Question

A submarine is built to dive to a depth of 90 m where the pressure in the water is about 1 MPa. The engineers want to build a window in the submarine, but the window can only take a force of 10 kN safely. What is the largest surface area window that can be used?

Answer 1

Answer:

The largest surface area window that can be used is $A=0.01\ m^2$

Explanation:

Pressure

The pressure is defined as force per unit area. The SI unit for pressure is the Pascal (Pa), defined as Newton per square meter.

If a force F acts on a surface area A, the pressure is calculated as:

$\displaystyle P=\frac{F}{A}$

The pressure at a depth of 90 m is P=1 Mpa= 1,000,000 Pa and the submarine's window can only take a force of F=10 kN=10,000 N.

We need to calculate the largest surface area of the window. We can solve the equation for A:

$\displaystyle A=\frac{F}{P}$

Substituting:

$\displaystyle A=\frac{10,000}{1,000,000}$

$A=0.01\ m^2$

The largest surface area window that can be used is $\mathbf{A=0.01\ m^2}$