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Chapter 15: Problem 36

Using a soap solution for which the surface tension is \(0.025 \mathrm{~N} / \mathrm{m}\), a child blows a soap bubble of radius \(1.40 \mathrm{~cm} .\) How much energy is expended in stretching the soap surface?

Short Answer

Expert verified
The energy expended in stretching the soap surface is \(7.75e-5 Joules\).

Step by step solution

01

List the Given Information

The surface tension (T) is \(0.025 N/m\) and the radius (r) of the bubble is \(1.40 cm\), which is converted to meters it's \(0.014 m\)
02

Calculate the Change in Surface Area

A bubble has two layers, so the surface area has doubled. The total change in surface area (\(\Delta A\)) of a sphere of radius r is given by the equation \(\Delta A = 2 \times 4\pi r^2 \). Plugging in the values gives \(\Delta A = 2 \times 4 \times 3.1416 \times (0.014 m)^2 = 0.0031 m^2\).
03

Calculate the Work Done

The work done (or energy expended) in stretching the bubble is given by the equation \(Work = T \times \Delta A\). Plugging the values in gives; \(Work = 0.025 N/m \times 0.0031 m^2 = 7.75e-5 Joules\).

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Most popular questions from this chapter

An office window is \(3.43 \mathrm{~m}\) by \(2.08 \mathrm{~m}\). As a result of the passage of a storm, the outside air pressure drops to \(0.962\) atm, but inside the pressure is held at \(1.00 \mathrm{~atm} .\) What net force pushes out on the window?

The Goodyear blimp Columbia (see Fig. \(15-20\) ) is cruising slowly at low altitude, filled as usual with helium gas. Its maximum useful payload, including crew and cargo, is \(1280 \mathrm{~kg} .\) How much more payload could the Columbia carry if you replaced the helium with hydrogen? Why not do it? The volume of the helium-filled interior space is \(5000 \mathrm{~m}^{3}\). The density of helium gas is \(0.160 \mathrm{~kg} / \mathrm{m}^{3}\) and the density of hydrogen is \(0.0810 \mathrm{~kg} / \mathrm{m}^{3}\).

How much energy is stored in the surface of a soap bubble 2.1 \(\mathrm{cm}\) in radius if its surface tension is \(4.5 \times 10^{-2} \mathrm{~N} / \mathrm{m} ?\)

Find the total pressure, in pascal, \(118 \mathrm{~m}\) below the surface of the ocean. The density of seawater is \(1.024 \mathrm{~g} / \mathrm{cm}^{3}\) and the atmospheric pressure at sea level is \(1.013 \times 10^{5} \mathrm{~Pa}\).

(a) If the small piston of a hydraulic lever has a diameter of \(3.72 \mathrm{~cm}\), and the large piston one of \(51.3 \mathrm{~cm}\), what weight on the small piston will support \(18.6 \mathrm{kN}\) (e.g., a car) on the large piston? (b) Through what distance must the small piston move to raise the car \(1.65 \mathrm{~m}\) ?
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