What am I doing wrong?: Buoyancy of an Object Homework Question

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In summary, the conversation is about finding the density of a liquid in which a spherical object with a diameter of 7.56 cm and a mass of 137.1 g is neutrally buoyant. The equations used include B-mg=0, B=V*density*g, and density=M/V. There is confusion about the volume formula being used, causing frustration in the attempt to solve the problem.
  • #1
talaroue
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Homework Statement



A 7.56 cm diameter sphere with a mass of 137.1 g is neutrally buoyant in a liquid. What is the density of the liquid?

Homework Equations



B-mg=0
B=V*density*g

The Attempt at a Solution



B=mg
V*density*g=mg
denisty=M/V
denisty= .1371 kg/(4/3*PI*r^2) because its a sphere

What am I doing wrong?
 
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  • #2
any ideas? It seems easy but it is not turning out correct.
 
  • #3
talaroue said:
B=mg
V*density*g=mg
denisty=M/V
denisty= .1371 kg/(4/3*PI*r^2) because its a sphere
Double-check that volume formula.
 
  • #4
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FAQ: What am I doing wrong?: Buoyancy of an Object Homework Question

What is buoyancy?

Buoyancy is the ability of an object to float or rise in a fluid. It is caused by the upward force exerted by the fluid on the object, known as the buoyant force.

How is buoyancy calculated?

Buoyancy 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 expressed mathematically as Fb = ρVg, where Fb is the buoyant force, ρ is the density of the fluid, V is the volume of the fluid displaced, and g is the acceleration due to gravity.

What factors affect buoyancy?

The buoyant force on an object is affected by the density of the fluid, the volume of the fluid displaced, and the acceleration due to gravity. It is also affected by the shape and density of the object itself.

Why do some objects float while others sink?

Objects float when the buoyant force acting on them is greater than or equal to their weight. This is usually the case for objects with a lower density than the fluid they are placed in. Objects will sink when the buoyant force is less than their weight, typically due to a higher density than the fluid.

How can buoyancy be used in real-world applications?

Buoyancy is used in many real-world applications, such as shipbuilding and submarine design. It is also used in hot air balloons and blimps to provide lift. In addition, the concept of buoyancy is important in understanding the behavior of fluids and how they interact with objects.

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