Chapter 3 - Energy Changes in motion and position -involves forces leads to changes in energy ENERGY - ability to do work position change, motion change: study, mow lawn, wind mill MECHANICAL WORK - transformation of forces into energy force must move object-displacement no force no movement } no work W = F d d F d = 1 N d = 1m does no work W = F d d = (1 N)(1 m) = 1 N m (kg m 2 /s 2 ) = 1 Joule = 1J Force in direction of motion F
EXAMPLE : weight lifting Work to lift a 100 kg barball a distance of 1 m ( @ constant speed) d=h=1m m = 100 kg Lift w/ no a F net = 0 = weight-F up F up =W=mg in direction of motion F up W W = F d d = F up d = (mg)h = (100 kg)(10 m/s 2 )(1 m) 1000 kg m 2 /s 2 = 1000 J mechanical work to change the position of the object Note: no mechanical work done to hold barbell d=0 when holding still above head
t o =0 x o =0 v ox = 0 t = 5s v x = 20 m/s x = a x Another example : car racing A 1000 kg car goes from 0 to 20 m/s in 5 seconds. How much work is done (by the engine)? CONNECT Newton’s 2nd law F=ma engine accelerates car W = F d d = F x d ma x d Work changes the motion of the car WORK - forces used to give energy to an object motional energy positional energy chemical, electrical, heat } MECHANICAL ENERGY
Power - rate at which work is done how fast work is done Powerful: can do work fast Power ( P ) = (Work-Energy)/time = W/t J/s = Watt = W SI unit for power Light bulb : 75 W How much (work) energy in 1 hour? P = (W-E)/ t E = W = Pt HORSEPOWER : compare machines to horses P = W/ t= (F d d)/t = F d (d/ t) = F d v 1 hp = 1 horsepower = 746 W Other Power units: megawatt = MW = 106 W POWER COMPANIES F=150 lbs English unit hp v= 2.5 mph 550 ft-lb/s
KINETIC ENERGY - energy associated with the motion of an object Applied forces cause objects to move - accelerates motional energy – mass and velocity velocity influences more K=1/2 mv 2 work increases velocity Work-Energy Theorem W = KE change in kinetic = 1/2 mv 2 -1/2 mv o 2 Work to bring an object to rest: W=1/2 mv 2 just the KE Car example: W= 200,000 J W= KE = ½ mv 2 What is the velocity? another way of looking at the problem!
POTENTIAL ENERGY - energy associated with the position of an object potential for doing work drop rock – falls – gains KE (motional) Transforms force of gravity into KE of motion - does work when released Definition: PE = -W work to achieve position Gravitational Potential Energy – work required to raise the object to a particular height PE grav = F d d = (mg)h =mgh like barbell h zero reference – always be consistent in zero height h=0 h=-2m h= 3m
Other types of PE SPRINGS PE= ½ kx 2 change position by compressing zero – uncompressed Electrical – work to move charge Chemical – work to break bond MECHANICAL ENERGY Energy associated with the mechanical work on an object – motional and positional E = KE + PE (grav) sum of both The mechanical energy is conserved when friction absent FRICTION – nonconservative – heats environment Law of CONSERVATION OF (MECHANICAL) ENERGY -energy is neither created or destroyed -assumption: no friction present E = KE+PE =constant energies transformed not lost
Conservation of energy E=KE+PE relates motion and position E initial = E final can solve for position or motion (v) EXAMPLE: ROLLER COASTER A 100 kg rollercoaster moves along the track shown starting from rest. For each position marked, find the: mechanical energy potential energy kinetic energy velocity h=0 PE=0 100 m 50 m 30 m v i =0 NO FRICTION
We will be looking at simpler problems EXAMPLE: A 1.4 kg PSC book is dropped out of a 20 m high building . a) What is the PE at the top? b) What is the KE at the bottom? c) What is the velocity of the book at the bottom? h=0 PE=0 20 m NOTE: PE at the top is transformed into KE at the bottom! E= (KE+PE) top = (KE+PE) bot PE top = KE bot 0 0 no energy lost – just transformed
All Energy Is Conserved!!! Can work problems with friction and other forces -leave this for more advanced course, but if whole system considered E tot = PEgrav + PE other + KE GENERALIZED WORK-ENERGY THEOREM E f - E i =W nc work due to friction change in mechanical energy NOW ALL ENERGY IS CONSERVED – everywhere the energy goes is taken care of -heat to environment -mechanical work -radiant -sound -electrical -nuclear -anything else
Work and Energy.
Energy is used to do work on an object, exerting a force through a distance.
This force is usually against something and there are five main groups of resistance.
