The maximum gauge pressure of a hydraulic ramp is 16 atm, with a support area whose diameter is 20 cm. What is the mass of the heaviest vehicle that can be lifted?

Step 1: We can use the formula for pressure:

P = \frac{F}{A}

where P is the pressure, F is the force, and A is the area.

Step 2: We can rearrange the formula to solve for the force:

F = P \times A

Step 3: We are given that the maximum gauge pressure is 16 atm. To convert this to Pascal (Pa), we multiply by the conversion factor:

1 \, \text{atm} = 101325 \, \text{Pa}

So, the maximum gauge pressure in Pascal is:

P = 16 \, \text{atm} \times 101325 \, \text{Pa/atm} = 1621200 \, \text{Pa}

Step 4: The support area is a circle with a diameter of 20 cm, which means it has a radius of 10 cm. We can calculate the area using the formula for the area of a circle:

A = \pi \times r^2

where \pi is a mathematical constant (approximately 3.14159) and r is the radius.

A = \pi \times 10 \, \text{cm}^2

Simplifying, we get:

A = 314.16 \, \text{cm}^2 = 0.031416 \, \text{m}^2

Step 5: Now we can calculate the force:

F = P \times A = 1621200 \, \text{Pa} \times 0.031416 \, \text{m}^2

Simplifying, we get:

F=50931.62\,\text{N}