Question

Theory The buoyant force is described by Archimedes’ principle as: an object, when placed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. The principle applies to an object either entirely or partially submerged in the fluid. The magnitude of the buoyant force depends only on the weight of the displaced fluid, and not on the object’s weight. Using Archimedes’ principle, you can deduce that an object: 1. will float in a fluid if the object’s density is less than the fluid’s density (?o < ?f). 2. will sink if the object’s density is greater than the fluid’s density (?o > ?f). 3. will remain in equilibrium at a given submerged depth if the object’s density is exactly equal to the fluid’s density at that depth (?o = ?f). The buoyant force on a floating object Fb is related to the properties of the displaced fluid by: Fb = mfg = ?fVog where ?f is the density of the fluid, Vo is the volume of the submerged part of the object, and g is the acceleration due to gravity. The volume of the submerged part of a cylinder oriented vertically is equal to its cross-sectional area A multiplied by the height h of the submerged part, so the buoyant force on it is: Fb = mfg = ?fAgh This is a linear relationship between Fb and h, so if you lower the cylinder into a fluid as you measure its weight, then plot Fb vs. h, the slope of the plotted straight line will be ?fAg, i.e., directly proportional to the density of the fluid. This is a cool way to determine the density of an unknown fluid. You can determine the density of an unknown solid object in a similar fashion. It’s easy to measure the mass of an object, but unless it has a regular shape it’s not so easy to measure its volume. But Archimedes showed us how to measure volume by measuring weight. When the object is completely submerged in water, its weight (but not its mass) will decrease by an amount equal to the upward buoyant force the water exerts on it. So: ?Wo = Wo (in air) – Wo (in water) This upward force is also equal to the weight of the displaced water, or: ?Wo = Ww = mwg = ?wgVw But the volume of the water is equal to the volume of the object, so:

Theory

The buoyant force is described by Archimedes’ principle as: an object, when placed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. The principle applies to an object either entirely or partially submerged in the fluid. The magnitude of the buoyant force depends only on the weight of the displaced fluid, and not on the object’s weight. Using Archimedes’ principle, you can deduce that an object:
1. will float in a fluid if the object’s density is less than the fluid’s density (?o < ?f).
2. will sink if the object’s density is greater than the fluid’s density (?o > ?f).
3. will remain in equilibrium at a given submerged depth if the object’s density is exactly equal to the fluid’s density at that depth (?o = ?f).

The buoyant force on a floating object Fb is related to the properties of the displaced fluid by:

Fb = mfg = ?fVog

where ?f is the density of the fluid, Vo is the volume of the submerged part of the object, and g is the acceleration due to gravity.

The volume of the submerged part of a cylinder oriented vertically is equal to its cross-sectional area A multiplied by the height h of the submerged part, so the buoyant force on it is:

Fb = mfg = ?fAgh

This is a linear relationship between Fb and h, so if you lower the cylinder into a fluid as you measure its weight, then plot Fb vs. h, the slope of the plotted straight line will be ?fAg, i.e., directly proportional to the density of the fluid. This is a cool way to determine the density of an unknown fluid.

You can determine the density of an unknown solid object in a similar fashion. It’s easy to measure the mass of an object, but unless it has a regular shape it’s not so easy to measure its volume. But Archimedes showed us how to measure volume by measuring weight.

When the object is completely submerged in water, its weight (but not its mass) will decrease by an amount equal to the upward buoyant force the water exerts on it. So:

?Wo = Wo (in air) – Wo (in water)

This upward force is also equal to the weight of the displaced water, or:

?Wo = Ww = mwg = ?wgVw

But the volume of the water is equal to the volume of the object, so:

Theory

The buoyant force is described by Archimedes’ principle as: an object, when placed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. The principle applies to an object either entirely or partially submerged in the fluid. The magnitude of the buoyant force depends only on the weight of the displaced fluid, and not on the object’s weight. Using Archimedes’ principle, you can deduce that an object:
1. will float in a fluid if the object’s density is less than the fluid’s density (?o < ?f).
2. will sink if the object’s density is greater than the fluid’s density (?o > ?f).
3. will remain in equilibrium at a given submerged depth if the object’s density is exactly equal to the fluid’s density at that depth (?o = ?f).

The buoyant force on a floating object Fb is related to the properties of the displaced fluid by:

Fb = mfg = ?fVog

where ?f is the density of the fluid, Vo is the volume of the submerged part of the object, and g is the acceleration due to gravity.

The volume of the submerged part of a cylinder oriented vertically is equal to its cross-sectional area A multiplied by the height h of the submerged part, so the buoyant force on it is:

Fb = mfg = ?fAgh

This is a linear relationship between Fb and h, so if you lower the cylinder into a fluid as you measure its weight, then plot Fb vs. h, the slope of the plotted straight line will be ?fAg, i.e., directly proportional to the density of the fluid. This is a cool way to determine the density of an unknown fluid.

You can determine the density of an unknown solid object in a similar fashion. It’s easy to measure the mass of an object, but unless it has a regular shape it’s not so easy to measure its volume. But Archimedes showed us how to measure volume by measuring weight.

When the object is completely submerged in water, its weight (but not its mass) will decrease by an amount equal to the upward buoyant force the water exerts on it. So:

?Wo = Wo (in air) – Wo (in water)

This upward force is also equal to the weight of the displaced water, or:

?Wo = Ww = mwg = ?wgVw

But the volume of the water is equal to the volume of the object, so:

Added by Shannon S.

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