Unit 7: Work and Energy. Section A: Work Corresponding Book Sections: Corresponding Book Sections:...

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


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


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


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


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


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


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.


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


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


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


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


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


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.


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


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

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