Buoyant force acting on an inverted glass in water

[MatinSAR]

Good... plug that in, solve for $\delta(h)$. I would suggest evaluating that solution at $h = 0$ to ensure you have chosen the correct form.

Ok I will but why should I find this ?

 

[erobz]

Ok I will but why should I find this ?

Because you to eliminate $\delta$ as an independent variable and get everything in terms of the depth $h$.

 

[MatinSAR]

Because you to eliminate $\delta$ as an independent variable and get everything in terms of the depth $h$.

If we consider h=0 :

 

[erobz]

If we consider h=0 :
View attachment 318757

Thats isn't what I meant.

Did you solve for $\delta$ as a function of $h$ yet?

Remember, $\delta$ is part of both the pressure and the volume of the gas. When I say solve for $\delta$ I mean solve the following for $\delta$:

$$P_{atm} A l = P(h,\delta) V\llap{-}(\delta)$$

 

[Frabjous]

If we consider h=0 :
View attachment 318757

Think about what h=0 physically corresponds to.

 

[MatinSAR]

Thats isn't what I meant.

Did you solve for $\delta$ as a function of $h$ yet?

Remember, $\delta$ is part of both the pressure and the volume of the gas. When I say solve for $\delta$ I mean solve the following for $\delta$:

$$P_{atm} A l = P(h,\delta) V\llap{-}(\delta)$$

Can I find δ using :

P_atmL/(L -δ) = P_atm+ρg(h-δ)

Think about what h=0 physically corresponds to.

The moment that the glass enters the water.

 

[erobz]

Can I find δ using :

P_atmL/(L -δ) = P_atm+ρg(h-δ)

Give it a try.

 

[MatinSAR]

Give it a try.

At h=0 delta should be zero. The above equation confirms this.
And we can see that if h goes to ∞ the delta goes to L.

 

[erobz]

View attachment 318764
At h=0 delta should be zero. The above equation confirms this.
And we can see that if h goes to ∞ the delta goes to L.

Seems good. I had to check whether that quadratic simplified, I didn't take it that far! Good Job!

 

[MatinSAR]

Seems good. I had to check whether that quadratic simplified, I didn't take it that far! Good Job!

I appreciate your help. I didn't use P_atmL/(L -δ) = P_atm+ρg(h-δ) because
2nd degree equation was obtained ...

I have used the formula you suggested ...

 

[erobz]

I appreciate your help. I didn't use P_atmL/(L -δ) = P_atm+ρg(h-δ) because
2nd degree equation was obtained ...

I have used the formula you suggested ...

What formula?

 

[MatinSAR]

Think about what h=0 physically corresponds to.

Thank you for you rhelp and time.

What formula?

This post :
https://www.physicsforums.com/threa...-inverted-glass-in-water.1047903/post-6831524

 

[erobz]

Thank you for you rhelp and time.

This post :
https://www.physicsforums.com/threa...-inverted-glass-in-water.1047903/post-6831524

I don't understand! I solved it as a quadratic. However, your result indicates that my quadratic must be factorable I believe?

 

[MatinSAR]

I don't understand! I solved it as a quadratic. However, your result indicates that my quadratic must be factorable I believe?

Maybe I made a mistake ...
was my answer correct ??

 

[erobz]

Maybe I made a mistake ...
was my answer correct ??

It plots identically to my solution?

 

[MatinSAR]

It plots identically to my solution?

Let me send you a picture of what I have done ...

 

[MatinSAR]

It plots identically to my solution?

My mistake is here :

So to find delta we have to solve a quadratic equation ...

The question only asked about the increase and decrease of F force, I didn't want to waste your time at all... I'm sorry...
edit :

I have solved that quadratic equation ...

 

[erobz]

My mistake is here :
View attachment 318768

So to find delta we have to solve a quadratic equation ...

The question only asked about the increase and decrease of F force, I didn't want to waste your time at all... I'm sorry...
edit :

View attachment 318770

I have solved that quadratic equation ...

What you did on accident the first time by omitting $\delta$ was actually a really good approximation for $\delta \ll h$. For the parameters I used I couldn’t tell the apart.

 

[erobz]

My mistake is here :
View attachment 318768

So to find delta we have to solve a quadratic equation ...

The question only asked about the increase and decrease of F force, I didn't want to waste your time at all... I'm sorry...
edit :

View attachment 318770

I have solved that quadratic equation ...

I wanted you to explore it. It wasn’t a waste of my time at all!

 

[MatinSAR]

I wanted you to explore it. It wasn’t a waste of my time at all!

Thank you for your help and time ...