Question

A jar with a 2.00 cm diameter lid is "vacuum sealed", giving it an interior pressure of 7.50 x 10^4 Pa. What force is exerted on the lid due to the difference between the exterior and interior air pressure?

Answer 1

The force exerted on the lid due to the difference between the exterior and interior air pressure is approximately 23.56 Newtons.

Step-by-step explanation:

To calculate the force exerted on the lid due to the difference between the exterior and interior air pressure, we can use the formula for pressure:

Pressure = Force / Area

Where:

Pressure (P) = 7.50 x 10^4 Pa (interior pressure)

Area (A) = The area of the lid

First, we need to find the area of the lid. The lid is circular, and the diameter is given as 2.00 cm. The formula for the area of a circle is:

Area = π * (radius)^2

where π (pi) is approximately 3.14159 and the radius is half the diameter. Let's calculate the radius first:

Radius = Diameter / 2 = 2.00 cm / 2 = 1.00 cm = 0.01 m

Now, we can find the area:

Area = π * (0.01 m)^2 ≈ 3.14159 * 0.0001 m^2 ≈ 3.14159 x 10^-4 m^2

Now, we can calculate the force exerted on the lid:

Force = Pressure * Area

Force = (7.50 x 10^4 Pa) * (3.14159 x 10^-4 m^2)

Force ≈ 23.56175 N

So, the force exerted on the lid due to the difference between the exterior and interior air pressure is approximately 23.56 Newtons.