Cutnell & Johnson “Physics” 6th Edition 11.1 Mass Density Cutnell & Johnson “Physics” 6th Edition

Fluids Substances that can flow Liquids Gases

Mass Density Designated by the Greek letter rho The mass density ρ is the mass m of a substance divided by its volume V ρ = m/V SI Units: kg/m3 Table 11.1 page 301

Mass Density Increasing mass density Gases → Liquids → Solids Depends on how tightly packed the molecules of a substance are Gases are very sensitive to changes in temperature and pressure

Example 1 The body of a man whose weight is about 690 N contains about 5.210-3 m3 (5.5 quarts) of blood. Find the blood’s weight Express it as a percentage of the body weight m = rho * V = (1060 kg /m^3) (5.2 x 10^-3 m^3) = 5.5 kg W = mg = (5.5 kg)(9.8 m/s^2) = 54 N b) Percentage = 54 N / 690 N X 100 = 7.8%

Solution

Specific Gravity A method of comparing mass densities of two substances Specific = Density of substance Gravity Density of water at 4 C = Density of substance 1.000  103 kg/m3

Cutnell & Johnson “Physics” 5th Edition John Wiley & Sons, Inc. 11.2 Pressure Cutnell & Johnson “Physics” 5th Edition John Wiley & Sons, Inc.

Air Pressure in a Tire In colliding with the inner walls of a tire, the air molecules (blue dots) exert a force on every part of the wall surface. If a small cube were inserted inside the tire, the cube would experience forces acting perpendicular to each of its 6 faces.

Pressure The pressure P is the magnitude F of the force acting perpendicular to a surface divided by the area A over which the force acts. P = F/A SI Units: N/m2 = pascal (Pa)

Other Units 105 Pa = 1 bar lbs/in2 = psi 1 psi = 6.895  103 Pa 1 atm = 1.013  105 Pa = 1.013 bar = 14.70 psi = 760 torr One atmosphere of pressure is a significant amount. If the air is pumped out of a can, the can will crumple. Lynx paws are large so that they can walk across the snow. The cat’s weight is a constant. The pressure on the snow can be reduced by a larger cross-sectional area.

Direction of Force Due to Pressure A static fluid cannot produce a force parallel to a surface If it did, the surface would apply a reaction force to the fluid, consistent with Newton’s 3rd law In response, the fluid would flow and then would not be static

Direction of Force Due to Pressure The force generated by the pressure of a static fluid is always perpendicular to the surface that the fluid contacts.

Example 2: The Force on a Swimmer P = 1.2105 Pa Ahand = 8.4 10-3 m2 Determine the magnitude of the force that acts on the hand. F = P * A = (1.2 x 10^5 N/m^2)(8.4 x 10^-3 m^2) = 1.0 x 10^3 N = 230 lb.

Solution