power, by definition, is the time rate of doing work; or the time rate transfer of energy. p = w /...
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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