A hot-air balloon can lift a weight of 5626 N (including its own weight). The density of the ai

step 1 we have a hot balloon which can lift a weight W equals to 5626 Newton and including its on weigh

A hot-air balloon can lift a weight of 5626 N (including...

A hot-air balloon can lift a weight of $5626 \mathrm{~N}$ (including its own weight). The density of the air outside the balloon is $1.205 \mathrm{~kg} / \mathrm{m}^{3}$. The density of the hot air inside the balloon is $0.9449 \mathrm{~kg} / \mathrm{m}^{3}$. What is the volume of the balloon?

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Key Concepts

Gravitational Force

Gravitational force, or weight, results from mass under the acceleration due to gravity. In this problem, the balloon’s lift capacity is given in Newtons, which is a measure of force. By relating weight (force) to mass (via gravitational acceleration), we can compute the volume of air needed to achieve the necessary lifting force.

Archimedes' Principle

This concept states that any object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced. In the hot-air balloon problem, the net lifting force comes from the difference between the weight of the ambient (colder) air displaced and the weight of the hot air inside the balloon.

Density

Density is defined as mass per unit volume. The densities of the air outside and the hot air inside are crucial because they determine how much weight is represented per unit volume of displaced air. The difference in density directly influences the net buoyant force that allows the balloon to lift off.

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