Chapter 4 Energy 4th Edition

Energy Energy is the capability to do work Energy Units: Work = force x distance Where “distance” is the distance over which the force is applied Energy Units: SI: joules (J) English: foot pound force (ft∙lbf) Exploring Engineering

Power Power is defined as time rate of doing work or time rate of change of energy Work = force x distance Power = work/time Where “time” is the time over which the work occurs Power Units: SI: watts (1 W = 1 J/s) English: Horsepower (1 hp = 550 ft∙lbf/s) Exploring Engineering

Power Example A person takes 2.0 seconds to lift a 1.0 kg book a height of 1.0 meter above the surface of earth. Calculate the power expended by the person. Need: Power Know: mass = 1.0 kg, distance = 1.0 m, time = 2.0 s How: work = force × distance, and power = work/time Solve: Work = [(ma)/gc]×(distance) = [(1.0 kg)(9.8 m/s2)]/1 × (1.0 m) = 9.8 kg(m2/s2) = 9.8 joules Then, Power = (9.8 joules)/(2.0 seconds) = 4.9 J/s = 4.9 W Need: Power Know: m = 1 kg, Z = 1 m, t = 2 seconds. Exploring Engineering

Kinds of Energy Kinetic Energy Potential Energy Other forms of energy: Magnetic energy Electrical energy Surface energy Internal energy etc. Exploring Engineering

Kinetic Energy Also known as “Translational Kinetic Energy” (TKE) TKE = ½mv2 /gc (SI units) Where m = mass, v = speed, gc = 1 (dimensionless in SI) OR TKE = ½mv2/gc (English units) Where m = mass, v = speed, gc = 32.2 lbm∙ft/lbf∙s2 Anything that has mass and is moving in a line has TKE. Exploring Engineering

Kinetic Energy Example What is the translational kinetic energy of an automobile with a mass of 1.00 × 103 kg traveling at a speed of 65.0 miles per hour (29.0 m/sec)? Need: TKE of the vehicle Know: Mass: 1.00 × 103 kg, velocity: 29.0 m/sec How: TKE= ½mv2 (SI units) Solve: TKE = 4.23 × 105 J Exploring Engineering

Gravitational Potential Energy GPE is the energy acquired by an object by virtue of its position in a gravitational field-- typically by being raised above the surface of the Earth. In SI, GPE = mgh   in units of joules In Engineering English units, GPE = mgh/gc  in units of ft∙lbf In English units, GPE = [lbm] [ft/s2][ ft][lbf s2/lbm ft] = ft lbf Exploring Engineering

Gravitational Potential Energy Mt. Everest is 29, 035 ft high. If a climber has to haul him/herself weighing 200. lbm (including equipment) to the top, what is his/her potential energy above sea level when on the summit. Give your answer in both in joules and in ft lbf. Exploring Engineering

Gravitational Potential Energy Need: GPE in English and SI units Know: m = 200. lbm = 90.7 kg; h = 29, 035 ft = 8850. m; g = 32.2 ft/s2 = 9.81 m/s2 and gc = 32.2 lbm∙ft/lbf∙s2 (English) and gc = 1 [0] (SI) How: GPE = mgh/gc Note: I have rounded up h from 8849.868 to one more sig. figure than I will need. Exploring Engineering

Gravitational Potential Energy Solve: English, GPE = mgh/gc = 200.  32.2  29,035/32.2 [lbm][ft/s2][ft][lbf.s2/lbm.ft] = 5.81  106 ft.lbf (to 3 significant figures) In SI, GPE = mgh/gc = 90.7  9.81  8850./1 = 7.87  106 J A check direct from the units converter: 5.81  106 ft lbf = 7.88  106 J …OK Why to 3 significant figures? That’s how well we know m. Convert has some roundoff error since we had already rounded the English answer Exploring Engineering

Potential Energy (PE) GPE is NOT the only form of PE. Chemical, nuclear and electromagnetic are other forms of PE For us, chemical and electrical energy are so important that we will reserve extra chapters and lectures to them for later presentation. Exploring Engineering

Thermal Energy Thermal energy, often referred to as heat, is a very special form of kinetic energy because it is the random motion of trillions and trillions of atoms and molecules that leads to the perception of temperature All higher forms of energy dissipate thermal thermal energy, the ultimate energy sink The laws of thermodynamics state 1) all energy is conserved and 2) that the thermal energy in the universe always increases Exploring Engineering

Energy We have defined energy is the capability to do work But energy comes in different forms Potential, translational kinetic, rotational kinetic, thermal and others And energy can be converted from one form to another The energy in the Universe is conserved A “control volume” is a subset of the Universe you construct to isolate the problem of interest. It exchanges energy with the rest of the Universe The conversion of one kind of energy to another, say chemical to mechanical, thermal to mechanical, or say mechanical to electrical, is a very large part of what several types of engineers do. Exploring Engineering

Energy Conservation “The Universe” : Energy exchanges System “The Universe” : Energy exchanges System energy changes Universe energy changes = 0 ¹ Energy = F  distance is the generic equation for energy Energy is conserved (although it may change form) Example of a book lying on a table and then falling on ground In theory, its problematic what the Universe in expanding against… Exploring Engineering

Energy Conservation Your class room C.V. boundary Insulated walls Door Control Volume Example C.V. boundary Insulated walls Your class room This is an example of a “Control Volume” (CV) The energy in the room is constant unless we allow exchange with the outside (e.g., the Universe) E.g., a person could walk through the door and add or subtract energy A heating duct could also add thermal energy On a winter day, a window could break and the c.v. would lose thermal energy Exploring Engineering

Energy Conservation Energy exchanges between a speeding car and the rest of the universe. Exploring Engineering

Application of Control Volumes In the last slide, we have TKE of the vehicle, RKE of the wheels, electrical energy in the lights, thermal energy from the radiator, etc. We deduce that all these energies are exactly equal to the loss in chemical (potential) energy in the fuel that is driving the vehicle. Exploring Engineering

Summary We specifically identified kinetic, gravitational, potential, and thermal energy We learned that energy is conserved in the universe, but not necessarily within a control volume. Deficiencies within a control volume mean that somewhere energy in leaking in or out of the control volume at an exactly compensating amount. Exploring Engineering