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Background: Archimedes discovered that he could find the density of an object by comparing it's weight to its apparent weight when immersed in water (see example 10-8 in the textbook). When immersed, the buoyancy due to the displaced water offsets the tension of the string supporting the mass. This tension thus measures the apparent weight of the object. The Buoyant Force, as described by Archimedes, is calculated as the weight of water displaced by the object. FB = mFg To find the mass of displaced water, just use the principle of density: ? = m / V Note that the volume of displaced water will be the same as the volume of the object. Combine these two equations to get the Buoyant Force in terms of water density and volume FB = We are now going to derive an equation to find the apparent mass of an object suspended in water. Take the image below, then draw and label all forces in the free-body diagram. Hint: There are three forces. The tension in the string will measure the apparent weight. What is the total acceleration? Use Newton's Second Law to add all of the forces together and solve for tension: ?F = ma Finally, solve for the apparent mass, knowing that Tension is your apparent weight. Apparent mass = mA = What are the buoyant force, tension, and the apparent mass of a 5.0-cm³ object with an original mass of 25.0 g when it is suspended in water? Recall: cm³ x (1m / 100cm)³ FB = N Apparent Weight = FT = N Apparent mass = mA = kg

          Background: Archimedes discovered that he could find the density of an object by comparing it's weight to its apparent weight when immersed in water (see example 10-8 in the textbook). When immersed, the buoyancy due to the displaced water offsets the tension of the string supporting the mass. This tension thus measures the apparent weight of the object.

The Buoyant Force, as described by Archimedes, is calculated as the weight of water displaced by the object. FB = mFg
To find the mass of displaced water, just use the principle of density: ? = m / V
Note that the volume of displaced water will be the same as the volume of the object. Combine these two equations to get the Buoyant Force in terms of water density and volume
FB =

We are now going to derive an equation to find the apparent mass of an object suspended in water. Take the image below, then draw and label all forces in the free-body diagram. Hint: There are three forces. The tension in the string will measure the apparent weight.

What is the total acceleration?

Use Newton's Second Law to add all of the forces together and solve for tension:
?F = ma

Finally, solve for the apparent mass, knowing that Tension is your apparent weight.
Apparent mass = mA =

What are the buoyant force, tension, and the apparent mass of a 5.0-cm³ object with an original mass of 25.0 g when it is suspended in water?
Recall: cm³ x (1m / 100cm)³
FB = N
Apparent Weight = FT = N
Apparent mass = mA = kg

Background: Archimedes discovered that he could find the density of an object by comparing it's weight to its apparent weight when immersed in water (see example 10-8 in the textbook). When immersed, the buoyancy due to the displaced water offsets the tension of the string supporting the mass. This tension thus measures the apparent weight of the object.

The Buoyant Force, as described by Archimedes, is calculated as the weight of water displaced by the object. FB = mFg
To find the mass of displaced water, just use the principle of density: ? = m / V
Note that the volume of displaced water will be the same as the volume of the object. Combine these two equations to get the Buoyant Force in terms of water density and volume
FB =

We are now going to derive an equation to find the apparent mass of an object suspended in water. Take the image below, then draw and label all forces in the free-body diagram. Hint: There are three forces. The tension in the string will measure the apparent weight.

What is the total acceleration?

Use Newton's Second Law to add all of the forces together and solve for tension:
?F = ma

Finally, solve for the apparent mass, knowing that Tension is your apparent weight.
Apparent mass = mA =

What are the buoyant force, tension, and the apparent mass of a 5.0-cm³ object with an original mass of 25.0 g when it is suspended in water?
Recall: cm³ x (1m / 100cm)³
FB = N
Apparent Weight = FT = N
Apparent mass = mA = kg

Added by Rebecca P.

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