Finding the Percentage of a Sphere Immersed in Water

In summary, the conversation discusses finding the percentage of a sphere submerged in water and using the density of ice and liquid water to solve the problem. The conversation also touches on drawing a free body diagram and using Archimedes' principle to solve for the percentage. The buoyant force is related to the densities and can be used to solve for the percentage.
  • #1
kswoff
3
0
So I'm in a general physics class and the teacher asked us to find the percentage of a sphere immerses in water and I can't seem to figure out how to find the percentage. I was wondering if there's an equation to use or what to find the answer. Thanks.
 
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  • #2
Welcome to PF.
When you get stuck like this, try thinking of a similar situation you do know the answer to.

Hint: you know ice floats approximately 90% submerged? (nine-tenths)

What is the density of ice divided by the density of liquid water?
What is that as a percentage?
 
  • #3
Okay that makes sense. In this same question, it asks to draw a free body diagram to find all the forces. I only found the buoyant force and the gravity force and those don't allow me to have two densities. So did I do the FBD wrong and I'm missing some forces or do I rearrange archimedes' principle to substitute another density? Hope this makes sense.
 
  • #4
Is the buoyant force related to the densities?
 
  • #5
I'm assuming so that way I can solve for the percentage.
 
  • #6
So if you have a buoyant force in your free body diagram, that accounts for the two densities right?
 

Related to Finding the Percentage of a Sphere Immersed in Water

1. How do you calculate the percentage of a sphere immersed in water?

To calculate the percentage of a sphere immersed in water, you will need to know the radius of the sphere and the depth of the water. The formula for finding the percentage is (4/3)πr³ / 4/3πr³ x 100. This will give you the percentage of the sphere that is submerged in water.

2. Is the formula for finding the percentage of a sphere immersed in water the same for all sizes of spheres?

Yes, the formula is the same for all sizes of spheres. As long as you have the radius of the sphere and the depth of the water, you can use the formula to calculate the percentage of immersion.

3. Can this calculation be used for objects other than spheres?

No, this calculation is specifically for spheres. The formula takes into account the unique shape and volume of a sphere, so it cannot be applied to other shapes or objects.

4. How accurate is this calculation?

This calculation is a close approximation and may not be 100% accurate. It also assumes that the sphere is a perfect shape and does not account for any irregularities in the surface of the sphere or the water level.

5. Can this calculation be used to determine the volume of a sphere immersed in water?

No, this calculation only gives the percentage of the sphere that is submerged in water. To determine the volume of the submerged portion, you would need to use a different formula that takes into account the depth of immersion.

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