Question

A lid is put on a box that is \(15 \mathrm{cm}\) long, \(13 \mathrm{cm}\) wide, and \(8.0 \mathrm{cm}\) tall and the box is then evacuated until its inner pressure is \(0.80 \times 10^{5} \mathrm{Pa} .\) How much force is required to lift the lid (a) at sea level; (b) in Denver, on a day when the atmospheric pressure is \(67.5 \mathrm{kPa}\) ( \(\frac{2}{3}\) the value at sea level)?

Short answer

Question: Calculate the force required to lift the lid of an evacuated box at sea level and in Denver, given the atmospheric pressure at sea level is 101.3 kPa, in Denver is 67.5 kPa, and the inner pressure of the evacuated box is 0.80 x 10^5 Pa. The lid has dimensions of 15 cm in length and 13 cm in width. Answer: To find the force required to lift the lid at sea level and in Denver, first calculate the pressure difference at each location, then find the area of the lid, and finally multiply the pressure difference by the area of the lid for each location.

Step-by-step solution

Find the pressure difference at sea level and in Denver

We are given the atmospheric pressure at sea level and in Denver, and also the inner pressure of the evacuated box. To find the pressure difference, subtract the inner pressure from the atmospheric pressure in both cases. (a) At sea level: Pressure difference = \(101.3 \times 10^3 \mathrm{Pa} - 0.80 \times 10^5 \mathrm{Pa}\) (b) In Denver: Pressure difference = \(67.5 \times 10^3 \mathrm{Pa} - 0.80 \times 10^5 \mathrm{Pa}\)

Find the area of the lid

The lid of the box has dimensions of \(15 \mathrm{cm}\) in length and \(13 \mathrm{cm}\) in width. To find the area, multiply the length and the width. Remember to convert the dimensions to meters (1 cm = 0.01 m): Area = \((15 \times 0.01 \ \mathrm{m}) (13 \times 0.01 \ \mathrm{m})\)

Calculate the force required to lift the lid

The force required to lift the lid is given by the product of the pressure difference and the area of the lid: (a) At sea level: Force = Pressure difference (at sea level) × Area (b) In Denver: Force = Pressure difference (in Denver) × Area