# Fluid Mechanics: Wooden plank floating in water at an angle

• TkoT
In summary, when a wooden plank is placed in water at an angle, it displaces a certain volume of water equal to its own weight, creating an upward force called buoyancy. The density, shape, and weight of the plank all affect its ability to float at an angle, with a lower density and flatter, wider shape being more conducive to floating. There is a limit to the angle at which a plank can float, known as the angle of stability, and the density of the water affects the plank's ability to float at a certain angle. A wooden plank cannot float completely vertically in water as the buoyancy force would be equal to the weight and cause it to sink.
TkoT

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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... )

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... )

berkeman

## What is fluid mechanics?

Fluid mechanics is the branch of physics that deals with the study of fluids (liquids and gases) and their behavior in motion. It involves the study of properties such as velocity, pressure, and density, and how these properties affect the motion of fluids.

## Why does a wooden plank float in water at an angle?

A wooden plank floats in water at an angle because of the principle of buoyancy. This principle states that an object will float in a fluid if the weight of the fluid it displaces is equal to or greater than its own weight. When the plank is placed in water at an angle, it displaces a certain volume of water, which exerts an upward force on the plank, keeping it afloat.

## How does the shape of the wooden plank affect its buoyancy?

The shape of the wooden plank affects its buoyancy because it determines the amount of water it will displace. A wider and flatter plank will displace more water and have greater buoyancy compared to a narrower and thicker plank. This is why boats are designed with a wide and flat bottom to increase their buoyancy and prevent them from sinking.

## What factors can cause a wooden plank to sink in water?

A wooden plank can sink in water if its weight is greater than the weight of the water it displaces. This can happen if the plank is too heavy or if it is damaged and takes in water, increasing its weight. Additionally, if the plank is placed in water at a steep angle, it may not displace enough water to counteract its weight, causing it to sink.

## How does surface tension affect the floating of a wooden plank in water?

Surface tension is the force that causes the surface of a liquid to behave like a thin elastic sheet. In the case of a wooden plank floating in water, surface tension can help keep the plank afloat by creating a layer of water molecules that support the plank's weight. However, if the plank is too heavy or if there is a disturbance in the water, surface tension may not be strong enough to keep the plank afloat, causing it to sink.

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