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Unit 7:Unit 7:Work and EnergyWork and Energy
Section A: WorkSection A: Work
Corresponding Book Sections:Corresponding Book Sections: 7.17.1
PA Assessment Anchors:PA Assessment Anchors: S11.C.3.1S11.C.3.1
What is “Work” ?What is “Work” ?
Work occurs when three conditions are met:Work occurs when three conditions are met:1.1. A force is applied to an objectA force is applied to an object
2.2. The object moves The object moves
3.3. At least At least somesome of the force being applied is in of the force being applied is in the direction of the motion of the objectthe direction of the motion of the object
General Equation for General Equation for WorkWork
W = FdUnit: Joule (J)
Practice ProblemPractice Problem
Find the work necessary to accomplish what Find the work necessary to accomplish what is shown in the picture.is shown in the picture.
m = 98 kg
Am I doing work?Am I doing work?
Let’s say I go shopping at Weis:Let’s say I go shopping at Weis: Picking out items from the shelfPicking out items from the shelf
Placing the groceries on the beltPlacing the groceries on the belt
Holding the bag of groceriesHolding the bag of groceries
Carrying the bag of groceries to my carCarrying the bag of groceries to my car
Work, version 2.0Work, version 2.0
What happens in this situation?What happens in this situation?
Does our equation for work “work” ?Does our equation for work “work” ?
The best equation for The best equation for WorkWork
W = Fd cos W = Fd cos θθ
Practice ProblemPractice Problem
Find the work done by gravity in this Find the work done by gravity in this situation:situation:
mass = 4970 kg
distance = 5 m
Positive, Negative, Zero Positive, Negative, Zero WorkWork
Work is positiveif the force has acomponent in the direction of motion
Work is zeroif the force has no component in the direction of motion
Work is negativeif the force has acomponent oppositethe direction of motion
Finding Total WorkFinding Total Work
Work can be added together, just like forces:Work can be added together, just like forces:
WWtotaltotal = W = W11 + W + W22 + W + W33 + … = ∑W + … = ∑W
WWtotaltotal = F = Ftotaltotald cos d cos θθSum of the Work
Practice ProblemPractice Problem
Find the work done in this situation:Find the work done in this situation:
Section B: Work & Section B: Work & EnergyEnergy
Corresponding Book Sections:Corresponding Book Sections: 7.27.2
PA Assessment Anchors:PA Assessment Anchors: S11.C.3.1S11.C.3.1
Work-Energy TheoremWork-Energy Theorem
The total work done on an object is equal to The total work done on an object is equal to the change in its kinetic energy.the change in its kinetic energy.
WWtotaltotal = = ΔK =ΔK =
1
2mv f
2 1
2mv i
2
Practice ProblemPractice Problem
A truck moving at 15 m/s has a kinetic energy A truck moving at 15 m/s has a kinetic energy of 140,000 J. What is the mass of the truck?of 140,000 J. What is the mass of the truck?
Practice Problem #2Practice Problem #2
How much work is required for a 74 kg How much work is required for a 74 kg sprinkler to accelerate from rest to 2.2m/s ?sprinkler to accelerate from rest to 2.2m/s ?
Pratice Problem #3Pratice Problem #3
A boy pulls a sled as shown. Find the work A boy pulls a sled as shown. Find the work done by the boy and the final speed of the done by the boy and the final speed of the sled after it moves 2 m, assuming initial sled after it moves 2 m, assuming initial speed of 0.5 m/s.speed of 0.5 m/s.
Let’s take another look Let’s take another look at PP#3at PP#3
Could we solve this using the kinematics Could we solve this using the kinematics equations and Newton’s 2nd Law?equations and Newton’s 2nd Law?
The answer is YES.The answer is YES.
Should we try?Should we try?
Work on a SpringWork on a Spring
““k” is referred to a the spring constantk” is referred to a the spring constant Remember…from the last unit…Remember…from the last unit…
W 1
2kx 2
Practice ProblemPractice Problem
In the chase scene from In the chase scene from Toy StoryToy Story the Slinky the Slinky Dog is stretched 1m, which requires 2J of Dog is stretched 1m, which requires 2J of work. Find the spring constant.work. Find the spring constant.
