Why does a log float horizontally?

[RubinLicht]

Homework Statement

Why does a log float horizontally as opposed to vertically?

Homework Equations

Nah

The Attempt at a Solution

I can kind of imagine why a vertical log would be in unstable equilibrium, but the thought isn't quite as logically cohesive as I'm comfortable with, so could anyone elaborate using concepts of buoyancy or even energy (which I think does have something to do with it)

Taken from the "questions" section of Halliday and resnick, chapter 17: fluid statics.

 

[Simon Bridge]

The concept you want is "balance" and "stabitity".
Sketch a log floating vertically - but tipped very slightly - and examine the forces on it: where is the center of mass and what happens?
Repeat for a log floating horizontally.

 

[RubinLicht]

The concept you want is "balance" and "stabitity".
Sketch a log floating vertically - but tipped very slightly - and examine the forces on it: where is the center of mass and what happens?
Repeat for a log floating horizontally.

Ah nvm the center of mass stays above the center of buoyancy, got it. Thanks!

 

[Simon Bridge]

Well done.

 

[haruspex]

Ah nvm the center of mass stays above the center of buoyancy, got it. Thanks!

No. A floating object of uniform density always has its centre of mass higher than its centre of buoyancy. Sketch the vertical log and the horizontal log and you will find it true for both.
Stability of floating objects is subtler. If the object is perturbed by a small rotation, its profile in the water can change. This shifts the centre of buoyancy. If it shifts the centre of buoyancy in the same direction as the centre of mass, but further, the resulting torque restore equilibrium.
See https://en.m.wikipedia.org/wiki/Buoyancy#Stability

For a long cylinder, its stability about its axis is neutral, i.e. there is no restoring torque, but the no reinforcing torque either.

In fact, the question is not correct without qualification. A very short fat log will float upright (in the sense that its cylindrical axis is upright), not on its side. There may even be a range of ratios for which the log will be stable at a jaunty angle.

 

[RubinLicht]

No. A floating object of uniform density always has its centre of mass higher than its centre of buoyancy. Sketch the vertical log and the horizontal log and you will find it true for both.
Stability of floating objects is subtler. If the object is perturbed by a small rotation, its profile in the water can change. This shifts the centre of buoyancy. If it shifts the centre of buoyancy in the same direction as the centre of mass, but further, the resulting torque restore equilibrium.
See https://en.m.wikipedia.org/wiki/Buoyancy#Stability

For a long cylinder, its stability about its axis is neutral, i.e. there is no restoring torque, but the no reinforcing torque either.

In fact, the question is not correct without qualification. A very short fat log will float upright (in the sense that its cylindrical axis is upright), not on its side. There may even be a range of ratios for which the log will be stable at a jaunty angle.

That was a very clear explanation, thanks.

 

[Leong]

Original question from the book: Logs dropped upright into a pond do not remain upright, but float ‘flat’ in the water. Explain.

A long log can float vertically but this position of equilibrium is unstable. So, a slight tilt will make it tilt further from the vertical position until it reaches a new equilibrium position which is more stable: the horizontal floating equilibrium position. When a log is dropped vertically into water, it will first oscillate up and down, the oscillation it experiences make it impossible to achieve the unstable upright equilibrium position. This is because when it is oscillating, a tilt, no matter how small it is, will occur.
The vertical equilibrium position of a long log is unstable because in this position, the metacentre is below the centre of gravity of the log. Metacentre is a concept used to determine if an equilibrium position is stable or unstable.

If we cut a portion of the long log to get a fat short log that looks like a disc, and drop it into the water, the log will float upright because this position of equilibrium is stable. The metacentre is above the centre of gravity. The log will still oscillate up and down when we drop it into the water, but since the equilibrium position is stable, a slight tilt will produce a restoring moment for the log to return to and reach the stable equilibrium position, as opposed to an overturning moment produced by a slight tilt in an unstable equilibrium position like the long log case.

This is an excerpt from Fluid Mechanics (by Frank M. White) on page 86:
‘A floating body as in Fig. 2.17 may not approve of the position in which it is floating. If so, it will overturn at the first opportunity and is said to be statically unstable, like a pencil balanced upon its point. The least disturbance will cause it to seek another equilibrium position which is stable.’

You can refer to the book if you need more information.

 

[haruspex]

You can refer to the book if you need more information.

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