Introduction to WorkIntroduction to Work

Where we have beenWhere we have been

Previously we used Newton’s Laws to Previously we used Newton’s Laws to analyze motion of objectsanalyze motion of objects

Force and mass information were used to Force and mass information were used to determine acceleration of an object determine acceleration of an object (F=ma)(F=ma)

We could use the acceleration to We could use the acceleration to determine information about velocity or determine information about velocity or displacementdisplacementDid the object speed up or slow down?Did the object speed up or slow down?How far did the object travel?How far did the object travel?

Where we are goingWhere we are going

Now we will take a new approach to Now we will take a new approach to looking at motionlooking at motion

We will now look at work and power in We will now look at work and power in relation to motionrelation to motion

Today we will focus on “work”Today we will focus on “work”

Definition of “work”Definition of “work”

The everyday definition of “work” and the The everyday definition of “work” and the one that we use in physics are quite one that we use in physics are quite different from each otherdifferent from each other

When most people think about “work”, When most people think about “work”, they think of the job that they havethey think of the job that they have

Although it is possible that you are doing Although it is possible that you are doing the physics definition of work while at your the physics definition of work while at your job, it is not always the casejob, it is not always the case

Physics Definition of “Work”Physics Definition of “Work”

Like so many other things in physics, we have to Like so many other things in physics, we have to use an exact definition to really explain what use an exact definition to really explain what “work” is“work” is

PHYSICS DEFINITIONPHYSICS DEFINITIONWork happens when a force causes an Work happens when a force causes an

object to move through a displacementobject to move through a displacement

When a force acts upon an object to cause a When a force acts upon an object to cause a displacement of the object, it is said that WORK displacement of the object, it is said that WORK has been done upon the objecthas been done upon the object

WorkWork

There are three key ingredients to workThere are three key ingredients to workForceForceDisplacementDisplacementCauseCause

In order for a force to qualify as having In order for a force to qualify as having done “work” on an object, there must be a done “work” on an object, there must be a displacement and the force must displacement and the force must causecause the displacementthe displacement

Everyday Examples of “Work”Everyday Examples of “Work”

There are several good examples of work There are several good examples of work which can be observed in everyday lifewhich can be observed in everyday lifeA horse pulling a plow through a fieldA horse pulling a plow through a fieldA person pushing a shopping cartA person pushing a shopping cartA student lifting a backpack onto her shoulderA student lifting a backpack onto her shoulderA weightlifter lifting a barbell above his headA weightlifter lifting a barbell above his head

In each case described here there is a In each case described here there is a force exerted upon an object to cause that force exerted upon an object to cause that object to be displacedobject to be displaced

WorkWork

WorkWork – Exerting force in a way that makes – Exerting force in a way that makes a change in the world.a change in the world.Throwing a rock is Throwing a rock is workwork: you’re exerting a : you’re exerting a

force, and the rock’s location changes (i.e. force, and the rock’s location changes (i.e. “the world has been changed”)“the world has been changed”)

Pushing on a brick wall is Pushing on a brick wall is notnot workwork: you’re : you’re exerting a force, but “the world doesn’t exerting a force, but “the world doesn’t change” (the wall’s position doesn’t change).change” (the wall’s position doesn’t change).

WorkWork So exerting force alone isn’t enough. You So exerting force alone isn’t enough. You

have to both have to both exert a forceexert a force, and , and make a make a changechange..

If you’re not exerting a force, you’re not doing If you’re not exerting a force, you’re not doing work.work.

Example: Example: Throwing a ball.Throwing a ball. While you are “throwing the ball” (as opposed to just While you are “throwing the ball” (as opposed to just

holding it) you are exerting a force on the ball. And holding it) you are exerting a force on the ball. And the ball is moving. So you’re doing the ball is moving. So you’re doing workwork..

After the ball leaves your hand, you are no longer After the ball leaves your hand, you are no longer exerting force. The ball is still moving, but you’re no exerting force. The ball is still moving, but you’re no longer doing longer doing work.work.