Practice Problem, Part 2Practice Problem, Part 2
How much work is required to stretch the dog How much work is required to stretch the dog from 1m to 2m?from 1m to 2m?
PowerPower
A measure of how quickly work is doneA measure of how quickly work is done
Units: Units: Joule / second: J/s Joule / second: J/s Watt: W (preferred unit)Watt: W (preferred unit)
P W
t or P = Fv
Typical values of powerTypical values of power
Practice Problem #1Practice Problem #1
Calculate the power needed to accelerate Calculate the power needed to accelerate from 13.4 m/s to 17.9 m/s in 3.00 s if your car from 13.4 m/s to 17.9 m/s in 3.00 s if your car has a mass of 1,300 kg.has a mass of 1,300 kg.
Practice Problem #2Practice Problem #2
What is the average power needed to What is the average power needed to accelerate a 950 kg car from 0 m/s to 26.8 accelerate a 950 kg car from 0 m/s to 26.8 m/s (60 mph) in 6 s. Ignore friction.m/s (60 mph) in 6 s. Ignore friction.
Section C: EnergySection C: Energy
Corresponding Book Sections:Corresponding Book Sections: 8.1, 8.2, 8.38.1, 8.2, 8.3
PA Assessment Anchors:PA Assessment Anchors: S11.C.3.1S11.C.3.1
Two main types of Two main types of energyenergy
Kinetic EnergyKinetic Energy Energy an object has while it’s in motionEnergy an object has while it’s in motion
Potential EnergyPotential Energy Energy an object has while it’s not movingEnergy an object has while it’s not moving
Kinetic EnergyKinetic Energy
Energy an object has while in motionEnergy an object has while in motion
Unit: Joule (J)Unit: Joule (J)
KE 1
2mv 2
Practice Problem #1Practice Problem #1
A truck moving at 15 m/s has KE of 14,000 J. A truck moving at 15 m/s has KE of 14,000 J. Find the mass.Find the mass.
Potential EnergyPotential Energy
Energy available to be converted to kinetic Energy available to be converted to kinetic energy (energy of non-motion)energy (energy of non-motion)
Unit: Joule (J)Unit: Joule (J)
Gravitational Potential Gravitational Potential EnergyEnergy
Your book uses “Your book uses “U”U” to represent Potential to represent Potential Energy -- I’ll use “PE”Energy -- I’ll use “PE”
PE mgh
Two types of forces:Two types of forces:
ConservativeConservative The work done by a conservative force is stored The work done by a conservative force is stored
as energy that can be released lateras energy that can be released later
Example: Lifting a box from the floorExample: Lifting a box from the floor As you lift the box, you exert force and do workAs you lift the box, you exert force and do work If you let go of the box, gravity exerts a force and If you let go of the box, gravity exerts a force and
does workdoes work
Two types of forces:Two types of forces:
NonconservativeNonconservative The work done by a nonconservative force The work done by a nonconservative force
cannot be recovered later as KEcannot be recovered later as KE
Example: Sliding box across floorExample: Sliding box across floor The work done to slide the box can’t be restored The work done to slide the box can’t be restored
as KEas KE Instead, the energy changes forms into heatInstead, the energy changes forms into heat
Examples of Examples of Conservative & Conservative &
Nonconservative ForcesNonconservative Forces ConservativeConservative
SpringsSprings GravityGravity
NonconservativeNonconservative FrictionFriction TensionTension
Sections D & E: Sections D & E: MomentumMomentum
Corresponding Book Sections:Corresponding Book Sections: 9.1, 9.2, 9.39.1, 9.2, 9.3
PA Assessment Anchors:PA Assessment Anchors: S11.C.3.1S11.C.3.1
What is momentum?What is momentum?
Linear momentumLinear momentum The product of an object’s mass and velocityThe product of an object’s mass and velocity
Units: kg m/sUnits: kg m/s
pmv
So, this means…So, this means…
If mass increases, momentum increasesIf mass increases, momentum increases
If speed increases, momentum increasesIf speed increases, momentum increases
Vice-versa if speed or mass decreaseVice-versa if speed or mass decrease
Sample Problem #1Sample Problem #1
A 1180 kg car drives along a street at 13.4 A 1180 kg car drives along a street at 13.4 m/s. Find the momentum.m/s. Find the momentum.
