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Chapter 7: Problem 985

A thin liquid film formed between a u-shaped wire and a light slider supports a weight of \(1.5 \times 10^{-2} \mathrm{~N}\) (see figure). The length of the slider is \(30 \mathrm{~cm}\) and its weight negligible. The surface tension of the liquid film is. (A) \(0.0125 \mathrm{Nm}^{-1}\) (B) \(0.1 \mathrm{Nm}^{-1}\) (C) \(0.05 \mathrm{Nm}^{-1}\) (D) \(0.025 \mathrm{Nm}^{-1}\)

Short Answer

Expert verified
The surface tension of the liquid film is \(0.025\ \mathrm{Nm}^{-1}\) (D).

Step by step solution

01

Convert the length of the slider from centimeters to meters

Before proceeding with the calculation, we need to convert the given slider length from centimeters to meters. Length of slider in meters = Length of the slider in centimeters/100 For a \(30\ \mathrm{cm}\) slider: Length of slider in meters = \(30/100 = 0.3\ \mathrm{m}\)
02

Set up the equation for surface tension

Now that we have the length of the slider in meters, we can set up the equation for surface tension using the force, length, and number of interfaces: \[F = T\cdot L\cdot n\]
03

Calculate the surface tension

Substitute the given force, length in meters, and the number of interfaces into the equation: \(1.5 \times 10^{-2}\ \mathrm{N} = T\cdot (0.3\ \mathrm{m})\cdot2\) Divide both sides of the equation by \(0.6\ \mathrm{m}\): \(T = \frac{1.5 \times 10^{-2}\ \mathrm{N}}{0.6\ \mathrm{m}}\) Calculate the value of T: \(T = 0.025\ \mathrm{Nm}^{-1}\)
04

Choose the correct answer

The surface tension of the liquid film is \(0.025\ \mathrm{Nm^{-1}}\), which corresponds to answer choice (D).

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Most popular questions from this chapter

Oxygen boils at \(183^{\circ} \mathrm{C}\). This temperature is approximately. (A) \(215^{\circ} \mathrm{F}\) (B) \(-297^{\circ} \mathrm{F}\) (C) \(329^{\circ} \mathrm{F}\) (D) \(361^{\circ} \mathrm{F}\)

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