Calculate the force required to separate the glass plates of area `10^(-2)m^(2)` with a film of water 0.05 mm thickness between them (surface tension of water `=70xx10^(-3)N//m)`)

Explanation

To solve the problem of calculating the force required to separate two glass plates with a film of water between them, we can follow these steps:

### Step 1: Understand the Problem
We have two glass plates with an area \( A = 10^{-2} \, m^2 \) and a water film of thickness \( t = 0.05 \, mm \) (which is \( 0.05 \times 10^{-3} \, m \)). The surface tension of water is given as \( \gamma = 70 \times 10^{-3} \, N/m \).

### Step 2: Identify the Pressure Difference
The pressure difference \( \Delta P \) between the outside atmospheric pressure \( P_A \) and the pressure inside the water film \( P_B \) can be expressed using the formula:
\[ \Delta P = P_A - P_B = \frac{2\gamma}{r} \]
where \( r \) is the radius of curvature of the water film.

### Step 3: Determine the Radius of Curvature
For a thin film of thickness \( t \), the radius of curvature \( r \) can be approximated as:
\[ r = \frac{t}{2} \]
Thus, substituting for \( r \):
\[ \Delta P = \frac{2\gamma}{\frac{t}{2}} = \frac{4\gamma}{t} \]

### Step 4: Calculate the Force
The force \( F \) required to separate the plates can be calculated using the pressure difference and the area:
\[ F = \Delta P \cdot A = \left(\frac{4\gamma}{t}\right) \cdot A \]

### Step 5: Substitute the Values
Now substituting the known values:
- \( \gamma = 70 \times 10^{-3} \, N/m \)
- \( A = 10^{-2} \, m^2 \)
- \( t = 0.05 \, mm = 0.05 \times 10^{-3} \, m \)

The force becomes:
\[ F = \frac{4 \times (70 \times 10^{-3})}{0.05 \times 10^{-3}} \cdot (10^{-2}) \]

### Step 6: Calculate the Numerical Value
Calculating the above expression:
\[ F = \frac{4 \times 70 \times 10^{-3}}{0.05 \times 10^{-3}} \cdot (10^{-2}) = \frac{280 \times 10^{-3}}{0.05 \times 10^{-3}} \cdot (10^{-2}) = \frac{280}{0.05} \cdot (10^{-2}) \]
\[ F = 5600 \cdot (10^{-2}) = 56 \, N \]

### Final Answer
The force required to separate the glass plates is \( F = 56 \, N \).

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