91Ó°ÊÓ

Problem 1

Someone steps on your toe, exerting a force of \(500 \mathrm{N}\) on an area of \(1.0 \mathrm{cm}^{2} .\) What is the average pressure on that area in atm?

Problem 2

The pressure inside a bottle of champagne is 4.5 atm higher than the air pressure outside. The neck of the bottle has an inner radius of \(1.0 \mathrm{cm} .\) What is the frictional force on the cork due to the neck of the bottle?

Problem 3

What is the average pressure on the soles of the feet of a standing 90.0 -kg person due to the contact force with the floor? Each foot has a surface area of \(0.020 \mathrm{m}^{2}\).

Problem 4

Atmospheric pressure is about \(1.0 \times 10^{5} \mathrm{Pa}\) on average. (a) What is the downward force of the air on a desktop with surface area $1.0 \mathrm{m}^{2} ?$ (b) Convert this force to pounds so you really understand how large it is. (c) Why does this huge force not crush the desk?

Problem 5

A 10 -kg baby sits on a three-legged stool. The diameter of each of the stool's round feet is \(2.0 \mathrm{cm} .\) A \(60-\mathrm{kg}\) adult sits on a four-legged chair that has four circular feet, each with a diameter of $6.0 \mathrm{cm} .$ Who applies the greater pressure to the floor and by how much?

Problem 6

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)?

Problem 7

A container is filled with gas at a pressure of $4.0 \times 10^{5} \mathrm{Pa}\( The container is a cube, \)0.10 \mathrm{m}$ on a side, with one side facing south. What is the magnitude and direction of the force on the south side of the container due to the gas inside?

Problem 8

A nurse applies a force of \(4.40 \mathrm{N}\) to the piston of a syringe. The piston has an area of \(5.00 \times 10^{-5} \mathrm{m}^{2} .\) What is the pressure increase in the fluid within the syringe?

Problem 9

A hydraulic lift is lifting a car that weighs \(12 \mathrm{kN}\). The area of the piston supporting the car is \(A\), the area of the other piston is \(a,\) and the ratio \(A / a\) is \(100.0 .\) How far must the small piston be pushed down to raise the car a distance of \(1.0 \mathrm{cm} ?[\text {Hint}:\) Consider the work to be done.]

Problem 10

In a hydraulic lift, the radii of the pistons are \(2.50 \mathrm{cm}\) and $10.0 \mathrm{cm} .\( A car weighing \)W=10.0 \mathrm{kN}$ is to be lifted by the force of the large piston. (a) What force \(F_{\mathrm{a}}\) must be applied to the small piston? (b) When the small piston is pushed in by $10.0 \mathrm{cm},$ how far is the car lifted?(c) Find the mechanical advantage of the lift, which is the ratio \(W / F_{\mathrm{a}}\).