Work calculation for lifting a Tetrahedron-shaped object from the water

[Steve4Physics]

@Frabjous, I tried sending a PM (private message) to you (and @NODARman). But the system wouldn't let me send it to you. I know the problem requires a method using integration, but If you are interested in how to do it without any explicit integration, let me know.

 

[Frabjous]

@Frabjous, I tried sending a PM (private message) to you (and @NODARman). But the system wouldn't let me send it to you. I know the problem requires a method using integration, but If you are interested in how to do it without any explicit integration, let me know.

If you are talking about not having to integrate 1-(h/h₀)³, I’d be interested.

 

[Steve4Physics]

If you are talking about not having to integrate 1-(h/h₀)³, I’d be interested.

I'll attempt to send it again.

 

[Charles Link]

Maybe I misread the above posts, but IMO the buoyancy (from Archimedes principle) needs to be $\int \rho g \,dV=\int \rho g A \, dh$. and note: $\rho$ is the density of the water, so it along with $g$ can be in front of the integral.). post 26 is trying to do an integral of $\int V \, dh$ , and that is incorrect.

 

[Frabjous]

Maybe I misread the above posts, but IMO the buoyancy (from Archimedes principle) needs to be $\int \rho g \,dV=\int \rho g A \, dh$. and note: $\rho$ is the density of the water, so it along with $g$ can be in front of the integral.). post 26 is trying to do an integral of $\int V \, dh$ , and that is incorrect.

It’s a work integral of a fully submerged volume. This is an incomplete thread because the discussion moved to a private conversation. I believe the OP is satisfied.

 

[Charles Link]

It’s a work integral of a fully submerged volume. This is an incomplete thread because the discussion moved to a private conversation. I believe the OP is satisfied.

The OP looks to me to still be doing an incorrect computation of the buoyant force.

 

[Frabjous]

The OP looks to me to still be doing an incorrect computation of the buoyant force.

He’s calculating the work done by gravity and buoyancy of a fully submerged constant volume that is lifted height L-h.

 

[Charles Link]

He’s calculating the work done by gravity and buoyancy of a fully submerged constant volume that is lifted height L-h.

Thank you=I just re-read the title of the post=the work to lift the object. I would expect to see $W=\int F \cdot ds$, but my mistake. :)