A cylindrical buoy with hemispherical ends is dropped in...

A cylindrical buoy with hemispherical ends is dropped in seawater of density $1027 \mathrm{~kg} / \mathrm{m}^{3}$ as shown in the figure. The mass of the buoy is $75.0 \mathrm{~kg}$, the radius of the cylinder and the hemispherical caps is $R=0.200 \mathrm{~m},$ and the length of the cylindrical center section of the buoy is $L=0.600 \mathrm{~m} .$ The lower part of the buoy is weighted so that the buoy is upright in the water, as shown in the figure. In calm water, how high (distance $h)$ will the top of the buoy be above the waterline?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Archimedes Principle

Archimedes’ Principle states that an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. This fundamental concept is used to determine the conditions under which an object floats or submerges by equating the buoyant force to the gravitational force acting on the object.

Hydrostatic Equilibrium

Hydrostatic equilibrium refers to the balance between the upward buoyant force and the downward gravitational force on a floating object. This balance determines how much of the object is submerged and how much remains above the fluid surface, which is crucial for analyzing floating bodies.

Composite Geometry and Volume Calculation

When analyzing floating bodies with complex shapes, it is important to break the object into simpler geometrical components, such as cylinders and spheres or hemispheres. Calculating the volume of each component allows us to determine the total displaced fluid volume, which is essential for applying Archimedes’ Principle and assessing the buoyant force acting on the object.

Transcript

Please give Ace some feedback