Calculating Buoyancy in Oil/Water: Solving for Height of Cylinder

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Homework Help Overview

The problem involves a solid cylinder floating in water with oil poured on top. The goal is to determine how much of the cylinder's height is submerged in the oil. The subject area includes buoyancy and fluid mechanics.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply the buoyancy equation to find the volume of oil but expresses uncertainty about how to calculate it. Some participants question the absence of a drawing that may clarify the situation.

Discussion Status

Participants are exploring the relationships between the forces acting on the cylinder and its submerged volumes. One participant has suggested a method to relate the heights of the cylinder in oil and water, but there is no explicit consensus on the approach yet.

Contextual Notes

There is a reference to a drawing that is not visible to some participants, which may impact their understanding of the problem setup. The original poster has provided specific measurements and properties of the fluids involved.

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1. A solid cylinder (radius = 0.150 m, height = 0.120 m) has a mass of 6.90 kg. This cylinder is floating in water. Then oil ( = 725 kg/m3) is poured on top of the water until the situation shown in the drawing results. How much of the height of the cylinder is in the oil?



2. (p)water(g)(V)water + (p) oil(g)(V) oil= mg
(V)water+ (V)oil= (V)cylinder
(h)oil= (V)oil/area of cylinder



3. using what i was given, i was able to calculate the area and volume of the cyclinder, which was easy enough. i know that once i use the first equation to get the volume of the oil I am supposed to subtract it from the volume of the cylinder. unfortunately I am not sure how to figure out the volume of the oil using the equation we were given (the first one i listed)
 
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I can't see any drawing.
 
Shooting star said:
I can't see any drawing.

http://smg.photobucket.com/albums/v456/andpull/?action=view&current=cylinder.gif
 
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Total buoyant force upward = weight of water displaced + weight of oil displaced. Is this enough for you to proceed?

Take h as the height of the cylinder in oil. Then H-h is in water, where H is ht of cylinder. Try it out.
 

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