Physics 2 Chapter 9 Section 2

Pressure Ratio of the magnitude of the force acting perpendicular to the surface to the area over which the force acts P = F / A [P] = N/m2 = Pascal, Pa since Pa is very small pressure is usually measured in kPa

Pressure cont’d. Other units for pressure [P] = lbs / in2 = psi [P] = torr = 133.3 Pa or 1/760 atm [P] = atm = 1.01 x 105 Pa = 14.7 lb/in2 which is pressure at sea level All fluids exert pressure perpendicular to the surface they are in contact with but never at an angle to the surface If a fluid exerted a force tangent to a surface the surface would push back and cause the fluid to flow (can’t if static)

Question At sea level the atmosphere presses down on us with a pressure equivalent to 14.7 pounds per square inch. Why aren’t we crushed by the air pushing in on us at every surface? Bodies are relatively permeable to air so our internal pressure stays the same as the external pressure (inward push = outward push) Usually notice pressure when it changes Ex – go up a mountain where air P drops your ear P is greater so yawn to open Eustachian tubes Ex – diving the pressure increases so have to force air into ears to balance pressure

Sample Problem A man weighs 200 lb. At one particular moment when he walks, his right heel is the only part of his body that touches the ground. If the heel of his shoe measures 3.5 in. by 3.25 in., what pressure does the man exert on the ground? 17.6 lb/in2

Sample Problem A woman weighs 100 lb and is wearing high- heeled shoes. The cross section of her high-heel shoe measures ½ in. by 5/8 in. At a particular moment when she is walking, only one heel of her shoe makes contact with the ground. What is the pressure exerted on the ground by the woman? 320 lb/in2 Examples of pressure – Snowshoes (large A so F/A is small) Bed of nails Cola can Candle and beaker egg and flask Papers and sticks

Pressure cont’d. Pressure in water is created by the weight of the water Pressure in air is created by the air being pulled down by gravity toward the center of the earth Air pressure (like water pressure) increases with depth

Sample Problem An airplane window has an area of 825 cm2. Cabin pressure is 1 atm and the outside pressure is 0.3 atm. Find the net force produced by air pressure on the window. -5832.8 N

Pressure cont’d. Pressure increases with depth Pressure at top surface equals F1/A Pressure at bottom surface equals F2/A ΣF = P2A – P1A – mg Since fluid is static can show P2 = P1 + ρgh Only good if ρ is same at any depth

Pascal’s Principle Any change in the pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and the enclosing walls Since P1 = P2 the F2 = F1 (A2/A1) Principle behind hydraulic lifts and hypodermic needles

Barometer 1643, Torricelli invented the barometer to measure atmospheric pressure Filled a glass tube with Hg and inverted it in a container of Hg When Hg drop in tube it creates a vacuum Using Pascal’s principle can show Poutside = ρgh Pressure is indicated by the height of Hg

Gauge Pressure Amount by which the container pressure exceeds atmospheric pressure Ex – tire gauge if car tire has a gauge pressure of 2 atm its actual pressure is 3 atm