Day 14, Physics 131

HW Problem 15-11

• Suppose that when you ride on your 7.7-kg bike that the weight of you and the bike is supported equally by the two tires.

• ? If the gauge pressure in the tires is 70.5 lb/in2 and the area of contact between each tire and the road is 7.13 cm2, what is your weight. ?

HW Problem 15-22

• A water storage tower is filled with fresh water to a depth of 6.4 m.

• ? What is the pressure at (a) 4.5 m and (b) 5.5 m below the surface. ?

• ? Why are the metal bands on such towers more closely spaced near the base of the tower. ?

HW Problem 15-34

• A 32-kg balloon is filled with helium (density = 0.179 kg/m3).

• ? If the balloon is a sphere with a radius of 4.9 m, what is the maximum weight it can lift. ?

HW Problem 15-37

• Block of wood has a steel ball glued to one surface. The block can be floated with the ball “high and dry” on its top surface.

• ? When the block is inverted, and the ball is immersed in water, does the volume of wood that is submerged increase, decrease, or stay the same. Why????

HW Problem 15-46

• A log floats in a river with one-fourth of its volume above the water.

• ? (a) What is the density of the log ?• ? (b) If the river carries the log into the ocean,

does the portion of the log above the surface of the water increase, decrease, or stay the same? Explain??

HW Problem 15-55

• A typical arteriole has a diameter of 0.030 mm and carries blood at the rate of 5.5 x 10-6 cm3/s.

• ? (a) What is the speed of the blood in an arteriole?

• ? (b) Suppose an arteriole branches into 340 capillaries, each with a diameter of 4.0 x 10-6 m. What is the blood speed in the capillaries.?

HW Problem 15-65

• ? (a) Find the pressure difference on an airplane wing if air flows over the upper surface with a speed of 115 m/s and along the bottom surface with a speed of 105 m/s. ?

• ? (b) If the area of the wing is 32 m2, what is the net upward force exerted on the wing ?

HW Problem 15-66

• Flying: Suppose the air outside your airplane window moved with a speed of approximately 170 m/s shortly after takeoff and that the air inside the plane is at atmospheric pressure.

• ? (a) Find the pressure difference between the inside and the outside of the window ?

• ? (b) If the window is 25 cm by 42 cm, find the force exerted on the window by air pressure ?

HW Problem 15-111

• A tank of water filled to a depth d has a hole in its side a height h above the table on which it rests.

• ? Show that water emerging from the holehits the table at a horizontal distance of 2((d-h)h)1/2 from the base of the tank ??

Thermal Physics

• Zeroth law of thermodynamics:• If object A is in thermal equilibrium with

object B, and object is also in thermal equilibrium with object B, then objects A and C will be in thermal equilibrium if brought into thermal contact.

Temperature Scales

• Tc= Temperature in degrees Celsius

• Tc = (5/9) (Tf – 32)

• Notice that -40o C = -40o F• SI unit of temperature is Tk, Temperature in

Kelvins, K• Tk = Tc + 273.15o

• See Tk = Tc

Problem 16-6

• Given F = 27o

• ? What is Co ?• ? What is K ?

Thermal Expansion

• Expansion in length• L = Lo T• = coefficient of linear expansion• I-40 in Durham County• A = 2 Ao T for expansion of an Area• V = Vo T, where approx. equal 3• We use 3 for our example and for HW.• Table 16-1, andcoefficients

Eiffel Tower

• On “Bones” it was reported that the Eiffel Tower shrinks 6” in cold weather.

• ? Is this claim reasonable ?

Sleeve and Shaft

• A cylindrical brass sleeve is to be shrink-fitted over a brass shaft whose diameter is 3.212 cm at 0oC. The diameter of the sleeve is 3.196 cm at 0o C.

• ? (a) to what temperature must the sleeve be heated before it will slip over the shaft ?

• ? (b) to what temperature must the shaft be cooled before it will slip into the sleeve ??

Grandfather clock

• The pendulum of a grandfather clock is 1.3-m long at 20oC.

• ? (a) What is the length of the pendulum at 0oC ?

• (b) Does the clock run faster or slower at 0oC ?

Circular Steel Casing

• The figure shows a circular steel casing with a gap.

• ? (a) If the casing is heated, does the width of the gap increase or decrease. ?

• The gap width is 1.600 cm when the temperature if 30oC.

• ? (b) What is the gap width when the temperature is 190oC. ?

Carbon Tetrachloride

• A steel container is full of carbontetrachloride.• The volume of the container is 50.0 m3.• steel = 11 x 10-6 / oC

• for carbontetrachloride = 5.81 x 10-4 / oC• Initial T = 10.0oC• Final T = 30.0oC• ? What volume of carbontetrachloride spills?

Aluminum gas can

• A 1.00-liter aluminum cylinder at 5.00oC is filled to the brim with gasoline at the same temperature.

• ? If the aluminum and gasoline are warmed to 65oC, how much of the gasoline spills out ?

