$V_{displaced}$

Definition

$V_{displaced}$ refers to the volume of fluid displaced by an object that is submerged or partially submerged in a liquid. This concept is central to Archimedes' Principle, which states that the buoyant force exerted on an object is equal to the weight of the fluid displaced by the object.

5 Must Know Facts For Your Next Test

1. The volume of fluid displaced by an object is equal to the volume of the object, as long as the object is fully submerged.
2. The buoyant force exerted on an object is directly proportional to the volume of fluid displaced, as well as the density of the fluid.
3. Archimedes' Principle can be used to determine the density of an object by measuring the volume of fluid displaced and the weight of the object.
4. The volume of fluid displaced is a key factor in calculating the upward buoyant force that counteracts the downward gravitational force on an object.
5. Knowing the volume of fluid displaced is essential for understanding the behavior of objects in fluids, such as the ability of objects to float or sink.

Review Questions

• Explain how the volume of fluid displaced ($V_{displaced}$) is related to the buoyant force exerted on an object.
  • According to Archimedes' Principle, the buoyant force exerted on an object is equal to the weight of the fluid displaced by the object. The volume of fluid displaced ($V_{displaced}$) is directly proportional to the buoyant force, as the buoyant force is calculated by multiplying the volume of fluid displaced by the density of the fluid. Therefore, the greater the volume of fluid displaced by an object, the greater the buoyant force acting on that object, which can counteract the object's weight and cause it to float or partially submerge.
• Describe how the volume of fluid displaced ($V_{displaced}$) can be used to determine the density of an object.
  • The volume of fluid displaced ($V_{displaced}$) by an object can be used, along with the object's weight, to determine the object's density. According to Archimedes' Principle, the buoyant force on an object is equal to the weight of the fluid displaced. By measuring the weight of the object and the volume of fluid displaced, and knowing the density of the fluid, one can calculate the density of the object using the formula: $\rho_{object} = \frac{W_{object}}{V_{displaced}\rho_{fluid}}$, where $\rho_{object}$ is the density of the object, $W_{object}$ is the weight of the object, $V_{displaced}$ is the volume of fluid displaced, and $\rho_{fluid}$ is the density of the fluid.
• Analyze the relationship between the volume of fluid displaced ($V_{displaced}$) and the ability of an object to float or sink in a fluid.
  • The volume of fluid displaced ($V_{displaced}$) by an object is a crucial factor in determining whether the object will float or sink in a fluid. According to Archimedes' Principle, an object will float if the buoyant force (which is proportional to $V_{displaced}$) is greater than or equal to the weight of the object. If the volume of fluid displaced is large enough such that the buoyant force exceeds the weight of the object, the object will float. Conversely, if the volume of fluid displaced is not sufficient to provide enough buoyant force to counteract the object's weight, the object will sink. Therefore, the relationship between $V_{displaced}$ and an object's ability to float or sink is a direct one, with larger values of $V_{displaced}$ favoring floating and smaller values favoring sinking.

Related terms

Buoyant Force:

The upward force exerted by a fluid on an object that is either fully or partially submerged in the fluid.

Archimedes' Principle:

The principle stating that the buoyant force on an object is equal to the weight of the fluid displaced by the object.

Density:

The mass per unit volume of a substance, which determines the amount of fluid displaced by an object.