How Do You Calculate the Radius of a Submerged Iron Ball?

First, determine the weight of the cylinder using its density and submerged height. Then, use the weight of the cylinder and the equation for buoyancy to find the volume of water displaced by the cylinder. Finally, use the volume of water displaced and the density of iron to find the radius of the iron ball. In summary, to find the radius of the iron ball suspended by a thread from a floating cylinder in water, treat each object separately and use equations for weight and buoyancy to find the necessary information.
  • #1
bearhug
79
0
An iron ball is suspended by a thread of negligible mass from an upright cylinder that floats partially submerged in water. The cylinder has a height of 6.00 cm, a face area of 12.0 cm^2 on the top and bottom, and a density of 0.30 g/cm^3. 2.00 cm of its height is above the surface. What is the radius of the iron ball?

The ball is completely submerged but the cylinder is floating so which a should I solve it first, submerged or floating. I'm approaching it as a floating object right now.

Using the equation p(liq)gV(obj)= Mg

Is this in the right direction?
 
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  • #2
I would treat each object separately, considering all the forces on them.
 
  • #3


Yes, you are on the right track. In order to determine the radius of the iron ball, you will need to consider both the buoyancy force on the cylinder and the weight of the iron ball. The buoyancy force on the cylinder is equal to the weight of the water displaced by the submerged portion of the cylinder. This can be calculated using the formula Fb = p(liq)gV(sub), where p(liq) is the density of the liquid (in this case, water), g is the acceleration due to gravity, and V(sub) is the volume of the submerged portion of the cylinder (which can be calculated using its height and face area).

Once you have calculated the buoyancy force on the cylinder, you can set it equal to the weight of the iron ball (which is equal to its mass multiplied by the acceleration due to gravity). This will allow you to solve for the mass of the iron ball. Then, using the mass and the density of iron, you can calculate its volume. Finally, using the formula for the volume of a sphere (V = (4/3)πr^3), you can solve for the radius of the iron ball.

It is important to consider both the buoyancy force and the weight of the iron ball in this problem, as they both play a role in determining the radius of the iron ball. Good luck with your calculations!
 

Related to How Do You Calculate the Radius of a Submerged Iron Ball?

1. What is buoyancy?

Buoyancy is the upward force exerted by a fluid on an object that is immersed in it. It is a result of the difference in pressure between the top and bottom of the object.

2. How does the radius of an object affect its buoyancy?

The radius of an object can affect its buoyancy because it determines the amount of fluid displaced by the object. The larger the radius, the more fluid is displaced, resulting in a greater buoyant force.

3. Can an object with a larger radius have less buoyancy than an object with a smaller radius?

Yes, an object with a larger radius can have less buoyancy than an object with a smaller radius. This is because the density of the object also plays a role in determining buoyancy. An object with a larger radius but a higher density may have less buoyancy than an object with a smaller radius but a lower density.

4. How does the density of an object affect its buoyancy?

The density of an object affects its buoyancy because it determines the weight of the object compared to the weight of the fluid it displaces. An object with a higher density will have a greater weight and therefore will experience a greater downward force, resulting in less buoyancy.

5. What is the relationship between an object's buoyancy and its weight?

An object's buoyancy and weight are inversely related. As the weight of an object increases, its buoyancy decreases. This is because a heavier object will displace more fluid, resulting in a greater upward buoyant force, but it will also experience a greater downward force due to its weight.

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