• Assume = 24 x 10-6 K-1 for aluminum• Assume = 9.6 x 10-4 K-1 for gasoline

Water is special!

Heat and Internal Energy

• Heat is the transfer of energy between a system and its environment due to a T between them.

• A calorie is defined a the heat required to move one gram of water from 14.5oC to 15.5oC.

• Food in the US is measured in kilocalories, k-cals, Calories, Cal, “C”. Food packages in Europe also cite the energy in Joules, J.

• 1 Cal = 4.186 J

Specific Heat

• The heat capacity of an object, C, is the amount of heat storied divided by T. It is mass dependent.

• The specific heat, c, of a material is a measure of its ability to store energy.

• c for a material is defined as Q/m T, where Q is energy in Joules, J. It is not mass dependent.

• Water has a huge specific heat.

Disc Brakes

• Desire to slow a car from 30 m/s to 15 m/s. The car’s mass is 1.5 x 103 kg.

• Suppose each brake rotor mass = 5 kg, there are four rotors, all aluminum.

• Given: caluminum = 900 J/kg oC

• Tinitial = 20oC

• ? Tfinal = ????

Drink off that birthday cake

• A student eats a piece of case (400 Cal). To prevent this energy from being stored as fat, she decides to drink ice water at 0oC. She reasons that her body will heat the water to 37oC and absorb the energy from the cake.

• cwater = 4.186 kJ/kg Co.• ? How much ice water would she have to

drink to absorb the energy generated by metabolizing the birthday cake ?

Calorimetry

• In a showdown on the streets of Loredo, the good guy drops a 5.0-g silver bullet at a temperature of 20oC into a 100-cm3 cup of water at 90oC. Simultaneously, the bad guy drops a 5.0-g copper bullet at the same initial temperature into an identical cup of water.

• csilver = 234 J/kg oC, ccopper = 387 J/kg oC.• The winner is the one with the coolest cup of

water in the west. • ? Who wins ? ? Quantify ??

Spoon in water

• Spoon at 100oC• 0.200 kg water at 20oC• Final temperature is 35oC• caluminum=960 J/kg oC, cwater = 4186 J/kgoC

• ? What is the mass of the spoon??

Melting a Bullet

• Lead bullet, c = 128 J/kgoC• Bullet mass 5.00 g• Fired at 300 m/s, stopped by a tree.• ½ of its kinetic energy goes to internal

heating, ½ to the tree.• ? T of the bullet ?

Heat Transfer

• Conduction • Convection • Radiation

Conduction

• Rate of energy transfer by conduction through a rod of area A and a length of L

Home Insulation

• Power, in Btu/hour = A (Th-Tc)/i Ri

• A = area of wall, length * height, in ft2

• Ri = “R values” for components of the wall

• Units of R values = ft2 * oF * hours / Btu• Btu is British Thermal Unit

R values

SI Insulation Calculations

Rate of energy transfer by conduction through a wall of area A made up of several layers.

Wall Insulation using ThermalConductivities

School Wall

• A = 3 m height, 10 m long, 30 m2

• T = 20oC inside, 10oC outside, T = 10oC• Wall has three layers– Inside is concrete, 15 cm thick. ki = 1.30

– Middle is air, 2 cm thick. ki = 0.0234

– Outside is brick, 10 cm thick. ki = 1.80

• Calculate Q/t

Convection

• Transfer of energy by movement of a substance is convection.

• “That window leaks”. Actually it gets cold when the air outside is cold, it cools the air inside, and the colder air sinks to the floor. Sit by the window and cool off!

• Most heating systems heat air and blow the air past our bodies, thus heating our bodies by convection.

Radiation

• Power = A e T+4, Stefan’s Law• = 5.6696 x 10-8 W/m2K4

• A = area in m2

• e = emissivity of the body• Value of “e” is close to 1 for a dull black body,

much less for a shiny, silver-colored body.• Radiators, and good old black wood stoves,

are designed to radiate!

Radiative Heating

• The sun heats radiatively.• The solar heating the walls of our south-facing

condo is a function of the time of day, a function of the direction the wall faces, and a function of the day of the year. It is most effective in the middle of the day.

• How effective is the sun in the middle of the winter?

Light Bulb

• Tungsten filament • e = 0.90• A = 2.5 x 10-5 m2

• Power = 35 W• Room T = 22oC = 295 K• ? What’s the temperature of the filament ??

A realistic thermal conduction problem

• A thermopane window consists of two glass panes, each 5.0 x 10-2 m thick, with a 1.0 x 10-2-m-thick sealed layer of air in between. If the inside surface temperature is 25 oC and the outside surface temperature is 0.0 oC, determine the rate of energy transfer (in watts) through 1.0 m2 of the window.

• Use Q / Dt = A (Th –Tc) / ( Li/ki ) for this calculation.

• For glass, use ki = 0.84 W / (m oC).

• For air, use ki = 0.0234 W/ (m oC).

• Li is thickness of layer “i”.