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The Nature of Energy
Power,Power,by definition, isby definition, is
the time rate of doing work;the time rate of doing work;or the time rate transfer of energyor the time rate transfer of energy..
PP == WW // ttPower is a scalar quantity.
The SI unit of poweris the Watt,
named in honor ofJames Watt.
One Watt, W, of powerOne Watt, W, of poweris the power achievedis the power achieved
when 1.0 J of work is done orwhen 1.0 J of work is done or1.0 J of energy is transferred1.0 J of energy is transferred
in a time of 1.0 s.in a time of 1.0 s.
Work is only done by a force on anWork is only done by a force on anobject if the force causes the objectobject if the force causes the objectto move in the direction of the force.to move in the direction of the force.
Objects that are at rest mayObjects that are at rest mayhave many forces acting on them,have many forces acting on them,
but no work is donebut no work is doneif there is no movementif there is no movement..
Work,Work,by definition, is
the product of the force exerted onthe product of the force exerted onan object and the distance the objectan object and the distance the objectmoves in the direction of the force.moves in the direction of the force.
WW == F·dF·dWork is a Work is a scalarscalar quantity. quantity.
The SI unit of workis the Joule,
named in honor ofJames Prescott Joule.
One Joule, J, of workOne Joule, J, of workis the work done whenis the work done when1.0 N of force is applied1.0 N of force is applied
through a distance of 1.0 m.through a distance of 1.0 m.
If the force and displacement are notin the exact same direction, then
work = Fd(cos),where is the angle between the forcedirection and displacement direction.
F =40 N
d = 3.0 m
The work done in moving the block 3.0 mThe work done in moving the block 3.0 mto the right by the 40 N force at an angleto the right by the 40 N force at an angle
of 35 to the horizontal is ...of 35 to the horizontal is ...
35
W = Fd(cos W = Fd(cos ) = (40N)(3.0 m)(cos 35) = 98 J) = (40N)(3.0 m)(cos 35) = 98 J
Energy
The ability to cause change or the ability to do work
Joule – the SI unit used to measure energy
EnergyTwo main types of energy:
KineticPotential
Other types of energy include… Thermal Light Sound Electrical Chemical Nuclear
Law of Conservation of Energy
Energy may change from one form to another, but the total amount of energy in a system does not change
MEi = MEf or…
KEi + PEi = KEf + PEf
Law of Conservation of Energy (example)
Fuels store energy in the form of chemical potential energy.
This energy is transformed into heat energy, which is then transformed into kinetic energy.
The energy an object has because of its motion or position; The sum of the kinetic energy and all forms of potential energy in a system; for now we will focus only on GPE
ME = KE +∑PE (real formula) ME – KE + GPE (current use of formula)
NOTE: This is NOT the total energy. Remember that other types also exist in the world… Thermal Light Sound Electrical Chemical Nuclear
Mechanical Energy
Ex: 1…gasoline put into your car (chem. Pot. Energy)…it is heated/combusted and a chemical reaction occurs so that the energy stored in the bonds can be released in the form of heat. Then, the heat energy is used to move parts like pistons, etc (kinetic energy) …which eventually moves your car!
Ex: 2…Candy bar has chemical potential energy…you eat it…your body digests it, meaning it breaks down the food – even breaking the bonds and releasing energy. Your body uses the energy to move (kinetic energy)!
Kinetic energy
Energy in the form of motionKinetic energy = ½ x mass x velocity2
KE = ½mv2
Work - Energy TheoremNet work = change in KE Wnet = ΔKE (“change in” means final minus initial)Wnet = KEf – KEi
When you combine the kinetic energy formula and the work energy theorem…you get
Wnet = (½ mv2)f – (½ mv2)i
Potential Energy
Energy stored in a motionless object, giving it the potential to cause change
3 Types of Potential EnergyElastic Potential Energy – Energy stored by
things that stretch or compress (springs, elastic, rubberbands)
Potential EnergyPotential Energyenergy of position or conditionenergy of position or condition
elastic potential energyelastic potential energy
PEPEee = ½ = ½ kxkx22
k – elastic constant in N/mk – elastic constant in N/m x - elongation or compression in mx - elongation or compression in m PEPEee – elastic potential energy in – elastic potential energy in JJ
Click Click here to investigate elastic constants. to investigate elastic constants.
Chemical Potential Energy - energy stored in chemical bonds between atoms (Snickers bar, food, even gasoline)
Gravitational Potential Energy – energy stored by things that are above Earth (book sitting on shelf, person standing on a cliff, rollercoaster perched at the top of a hill)
Gravitational Potential Energy
GPE = mass x acceleration due to gravity x height
GPE = mgh
Be aware that U is the general variable used for all types of potential energy in upper level physics…different types are denoted by subscripts on the U.
Ug = mgh
Example Problem 1
A 50 kg boy and his 100 kg father went jogging. Both ran at a rate of 5 m/s. Who had more kinetic energy? Show your work and explain.
Example Problem - answer
KE = ½mv2
Boy…
KE = ½(50 kg)(5 m/s)2
KE = 625 JDad…
KE = ½(100 kg)(5 m/s)2
KE = 1250 J
Dad had more Kinetic energy because his mass was greater.
Example Problem 2
What is the potential energy of a 10 N book that is placed on a shelf that is 2.5 meters high?
Example Problem 2 - answer
GPE = mghGPE = (10 N) (2.5m)GPE = 25 JRemember that weight = mg
and that the force provided is weight.
NOTE: you may want to change your variable for weight to Fg.