Sample Problem #2Sample Problem #2
A major league pitcher can throw a 0.142 kg A major league pitcher can throw a 0.142 kg baseball at 45.1 m/s. Find the momentum.baseball at 45.1 m/s. Find the momentum.
Change in MomentumChange in Momentum
Just like the change in speed, distance, etc.Just like the change in speed, distance, etc. Final - initialFinal - initial
Equation:Equation:
pp f pi
Adding momentumAdding momentum
Since momentum is a vector quantity, it will Since momentum is a vector quantity, it will add like vectors addadd like vectors add
We’ll keep it simple and say that:We’ll keep it simple and say that:
ptotal p1 p2 p3 ...
or
ptotal p
Practice Problem #1Practice Problem #1
Two 4.00 kg ducks and 9.00 kg goose swim Two 4.00 kg ducks and 9.00 kg goose swim toward some bread that was thrown in the toward some bread that was thrown in the pond. The ducks each have a speed of 1.10 pond. The ducks each have a speed of 1.10 m/s while the goose has a speed of 1.30 m/s. m/s while the goose has a speed of 1.30 m/s. Find the total momentum.Find the total momentum.
Momentum and Momentum and Newton’s 2nd LawNewton’s 2nd Law
Remember that Newton’s 2nd Law is Remember that Newton’s 2nd Law is ƩƩF=maF=ma
We can relate this to momentum:We can relate this to momentum:
F pt
ImpulseImpulse
Relationship between applied force and timeRelationship between applied force and time
I Favgt
What is impulse?What is impulse?
Vector quantityVector quantity
Units: kg m/sUnits: kg m/s
Points in same direction as average forcePoints in same direction as average force
Another way to Another way to represent Impulse:represent Impulse:
If:If:
Then:Then:
And if:And if:
Then: Then:
F pt
Ft p
I Favgt
I p
Practice Problem #1Practice Problem #1
A 0.144 kg baseball is moving toward home A 0.144 kg baseball is moving toward home plate at 43.0 m/s when it is hit. The bat plate at 43.0 m/s when it is hit. The bat exerts a force of 6,500 N for 0.0013s. Find exerts a force of 6,500 N for 0.0013s. Find the final speed of the ball.the final speed of the ball.
Practice Problem #2Practice Problem #2
After winning a prize on a game show, a 72 After winning a prize on a game show, a 72 kg contestant jumps for joy with a speed of kg contestant jumps for joy with a speed of 2.1 m/s. Find the impulse experienced.2.1 m/s. Find the impulse experienced.
Rain vs. HailRain vs. Hail
As you’re holding an As you’re holding an umbrella, does it umbrella, does it require more force, less require more force, less force, or the same force force, or the same force to hold up the umbrella to hold up the umbrella if the raindrops turn to if the raindrops turn to hail?hail?
Conservation of Conservation of momentummomentum
If the net force acting on an object is zero, its If the net force acting on an object is zero, its momentum is conservedmomentum is conserved
In other words, the momentum before a In other words, the momentum before a collision is the same as the momentum after collision is the same as the momentum after a collisiona collision
ppff = p = pii
Practice Problem #1Practice Problem #1
A honeybee with a mass of 0.150g lands on a A honeybee with a mass of 0.150g lands on a 4.75g popsicle stick. The bee runs toward the 4.75g popsicle stick. The bee runs toward the opposite end of the stick. The stick moves opposite end of the stick. The stick moves with a speed of 0.120 cm/s relative to the with a speed of 0.120 cm/s relative to the water. Find the speed of the bee.water. Find the speed of the bee.
Elastic vs. Inelastic Elastic vs. Inelastic CollsionsCollsions
ElasticElastic Momentum is Momentum is
conservedconserved Kinetic energy is Kinetic energy is
conservedconserved
In other words:In other words: Objects bounce off Objects bounce off
each othereach other
InelasticInelastic Momentum is Momentum is
conservedconserved Kinetic Energy is NOT Kinetic Energy is NOT
conservedconserved
In other words:In other words: Objects either stick Objects either stick
or stopor stop