Examkin

Question

Difficulty: MediumBuoyancy and Archimedes' Principle

During a hydro-engineering project, a completely sealed hollow steel sphere is used as an underwater sensor housing. The sphere has an external volume of 2.5 m32.5 \text{ m}^3 and a dry weight of 35,000 N35,000 \text{ N} in the air. When completely submerged in a testing pool where the water's weight density is 10,000 N/m310,000 \text{ N/m}^3, what is the net downward force (apparent weight) of the housing in Newtons?

Answer: 10000 N

Answer

10000
The net downward force, or apparent weight, is found by subtracting the upward buoyant force from the object's true dry weight. Since the object displaces 2.5 m32.5 \text{ m}^3 of water with a weight density of 10,000 N/m310,000 \text{ N/m}^3, the buoyant force is 25,000 N25,000 \text{ N}. Subtracting this upward force from the 35,000 N35,000 \text{ N} downward dry weight leaves a net downward force of 10,000 N10,000 \text{ N}.

Step-by-Step Solution

1
Calculate the buoyant force acting on the submerged housing.
25,000 N
According to Archimedes' principle, the buoyant force equals the weight of the fluid displaced by the object's external volume (2.5 m3×10,000 N/m3=25,000 N2.5 \text{ m}^3 \times 10,000 \text{ N/m}^3 = 25,000 \text{ N}).
2
Calculate the apparent weight (net downward force).
10,000 N
The apparent weight is the actual weight in air minus the upward buoyant force (35,000 N−25,000 N=10,000 N35,000 \text{ N} - 25,000 \text{ N} = 10,000 \text{ N}).

Key Concept

Archimedes' Principle and Apparent Weight
Rate this question

Topics

Buoyancy and Archimedes' Principle

More questions from this topic