Question

Lab 7-Archimedes-background knowl... calculating the maximum possible volume of fluid displaced by the object. When the maximum possible volume of fluid displaced by the object is occupied only by the material of the object and not by other materials (like air spaces, for example), then the prediction can be done without calculations by comparing the density of the object with the density of the fluid as follows: If $ ho_{object} < ho_{fluid}$: The object floats. If $ ho_{object} = ho_{fluid}$: The object stays fully submerged at any depth but won't sink to the bottom. If $ ho_{object} > ho_{fluid}$: The object sinks to the bottom. For example, a steel ball ($ ho_{object} = 7.6 ext{ g/cm}^3$) sinks in water ($ ho_{fluid} = 1 ext{ g/cm}^3$) but floats in mercury ($ ho_{fluid} = 13.7 ext{ g/cm}^3$). However, a gold ball ($ ho_{object} = 19.3 ext{ g/cm}^3$) sinks in water and also in mercury. Questions: 1. What is the weight of liquid mercury displaced by a 2 cm radius solid gold sphere fully submerged? Show your work. Note: the volume of a sphere of radius R is $V = (4/3) pi R^3$. Show your work. 2. A solid sphere of 2 cm radius floats on liquid mercury showing ½ of its shape above the surface of the liquid. Calculate the buoyancy force acting on the sphere. 3. Someone wants to use as a boat a hollow steel box with its top removed. The dimensions are length=2 m, width = 2m and height = 0.5 m. Calculate the maximum buoyancy force that water can apply on this box. Show your work. 4. The person in problem #3 above wants to load 1,500 kg of rocks in this "boat". The empty boat has a mass of 200 kg. Predict if the loaded boat is able to float. Show your work. 5. Can a solid sphere of a material with a density of 0.9 g/cm³ float in water? Justify your answer. 6. Can a solid lead sphere float in liquid mercury? Justify your answer.

          Lab 7-Archimedes-background knowl...
calculating the maximum possible volume of fluid displaced by
the object.
When the maximum possible volume of fluid displaced by the
object is occupied only by the material of the object and not by
other materials (like air spaces, for example), then the prediction
can be done without calculations by comparing the density of
the object with the density of the fluid as follows:
If $
ho_{object} < 
ho_{fluid}$: The object floats.
If $
ho_{object} = 
ho_{fluid}$: The object stays fully submerged at any
depth but won't sink to the bottom.
If $
ho_{object} > 
ho_{fluid}$: The object sinks to the bottom.
For example, a steel ball ($
ho_{object} = 7.6 	ext{ g/cm}^3$) sinks in water
($
ho_{fluid} = 1 	ext{ g/cm}^3$) but floats in mercury ($
ho_{fluid} = 13.7 	ext{ g/cm}^3$).
However, a gold ball ($
ho_{object} = 19.3 	ext{ g/cm}^3$) sinks in water and
also in mercury.
Questions:
1. What is the weight of liquid mercury displaced by a 2 cm
radius solid gold sphere fully submerged? Show your work.
Note: the volume of a sphere of radius R is $V = (4/3) pi R^3$.
Show your work.
2. A solid sphere of 2 cm radius floats on liquid mercury
showing ½ of its shape above the surface of the liquid.
Calculate the buoyancy force acting on the sphere.
3. Someone wants to use as a boat a hollow steel box with its top
removed. The dimensions are length=2 m, width = 2m and
height = 0.5 m. Calculate the maximum buoyancy force that
water can apply on this box. Show your work.
4. The person in problem #3 above wants to load 1,500 kg of
rocks in this "boat". The empty boat has a mass of 200 kg.
Predict if the loaded boat is able to float. Show your work.
5. Can a solid sphere of a material with a density of 0.9 g/cm³
float in water? Justify your answer.
6. Can a solid lead sphere float in liquid mercury? Justify your
answer.

Lab 7-Archimedes-background knowl...
calculating the maximum possible volume of fluid displaced by
the object.
When the maximum possible volume of fluid displaced by the
object is occupied only by the material of the object and not by
other materials (like air spaces, for example), then the prediction
can be done without calculations by comparing the density of
the object with the density of the fluid as follows:
If hoobject <
hofluid: The object floats.
If hoobject =
hofluid: The object stays fully submerged at any
depth but won't sink to the bottom.
If hoobject >
hofluid: The object sinks to the bottom.
For example, a steel ball (hoobject = 7.6 ext g/cm^3) sinks in water
(hofluid = 1 ext g/cm^3) but floats in mercury (hofluid = 13.7 ext g/cm^3).
However, a gold ball (hoobject = 19.3 ext g/cm^3) sinks in water and
also in mercury.
Questions:
1. What is the weight of liquid mercury displaced by a 2 cm
radius solid gold sphere fully submerged? Show your work.
Note: the volume of a sphere of radius R is V = (4/3) pi R^3.
Show your work.
2. A solid sphere of 2 cm radius floats on liquid mercury
showing ½ of its shape above the surface of the liquid.
Calculate the buoyancy force acting on the sphere.
3. Someone wants to use as a boat a hollow steel box with its top
removed. The dimensions are length=2 m, width = 2m and
height = 0.5 m. Calculate the maximum buoyancy force that
water can apply on this box. Show your work.
4. The person in problem #3 above wants to load 1,500 kg of
rocks in this "boat". The empty boat has a mass of 200 kg.
Predict if the loaded boat is able to float. Show your work.
5. Can a solid sphere of a material with a density of 0.9 g/cm³
float in water? Justify your answer.
6. Can a solid lead sphere float in liquid mercury? Justify your
answer.

Added by Christopher D.

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