Assume a balloon material with a constant surface tension of 𝒮=2 N / m. What is the work require

step 1 Here in this question, assume the initial area is small as that we have two surfaces inside and

Assume a balloon material with a constant surface tension of...

Assume a balloon material with a constant surface tension of $\mathscr{S}=2 \mathrm{N} / \mathrm{m}$. What is the work required to stretch a special balloon up to a radius of $r=0.5 \mathrm{m} ?$ Neglect any effect from atmospheric pressure.

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Key Concepts

Surface Tension

Surface tension is a physical property that describes the force per unit length existing at the interface of a material, typically associated with a liquid film or a thin elastic surface. It represents the energetic cost per unit area required to create additional surface and plays a crucial role in phenomena involving stretching or deformation of the interface.

Mechanical Work

Mechanical work in the context of stretching a material refers to the energy required to change the configuration of the system. When a material with surface tension is stretched, the work done is stored as surface energy. This work is computed by integrating the force applied over an incremental change in the area of the stretched material.

Differential Area and Integration

Calculating the work done in stretching a surface involves integrating over the continuously changing area of the object. Differential calculus is used to consider small incremental changes in surface area, with the total work obtained by summing these infinitesimal contributions. This approach allows the evaluation of work done over a finite change in the configuration of the system.

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