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

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

Step-by-step 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=(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=(F)/(P)`

Substituting:

`\displaystyle A=(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}`