Solution Found!
Evaluating WorkA soap film is suspended on a wire frame,
Chapter 2, Problem 41P(choose chapter or problem)
A soap film is suspended on a wire frame, as shown in Fig. 2.10. The movable wire is displaced by an applied force F. If the surface tension remains constant,
(a) obtain an expression for the work done in stretching the film in terms of the surface tension \(\tau\), length \(\ell\), and a finite displacement \(\Delta x\).
(b) evaluate the work done, in J, if \(\ell=5 \mathrm{~cm}, \Delta x=0.5 \mathrm{~cm}\), and \(\tau=25 \times 10^{-5} \mathrm{~N} / \mathrm{cm}\).
Questions & Answers
QUESTION:
A soap film is suspended on a wire frame, as shown in Fig. 2.10. The movable wire is displaced by an applied force F. If the surface tension remains constant,
(a) obtain an expression for the work done in stretching the film in terms of the surface tension \(\tau\), length \(\ell\), and a finite displacement \(\Delta x\).
(b) evaluate the work done, in J, if \(\ell=5 \mathrm{~cm}, \Delta x=0.5 \mathrm{~cm}\), and \(\tau=25 \times 10^{-5} \mathrm{~N} / \mathrm{cm}\).
ANSWER:Part (a)
Step 1 of 5:
Consider a wire frame dipped in a soap solution and soap film formed on it. One end of the frame can be moved back and forth with an application of a force F. The surface tension is constant. We are going to find the work done in terms of surface tension, the length of the frame (l) and the displacement Δx.
The force applied in terms of surface tension is expressed as
Here 2 represents the film has two free surfaces.
The work done by moving the frame through a distance Δx is expressed as
