A U-shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire and the light slider supports a weight of 1.5 × 10–2 N (which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film ?
A U-shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire and the light slider supports a weight of 1.5 × 10–2 N (which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film ?
Solution and Explanation
Given Data
- Weight supported by film, \( W = 1.5 \times 10^{-2} \) N [web:1][page:0]
- Length of slider, \( l = 30 \) cm = 0.3 m [web:1][page:0]
Formula
A thin soap film has two free surfaces. The force due to surface tension balances the weight:
\( W = 2 T l \)
where \( T \) is the surface tension [web:1][page:0].
Calculation
Total effective length = \( 2l = 2 \times 0.3 = 0.6 \) m [web:1][page:0].
Thus,
\( T = \frac{W}{2l} = \frac{1.5 \times 10^{-2}}{0.6} = 2.5 \times 10^{-2} \) N/m [web:1][page:0].
Final Answer
Surface tension \( T = 2.5 \times 10^{-2} \) N/m [web:1][page:0].
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