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Question

# A dike in Holland springs a leak through a hole of area $1 \mathrm{~cm}^2$ at a depth of $2 \mathrm{~m}$ below the water surface. How much force must a boy apply to the hole with his thumb to stop the leak? Could he do it?

Solution

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$\textbf{Given}$

$h = 2 \text{ m}$

$A = 1 \text{ cm}^2$

$\textbf{Approach}$

Water pressure at a depth $(h)$ is calculated with the following equation:

$p = \rho \cdot g \cdot h$

While the force is calculated as a product of pressure and area:

$F = p \cdot A$

$\textbf{Solution}$

Before inserting the numerical values it is necessary to convert $\text{cm}^2$ to $\text{m}^2$:

$1 \text{ cm}^2 = 1 \cdot \dfrac{1}{100 \cdot 100} \text{ m}^2 = 1 \cdot 10^{-4} \text{ m}^2$

Now the pressure and the force can be calculated:

$p = 1000 \cdot 10 \cdot 2 = 20000 \text{ Pa}$

$F = 20000 \cdot 1 \cdot 10^{-4} = \boxed{2 \text{ N}}$

$\boxed{\text{Yes the boy could stop the leak!}}$

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