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Chapter 7: Problem 982

The force required to separate two glass plates of area $10^{-2} \mathrm{~m}^{2}\( with a film of water \)0.05 \mathrm{~mm}$ thick between them is (surface tension of water is \(70 \times 10^{-3} \mathrm{~N} / \mathrm{m}\) ) (A) \(28 \mathrm{~N}\) (B) \(14 \mathrm{~N}\) (C) \(50 \mathrm{~N}\) (D) \(38 \mathrm{~N}\)

Short Answer

Expert verified
The force required to separate the two glass plates with a water film between them can be calculated using the formula \(F = 2 \times T \times P\), where 'T' is the surface tension of water, and 'P' is the perimeter of the glass plates. Given the area of the glass plates \(A = 10^{-2}\mathrm{~m}^{2}\), the water film thickness \(t = 5\times10^{-5}\mathrm{~m}\), and the surface tension of water \(T = 70 \times 10^{-3}\mathrm{~N}/\mathrm{m}\), we can find the perimeter of the glass plates assuming a square shape. Then, substitute the values into the formula and calculate the force. The correct answer is (B) \(14 \mathrm{~N}\).

Step by step solution

01

Identify the given information

The given information in the problem is: - Area of glass plates: \(A = 10^{-2}\mathrm{~m}^{2}\) - Thickness of water film: \(t = 0.05\mathrm{~mm}\) or \(5\times10^{-5}\mathrm{~m}\) - Surface tension of water: \(T = 70 \times 10^{-3}\mathrm{~N}/\mathrm{m}\)
02

Convert thickness of water film to meters

Make sure that all quantities have the same units (meters in this case). So, we find the thickness in meters: \(t = 0.05\mathrm{~mm}\times\frac{1\mathrm{~m}}{1000\mathrm{~mm}} = 5\times10^{-5}\mathrm{~m}\)
03

Calculate the perimeter of the glass plates

Assume that the glass plates are square in shape. Let 's' be the length of one side. Then, \(A = s^2\). Thus, the length is: \(s = \sqrt{A} = \sqrt{10^{-2}\mathrm{~m}^{2}} = 10^{-1}\mathrm{~m}\) The perimeter (length of contact between the water film and the glass plate) is: \(P = 4s = 4\times10^{-1}\mathrm{~m}\)
04

Calculate the force required to separate the glass plates

The force required to separate the two glass plates can be found using the formula: \(F = 2 \times T \times P\) Here, we multiply by 2 because there are 2 interfaces between the glass plates and the water film (one between the top glass plate and the water film, and one between the bottom glass plate and the water film). \(F = 2 \times (70 \times 10^{-3}\mathrm{~N}/\mathrm{m}) \times (4\times10^{-1}\mathrm{~m})\)
05

Calculate the force

Plug in the given values and calculate the force: \(F = 2 \times (70 \times 10^{-3}\mathrm{~N}/\mathrm{m}) \times (4\times10^{-1}\mathrm{~m}) = 14\mathrm{~N}\)
06

Find the correct answer from the given options

The calculated force is \(14\mathrm{~N}\), which matches option (B). So, the force required to separate the two glass plates is \(14\mathrm{~N}\). The correct answer is (B) \(14 \mathrm{~N}\).

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