A balloon and its gondola have a total (empty) mass of 2.0 ×10^2 kg. When filled, the balloon co

step 1 here in this given problem mass of the empty balloon and its empty gondola that is m is equal to

A balloon and its gondola have a total (empty) mass of 2.0...

A balloon and its gondola have a total (empty) mass of $2.0 \times 10^{2}$ kg. When filled, the balloon contains $900 \mathrm{~m}^{3}$ of helium at a density of $0.183 \mathrm{~kg}$. Find the added load, in addition to its own weight, that the balloon can lift. The density of air is $1.29 \mathrm{~kg}$.

Key Concepts

Archimedes' Principle

This principle states that any object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. It is fundamental to understanding how objects float or sink and is directly used to calculate the lifting force available in a buoyant system, such as a balloon buoyed by a lighter-than-air gas.

Buoyant Force

The buoyant force is the upward force that acts on an object immersed in a fluid, arising from the pressure difference exerted by the fluid on the object. In applications like balloons, it is calculated as the weight of the displaced fluid, which is determined by the fluid's density and the volume of the displacement.

Density and Mass Relationship

Density is defined as mass per unit volume, and it is a critical concept in determining the mass of substances given their volume, or vice versa. In problems involving buoyancy, knowing the densities of the lifting gas and the surrounding fluid allows us to compute their respective weights, which is essential in determining net lift.

Net Lift Calculation

The net lift is the amount of additional load that can be carried by a buoyant system. It is found by subtracting the weight of the lighter-than-air gas and any inherent mass of the system (such as the balloon material and any attached equipment) from the total buoyant force. This concept is crucial for practical applications in aerostatics, where balancing these forces determines the effectiveness and capacity of the lifting mechanism.

Transcript

Please give Ace some feedback