Work against inertia.
Since inertia is an objects resistance to change of motion, it naturally follows that this would resist forces acting upon it.
Work against fundamental forces.
Nuclear forces .
Work against friction
Friction is always present when two objects are in contact with each other.
Friction is always a force in the opposite direction of the applied force .
Work against shape.
Work is needed to stretch or compress an object.
This is what happens when we work against the shape of a spring.
Work against any combination of inertia, fundamental forces, friction, or shape.
Some kind of energy change has taken place, which may include one of the following:
Increased kinetic energy.
Work against inertia results in energy of motion for an object .
Increased potential energy.
Work against fundamental forces and work against shape result in an increase in energy of position (potential energy)
Work against friction always results in an increase in temperature.
Increased combination of kinetic energy, potential energy, and/or temperature.
Energy Forms. (five forms).
Usually associated with the kinetic energy of everyday objects and potential energy that results from the effect of gravity.
Mechanical energy is the energy of motion, or the energy of position, of many familiar objects. This boat has energy of motion.
Chemical energy is the form of energy associated with chemical reactions.
Chemical energy is released during the process known as oxidation.
Chemical energy is potential energy that is released when chemical reactions break bonds in molecules .
Chemical energy is a form of potential energy that is released during a chemical reaction. Both (A) wood and (B) coal have chemical energy that has been stored through the process of photosynthesis. The pile of wood may provide fuel for a small fireplace for several days. The pile of coal might provide fuel for a power plant for a hundred days.
Radiant energy is the form of energy that travels through space.
Also called electromagnetic radiation.
Visible light is one small part of the electromagnetic radiation.
Largest form of energy Earth receives
The electromagnetic spectrum includes many forms of radiant energy. Note that visible light occupies only a tiny part of the entire spectrum.
Electrical energy is a form of energy that comes from electromagnetic interactions.
Electrical energy that travels through the wires in our homes to light or houses is a familiar form of electrical energy.
The blades of a steam turbine. In a power plant, chemical or nuclear energy is used to heat water to steam, which is directed against the turbine blades. The mechanical energy of the turbine turns an electric generator. Thus a power plant converts chemical or nuclear energy to mechanical energy, which is then converted to electrical energy.
this is the form of energy generated in nuclear power plants.
Fission-split heavy nucleus
Fusion-combine light nucleus
Energy can be converted from one form to another.
For example, during a fall PE lost = KE gained
mgh = 1/2mv 2
Solving for v f
v f = 2gh
This allows you to calculate the final velocity of a falling object after its potential energy is converted into kinetic energy.
This pendulum bob loses potential energy (PE) and gains an equal amount of kinetic energy (KE) as it falls through as distance h. The process reverses as the bob moves up the other side of its swing.
The energy forms and some conversion pathways.
Energy Conservation .
Any form of energy can be converted into another form.
The total amount of energy remains constant.
Law of Conservation of Energy :
Energy is never created or destroyed. Energy can be converted from one form to another, but the total energy remains constant.
Energy Sources Today.
Petroleum is our most widely used source of energy.
Petroleum provides about 40 percent of the energy used by the US.
Natural gas provides about 20 percent of our energy needs.
Coal provides about 25 percent of our energy needs.
Alternative energies (solar, wind, geothermal) provide less than 2 percent of the total.
Over 99 percent of our energy needs are supplied by 4 sources:
(A) The sources of energy and (B) the uses of energy during the 1990s.
Petroleum is oil that comes from oil bearing rocks.
Petroleum and natural gas come from organic sediments, material that have settled out of water.
Most of the organic material comes from plankton. The process of converting organisms into petroleum and natural gas takes millions of years.
Natural gas forms under higher temperatures than petroleum.
Coal forms from an accumulation of plant materials that collected millions of years ago.
Carbon rich decayed plant material is called peat.
Pressure, compaction, and heating are brought about by movement of the Earth's crust eventually change the water content and release the carbon in the materials, it has now begun the process toward coal formation.
Coal is ranked according to how long it took to form and how hard it is.
Lignite is the lowest ranked and is softest, took the least time to form, and burns quickest so contains the least amount of usable energy.
Bituminous is the next highest raking.
Anthracite is the hardest and took the longest to form and so contains the most usable energy.
Softer coal also has more impurities which contribute to increased pollution levels.
Water Power .
Moving water is a source of renewable energy that has been used for thousands of years.
At present in the US we have built about all of the hydropower plants that we can as we have no usable sources of moving water left.
Nuclear Power .
Nuclear power plants use the energy that is release from the splitting of uranium atoms and plutonium atoms to produce electrical energy .