Buoyancy of sphere in water

In summary, a hollow plastic sphere with a volume of 0.65 m^3 and a tension of 842 N in the cord holding it in a fresh water lake has a mass of 564 kg. This may seem high, but it is correct. If the sphere was made of PVC plastic, with a wall thickness of 148.12 mm and containing air at atmospheric pressure, its mass would be even higher at approximately 910 kg.
  • #1
dnp33
40
1

Homework Statement



A hollow plastic sphere is held below the surface of a fresh water lake by a cord anchored to the bottom of the lake. The sphere has a volume of 0.65 m^3 and the tension in the cord is 842 N. What is the mass of the sphere, in kg? Enter your answer using 3 decimal places, don't enter the units

Homework Equations



[tex] \rho *V*g=F[/tex]
F=mg

The Attempt at a Solution



because the system is in equilibrium
F tension + Force of gravity = Buoyant Force.
842N + (9.81m/s^2)m = (1000kg/m^3)(0.65m^3)(9.81m/s^2)
the answer turns out to be 564kg, unless I'm doing something really stupid.
but that seems to be really high for a hollow plastic sphere.
 
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  • #2


Your calc looks correct! And your physical intuition. I guess whoever made up the question estimated the mass rather high.
 
  • #3


yeah i can't think of anything that I'm doing wrong, it just seems really weird that the mass would be so high.
when i worked out the density of the ball it was lower than that of water so it should float it just seems weird thinking about something that heavy floating.
 
  • #4
dnp33: Your answer is correct. Let's say the hollow sphere in your given problem is made of polyvinyl chloride (PVC) plastic, has a wall thickness of t = 148.12 mm, and contains air at atmospheric pressure. The density of polyvinyl chloride is rhop = 1400 kg/m^3. Can you compute the mass of this sphere? Neglect the density of air.
 

1. What is buoyancy and how does it affect a sphere in water?

Buoyancy is the upward force that a fluid exerts on an object immersed in it. The buoyant force is equal to the weight of the fluid that the object displaces. For a sphere in water, the buoyant force acts in an upward direction, which helps to keep the sphere afloat.

2. How is the buoyant force calculated for a sphere in water?

The buoyant force on a sphere in water is calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. This can be calculated by multiplying the volume of the displaced fluid by the density of the fluid and the acceleration due to gravity.

3. What factors affect the buoyancy of a sphere in water?

The buoyancy of a sphere in water is affected by its volume, density, and the density of the fluid it is immersed in. The greater the volume of the sphere, the greater the buoyant force. Similarly, a less dense sphere will experience a greater buoyant force, and if the fluid is more dense, the buoyant force will decrease.

4. Can a sphere sink in water if it is less dense than water?

Yes, a sphere can sink in water if its density is less than that of water. This happens when the weight of the sphere is greater than the buoyant force acting on it. In this case, the sphere will continue to sink until it reaches a depth where the buoyant force is equal to its weight.

5. How can the buoyancy of a sphere in water be increased?

The buoyancy of a sphere in water can be increased by increasing its volume or decreasing its density. This can be achieved by adding air to the sphere, which will increase its volume and decrease its density. Alternatively, the buoyant force can also be increased by increasing the density of the fluid in which the sphere is immersed.

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