Question

A soda can has a surface area of 300cm^2. For this problem, take atmospheric pressure to be

1.00x 10^5Pa
An empty soda can can be crushed by air molecules bouncing off it if the total inward force on the walls of the can reaches 480 N.This can be achieved by reducing the pressure inside the can. What does the pressure inside the can have to be to crush the can? Assume that the pressure outside the can is atmospheric pressure.

Answer 1

The internal pressure required to crush an empty soda can is calculated using the formula P = Pₒ - F / A. With an atmospheric pressure of 1.00 x 10⁵ Pa and a total inward force of 480 N, the pressure inside the can must be 8.40 x 10⁴ Pa.

Step-by-step explanation:

To find the pressure inside the can required to crush it, we can use the relationship between force, area, and pressure. Given that the pressure outside the can is atmospheric pressure and that when the can is crushed the total inward force is 480 N, we can calculate for the missing pressure inside the can.

The pressure exerted by a force on an area is calculated by the formula P = F / A, where P is the pressure, F is the force, and A is the area. In this case, A = 300 cm² (which is 0.03 m² in SI units), and F = 480 N. Using atmospheric pressure, Pₒ = 1.00 x 10⁵ Pa, we want to find the internal pressure, P, that when combined with the external pressure will exert a force of 480 N on the walls.

The total force exerted on the can is the difference between the force due to external pressure and internal pressure, thus F = Pₒ x A - P x A. Solving for P gives us P = Pₒ - F / A. Substituting the known values, we get P = 1.00 x 10⁵ Pa - (480 N / 0.03 m²). Therefore, the internal pressure needed to crush the can is P = 1.00 x 10⁵ Pa - 16 x 10⁴ Pa, which equals 8.40 x 10⁴ Pa.