direction. But in2D or 3D we need vectors like $\vec F_a=a\hat i +b \hat j$

 

[rudransh verma]

It's best to use a scalar equation for Archimedes principle with the understanding that the buoyant force acts in an upward direction. That way things are kept simple and one can start applying it to problem at hand without unecessary confusion.

You are right but some confusions can become a problem of future.

 

[vcsharp2003]

You are right but some confusions can become a problem of future.

Also, remember when you express both sides of the equation in terms of unit vectors in one dimension, you are free to take +ve direction of x-axis pointing downward or upward. Accordingly, your vector equation in one dimension will change.

 

[rudransh verma]

Also, remember when you express both sides of the equation in terms of unit vectors in one dimension, you are free to take +ve direction of x-axis pointing downward or upwards. Accordingly, your vector equation in one dimension will change.

Let’s keep the sign convention constant. I always take +ve as up and right as +ve.

The problem arised I think because in Resnik the free body diagrams and fig. have vectors indicated. And then they write some thing like -mg+F_N=m(0). So I thought they are vectors.

 

[Doc Al]

Sadly, you are making a rather simple problem way too complicated. (And why in the world did you bring up friction?)

As the stone is raised, what forces act on it? What are their directions? Then you can choose a sign convention and write an equation for their components.

because in Resnik the free body diagrams

What book are you using? (Title, author, and edition.)

 

[vcsharp2003]

So I thought they are vectors.

First draw a free body diagram and then choose your axes system. Then simply write down the equations. This is what probably is done in the book by Resnick Halliday.

 

[rudransh verma]

Sadly, you are making a rather simple problem way too complicated. (And why in the world did you bring up friction?)

No I am not trying to solve that problem. But I am asking you to clear my doubts on vector and scalar form of any eqn in a general sense. First that needs to be solved and then I will come back to the original problem in OP.
Principles of Physics International student edition.

 

[vcsharp2003]

Let’s keep the sign convention constant. I always take +ve as up and right as +ve.

The problem arised I think because in Resnik the free body diagrams and fig. have vectors indicated. And then they write some thing like -mg+F_N=m(0). So I thought they are vectors.

Can you post the figure you are talking about in the book by Resnick Halliday?

 

[rudransh verma]

Can you post the figure you are talking about in the book by Resnick Halliday?

 

[vcsharp2003]

What's the doubt you have about the free body diagrams you posted?

 

[rudransh verma]

What's the doubt you have about the free body diagrams you posted?

See in FBD they are showing vectors but when solving they are writing like T-mg=-ma.

 

[Doc Al]

See in FBD they are showing vectors but when solving they are writing like T-mg=-ma.

The equations are for the components of those vectors. (Vectors themselves aren't positive or negative, they just point in some direction.)

 

[vcsharp2003]

See in FBD they are showing vectors but when solving they are writing like T-mg=-ma.

Showing forces in vector notation is entirely upto you. There is no harm in using vector notation in free body diagram. Personally, I don't use vector notation in free body diagram. But, you must note that each vector/force in FBD must be broken into its components along the axes system chosen and then the equations for each axis is written in terms of magnitude of vector components.
That is the process in going from FBD to equations.

 

[rudransh verma]

The equations are for the components of those vectors.

I think the proper way is to write with unit vectors or just write the scalar eqns and solve. This seems like -mg is a vector.

terms of magnitude of vector components.

That’s what I have been doing , breaking vectors into its components like mgcostheta and mgsintheta.

 

[Doc Al]

I think the proper way is to write with unit vectors or just write the scalar eqns and solve. This seems like -mg is a vector.

Expressing a vector using unit vectors is always fine. But you'll eventually have to deal with components. "-mg" is the component of the weight (a vector) using the typical "up is positive" sign convention.

 

[vcsharp2003]

I think the proper way is to write with unit vectors

For components there's no need to write as vectors. The idea to use components rather than orginal vectors is to simplify things so we use magnitudes along an axis to get equations.

-mg is not a vector, but just part of an equation along a certain axis.

 

[rudransh verma]

-mg" is the component of the weight (a vector)

It’s better to say $-mg\hat j$ is component.

Can we now concentrate on the question in OP.
What will be the V displaced?

 

[Doc Al]

It’s better to say $-mg\hat j$ is component.

No it isn't.

Can we now concentrate on the question in OP.
What will be the V displaced?

Just call the volume of the stone V. You don't need to know the actual volume, just the mass of the displaced water. All the info to solve for that is given.

 

[rudransh verma]

Just call the volume of the stone V. You don't need to know the actual volume, just the mass of the displaced water. All the info to solve for that is given.

W=(-mg+rhoVg)d=-250J

 

[Doc Al]

Hint: The mass of anything = ρV.

 

[rudransh verma]

Hint: The mass of anything = ρV.

I solved it. -250J

 

[Doc Al]

I solved it. -250J

The work to raise the stone should be positive.

 

[rudransh verma]

The work to raise the stone should be positive.

How? The net force is downwards and displacement is upwards.

 

[vcsharp2003]

How? The net force is downwards and displacement is upwards.

I would use the following equation to solve this problem.

$W_{net}= \Delta KE + \Delta PE$, where $W_{net}$ is work done by applied forces (excluding force of gravity)