Group Work When a 40.0-kg diver stands at rest at the end of a diving board, the board deflects downward 10.0 cm. When she jumps up and lands back on the board, it deflects downward 25.0 cm. What is her acceleration when the board is defected 25.0 cm downward?

Pressure and Fluids We’re surrounded Chapter 11

Relating “how big” to “how much” Density Relating “how big” to “how much” § 11.1

Density Mass per volume r = m/V SI units kg/m3; conventionally g/cm3 Intensive quantity Depends on substance and conditions, not amount

Some Densities Substance kg/m3 g/cm3 Air 1.20 0.0012 Plain water 1,000 1.000 Sea water 1,030 1.03 Lead 11,300 11.3

Pressure One type of stress § 11.2

Pressure Force per unit area p = F/A F is component perpendicular to surface Scalar quantity

Units of Pressure SI Units: N/m2 = pascal = Pa Bar = 100,000 Pa; mbar = hPa = 100 Pa Atmosphere = atm = mean sea level pressure = 101,325 Pa = 1.01 bar Torr: Height in mm of a mercury barometer (760 torr = 1 atm) lb/in2 = psi (14.696 psi = 1 atm)

Gauge and Absolute Pressure Gauge: increase above surrounding atmosphere e.g. tire pressure 32 psig Absolute: total

Question When a molecule bounces elastically off a frictionless surface, what is the direction of its momentum change? A. B. C. D.

Question When a molecule bounces elastically off a surface, what is the direction of the force it applies to the surface? A. B. C. D.

Collisions Collision exerts a force into surface Pressure from force averaged over time and area

Pressure in a fluid Pascal’s Principle: pressure in a fluid is exerted uniformly in all directions throughout the fluid. § 11.5

just another simple machine Hydraulics just another simple machine § 11.5

Quick Question If a force F1 is applied to the small piston with area A1, what is the pressure increase in the fluid? Dp = F1A1. Dp = F1 + A1. Dp = A1/F1. Dp = F1/A1. 1 2

Question If a force F1 is applied to the narrow piston with area A1, How does the magnitude of the force F2 exerted by the fluid on the wide piston compare to F1? F2 = F1. F2 < F1. F2 > F1. 1 2

Hydraulics Pistons have different areas Pressure p = F/A for both pistons F1 A1 F2 A2 = rearranges to F1 F2 A1 A2 =

Question If the narrow piston with area A1 is moved a distance Dx1, How does the distance Dx2 that the wide piston moves compare to Dx1? Dx2 = Dx1. Dx2 < Dx1. Dx2 > Dx1. Dx2 ? Dx1 1 2

Hydraulics are Simple Machines F1 A1 F2 A2 = Volume changes DV are opposites DV = A1Dx1, so Dx1 = DV/A1; Dx2 = –DV/A2 = DV A1 F1 A2 F2 F1Dx1 = –F2Dx2 input, output work equal and opposite

Example Problem In an auto shop a hydraulic jack is used to lift vehicles for service. If the radius of the cylinder below piston 1 is r1 = 0.02 m, and the radius of the cylinder below the piston holding the car is r2 = 0.1 m, what force F1 must be exerted on the small piston to lift a 1500-kg car?

Pressure with Depth Why does it increase? § 11.6

Pressure within a fluid Force comes from weight of fluid above Pressure increases with depth Supports weight above

Pressure in a liquid weight of fluid above cross-section p = F/A = = mass  g A h density  volume  g A = A rAhg = = rgh p = pressure here

Depth Pressure Formula p0 = pressure here p = p0 + rgh h p0 = pressure at depth 0 p = pressure at depth h r = constant density of liquid h = depth under top of liquid p = pressure here

Whiteboard Work What is the water pressure at the bottom at the deepest point of Lake Superior? Lake depth = 406 m, density of water = 1000 kg/m3.

Buoyancy How do things float? Why? § 11.6

What forces are present?

What forces are present?

What forces are present?

What forces are present?

Pressure in a fluid Pressure increases with depth Greater pressure at bottom than top of an immersed object Results in upward buoyancy force that is the (vector) sum of all pA forces F =  p dA A

Buoyancy Force Area A Force F = F1 + F2 P1 = rgh = P1A + P2A↑ = rghA + rg(h+L)A↑ = rg(h+L–h)A↑ = rgLA↑ = rgV↑ P1 = rgh P2 = rg(h+L) Length L Volume V = LA

Buoyancy Force Principle of Archimedes: Buoyancy force = weight of fluid displaced F = rVg r = constant density of fluid V = volume of fluid displaced = volume of object submerged g = 9.8 N/kg

Quick example The density of fresh water r = 1000 kg/m3. What is the buoyancy force on a 1-m3 parcel of water? What is the buoyancy force on a 1-m3 rock submerged under water? What is the buoyancy force on a 1-m3 chunk of Styrofoam submerged under water?

Quick Questions All blocks are cubes with 1-m sides. Which ones float? Which one makes the water level change the most? Which one makes the water level change the least?

Buoyancy and Density If an object is more dense than the surrounding fluid, it sinks If an object is less dense than the surrounding fluid, it rises A floating object displaces exactly enough fluid to support its weight

Quick Question Which boat (with cargo) has the greatest volume? The high boat (left). The low boat (right). Both have the same volume.

Quick Question Which boat (with cargo) has the greatest volume under the water line? The high boat (left). The low boat (right). Both have the same volume under water.

Quick Question Which boat (with cargo) experiences the greatest buoyancy force? The high boat (left). The low boat (right). Both experience the same buoyancy force.

Quick Question Which boat (with cargo) has the greatest mass? The high boat (left). The low boat (right). Both have the same mass.

Discussion Question After a boat sinks, it displaces more water than when it floated. less water than when it floated. the same volume and weight of water as when it floated.