Fluid Mechanics: Wooden plank floating in water at an angle

AI Thread Summary
The discussion focuses on the buoyancy of a wooden plank floating at an angle in water, with the plank's density at 0.5 and the water's density at 2 times that. A suggestion is made to use subscripts for clarity in calculations, specifically referencing the water's density in relation to the angle of the plank. The importance of establishing an upper limit for the angle is highlighted for verification purposes. The conversation emphasizes the need for precise notation in fluid mechanics problems. Understanding these principles is crucial for analyzing the behavior of floating objects.
TkoT
Messages
7
Reaction score
2
1571618520503.png
1571618529690.png
 
Last edited by a moderator:
Physics news on Phys.org
Plank has density ##\rho = 0.5##. Water has ##2\rho##.

I find it much better to use a subscript in such cases: ##\rho_{\text {water}}l/\cos\theta## (plus add an upper limit for ##\theta## for a check later on... )
 
  • Like
Likes TkoT
BvU said:
Plank has density ##\rho = 0.5##. Water has ##2\rho##.

I find it much better to use a subscript in such cases: ##\rho_{\text {water}}l/\cos\theta## (plus add an upper limit for ##\theta## for a check later on... )
thank you for your help
 
  • Like
Likes berkeman
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
Back
Top