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.