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Chapter 8: Problem 40

When does a solid float in a given liquid? When does it sink?

Short Answer

Expert verified
Question: Explain under what conditions a solid object will float or sink in a given liquid. Answer: A solid object will float in a given liquid if its density is less than the density of the liquid, as the buoyant force acting on it will be greater than or equal to the gravitational force. On the other hand, the object will sink if its density is greater than the density of the liquid, since the buoyant force will be less than the gravitational force in this case.

Step by step solution

01

Understand Archimedes' Principle

Archimedes' principle states that the upward buoyant force on an object submerged in a fluid, whether partially or fully, is equal to the weight of the liquid that the object displaces. The principle depends on the densities of the submerged object and the fluid in which it is submerged.
02

Determine the Densities

The density of an object (ρ_object) can be determined by dividing its mass (m) by its volume (V), according to the formula: ρ_object = m/V Similarly, the density of the liquid (ρ_liquid) can be determined using its mass (M) and volume (V_liquid), as follows: ρ_liquid = M/V_liquid
03

Compare the Densities

After determining the densities of both the object and the liquid, compare them to decide whether the object will float or sink. If the density of the object is less than the density of the liquid, the object will float. If the density of the object is greater than the density of the liquid, the object will sink.
04

Apply the concept of buoyancy

Buoyancy is the force acting on an object submerged in a fluid, such as a liquid, that opposes the force of gravity. An object will float when the buoyant force is greater than or equal to the gravitational force acting on the object. Buoyant force (F_b) can be calculated as follows: F_b = ρ_liquid * V_liquid * g where g is the acceleration due to gravity.
05

Determine if the object floats or sinks

Now, apply the concepts of density and buoyancy to determine whether the object floats or sinks: - If ρ_object < ρ_liquid, the buoyant force will be greater than or equal to the gravitational force, meaning the object will float. - If ρ_object > ρ_liquid, the buoyant force will be less than the gravitational force, meaning the object will sink.

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