Power,Power,by definition, isby definition, is

the the time ratetime rate of doing of doing workwork;;or the or the time rate transfertime rate transfer of of energyenergy..

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 when 1.0 J of work1.0 J of work is done or is done or1.0 J of energy is transferred1.0 J of energy is transferred

in a in a time of 1.0 stime of 1.0 s..

Power example

• An 80 kg human walks up a flight of stairs in .22 s that have an altitude gain of 3.75 m. What is the power of the person?

Power Example

• First find the work= force*distance. F=mg 80*9.8=784N

• W=Fd

• 784N*3.75m=2940J

• P=W/t=2940/.22=13363.64W

Work,Work,by definition, is

the product of the the product of the forceforce exerted on exerted onan object and the an object and the distancedistance the object 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.

Work Example

• An intern pushes a 75 kg patient on a 15 kg gurney, producing an accleration of .06m/s2. How much work does the intern do by pushing the patient and gurney through a distance of 2.5 m? Assume there is no friction.

• Find the F= ma 15+75=90 kg* .60 m/s2

• F= ma 90*.6= 54N

• W=Fd= 54*2.5=135J

Graphically, work isGraphically, work isthe area under athe area under a

““Force vs. Displacement” graph.Force vs. Displacement” graph.

displacement, mdisplacement, 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

Example 2:The work done in moving the block 3.0 mExample 2:The 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

Law of Conservation of EnergyLaw of Conservation of Energy““Energy can be neither created nor destroyed.Energy can be neither created nor destroyed.

It may only change forms.”It may only change forms.”

all types of energy before the event all types of energy before the event = = all types of energy after the event all types of energy after the event

Examples:Examples:•A dropped object loses gravitational PE as it gains KE.A dropped object loses gravitational PE as it gains KE.•A block slides across the floor and comes to a stop.A block slides across the floor and comes to a stop.•A compressed spring shoots a ball into the air.A compressed spring shoots a ball into the air.

EnergyEnergythe ability (capacity) to do workthe ability (capacity) to do work

Energy comes in many forms:Energy comes in many forms:mechanical, electrical , magnetic, solar,mechanical, electrical , magnetic, solar,

thermal, chemical, etc...thermal, chemical, etc...

The SI unit of energy is the The SI unit of energy is the JouleJoule..

Energy, like work, is a Energy, like work, is a scalarscalar..

Kinetic EnergyKinetic Energyenergy of motion

All moving objects thatAll moving objects thathave mass have kinetic energy.have mass have kinetic energy.

KE = 1/2 mvKE = 1/2 mv22

mm - mass of the object in - mass of the object in kgkgvv - speed of the object in - speed of the object in m/sm/sKEKE - the kinetic energy in - the kinetic energy in JJ

Energy Example

• 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.

Work-Energy TheoremWork-Energy Theoremthe net work done on an object is

equal to its change in kinetic energy

W KEnet

Potential Energy

• Energy stored in a motionless object, giving it the potential to cause change

• Chemical Potential Energy - energy stored in chemical bonds between atoms (Snickers bar, food, even gasoline)

Potential EnergyPotential Energyenergy of position energy of position

or conditionor condition

Potential EnergyPotential Energyenergy of position or conditionenergy of position or condition

gravitational potential energygravitational potential energy

PEPEgg = mgh = mgh mm - mass of object in - mass of object in kg kg gg - acceleration of gravity in - acceleration of gravity in m/sm/s22

h h - height of object, in - height of object, in mm,, from some arbitrary reference pointfrom some arbitrary reference pointPE PE – gravitational potential energy in – gravitational potential energy in JJ

Example Problem

• What is the potential energy of a 10 N book that is placed on a shelf that is 2.5 meters high?

Example Problem - answer• GPE = mgh• GPE = (10 N) (2.5m)• GPE = 25 J• Remember that weight = mg and

that the force provided is weight.NOTE: you may want to change

your variable for weight to Fg.

Potential EnergyPotential Energyenergy of position or conditionenergy of position or condition

elastic potential energyelastic potential energy

PEPEee = ½ = ½ kxkx22

kk – elastic constant in – elastic constant in N/mN/m xx - elongation or compression in - elongation or compression in mm PEPEee – elastic potential energy in – elastic potential energy in JJ

Click Click here to investigate elastic constants. to investigate elastic constants.

Example

• A spring with a spring constant of 120 N/m is compressed a distance of 2.3 cm. How much potential energy is stored in the spring?

Example

• U= ½ kx2

• U= ½ (120)*(.025)2

• Remember we work in meters!

• U= .032J