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

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In summary, a solid cylinder with a radius of 0.150 m and height of 0.120 m and a mass of 6.90 kg is floating in water. Oil with a density of 725 kg/m3 is poured on top of the water, resulting in a situation where the height of the cylinder in oil needs to be determined. Using the given equations, the area and volume of the cylinder can be calculated. The volume of the oil can then be determined by using the first equation and subtracting it from the volume of the cylinder. The total buoyant force upwards is equal to the weight of water displaced plus the weight of oil displaced. By taking h as the height of the cylinder in oil and using H-h
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ncote
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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.
 
  • #3
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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  • #4
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.
 

1. What is buoyancy in oil/water?

Buoyancy in oil/water refers to the upward force that a submerged object experiences when placed in a liquid with different densities, such as oil and water. This force is known as the buoyant force and is equal to the weight of the liquid displaced by the object.

2. How does the density of an object affect its buoyancy in oil/water?

The density of an object plays a crucial role in its buoyancy in oil/water. If the object has a higher density than the liquid, it will sink as it is heavier than the liquid. On the other hand, if the object has a lower density than the liquid, it will float as it is lighter than the liquid. The degree of buoyancy also depends on the difference in density between the object and the liquid.

3. Can an object float in both oil and water simultaneously?

Yes, an object can float in both oil and water simultaneously, depending on its density. If the object has a density between that of oil and water, it will float in the middle layer due to the balance of the buoyant forces acting on it.

4. How does surface tension affect buoyancy in oil/water?

Surface tension, which is the force that allows liquids to resist external forces and hold their shape, can affect buoyancy in oil/water. In the case of oil and water, the surface tension between the two liquids creates a barrier that prevents oil from mixing with water. This can result in objects floating on the surface of the water, as the oil layer creates an additional buoyant force.

5. How is the buoyancy of an object in oil/water calculated?

The buoyancy of an object in oil/water can be calculated by subtracting the weight of the object from the weight of the liquid it displaces. This is known as Archimedes' principle and is expressed as Fb = ρVg, where Fb is the buoyant force, ρ is the density of the liquid, V is the volume of the displaced liquid, and g is the acceleration due to gravity.

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