WorkWork So, mathematically, we define So, mathematically, we define workwork as “exerting a force as “exerting a force

that causes a displacement”:that causes a displacement”:

(Work) = (Force exerted) (Displacement of object) (cos (Work) = (Force exerted) (Displacement of object) (cos ΘΘ))

oror

W = F*d*cosW = F*d*cosΘΘ

WW = Work done (J) = Work done (J) FF = Force exerted on object (N) = Force exerted on object (N)dd = Displacement of object (m) = Displacement of object (m)ΘΘ = Angle between the force and the = Angle between the force and the

displacementdisplacement

New Unit!New Unit!

The units for The units for workwork are Nm (Newtons are Nm (Newtons × meters). × meters). As we did with Newtons (which are kg m/sAs we did with Newtons (which are kg m/s22), we ), we will “define” the Newton-meter to be a new unit. will “define” the Newton-meter to be a new unit. We’ll call this unit the We’ll call this unit the JouleJoule..

Abbreviation for Joule:Abbreviation for Joule: JJ So, 1 Nm = 1 JSo, 1 Nm = 1 J

Example: 1 joule = work done to lift a Example: 1 joule = work done to lift a ¼ lb hamburger (1 N) 1 meter¼ lb hamburger (1 N) 1 meter

Defining Defining ΘΘ – “the angle” – “the angle”

This is a very specific angleThis is a very specific angleNot just “any” angle - It is the angle Not just “any” angle - It is the angle

between the force and the displacementbetween the force and the displacement Scenario A: A force acts rightward (@ 0Scenario A: A force acts rightward (@ 0°)°) upon upon

an object as it is displaced rightward (@ 0an object as it is displaced rightward (@ 0°)°) . . The force vector and the displacement vector The force vector and the displacement vector are in the same direction, therefore the angle are in the same direction, therefore the angle between F and d is 0 degreesbetween F and d is 0 degrees

F

d

Θ = 0 degrees

0° - 0° = 0°

Subtract the smaller angle from the larger angle to determine the angle “between” the vectors

Defining Defining ΘΘ – “the angle” – “the angle”

Scenario B: A force acts leftward (@ 180Scenario B: A force acts leftward (@ 180°)°) upon upon an object which is displaced rightward (@ 0an object which is displaced rightward (@ 0°)°) . . The force vector and the displacement vector The force vector and the displacement vector are in the opposite direction, therefore the angle are in the opposite direction, therefore the angle between F and d is 180 degreesbetween F and d is 180 degrees

F

d

Θ = 180 degrees180° - 0° = 180°

Subtract the smaller angle from the larger angle to determine the angle “between” the vectors

Defining Defining ΘΘ – “the angle” – “the angle”

Scenario C: A force acts upward (@ 90Scenario C: A force acts upward (@ 90°)°) upon upon an object as it is displaced rightward (@ 0an object as it is displaced rightward (@ 0°)°) . . The force vector and the displacement vector The force vector and the displacement vector are at a right angle to each other, therefore the are at a right angle to each other, therefore the angle between F and d is 90 degreesangle between F and d is 90 degrees

F

d

Θ = 90 degrees90° - 0° = 90°

Subtract the smaller angle from the larger angle to determine the angle “between” the vectors

To Do Work, To Do Work, Forces must CAUSE DisplacementForces must CAUSE Displacement

Consider scenario C from the previous slideConsider scenario C from the previous slide The situation is similar to a waiter who carried a The situation is similar to a waiter who carried a

tray full of meals with one arm (F=20N) straight tray full of meals with one arm (F=20N) straight across a room (d=10m) at constant speedacross a room (d=10m) at constant speed

W = F*d*cosW = F*d*cosΘΘ W = (20N)(10m)(cos 90°)W = (20N)(10m)(cos 90°) W = 0JW = 0J The waiter does not do work The waiter does not do work

upon the trayupon the tray as he carries it as he carries it across the roomacross the room

The Meaning of Negative WorkThe Meaning of Negative Work On occasion, a force acts upon a moving object On occasion, a force acts upon a moving object

to hinder a displacementto hinder a displacement A car skidding to a stop on a roadway surfaceA car skidding to a stop on a roadway surface A baseball player sliding to a stop on the infield dirtA baseball player sliding to a stop on the infield dirt

In such cases the force acts in the direction In such cases the force acts in the direction opposite the objects motion in order to slow it opposite the objects motion in order to slow it downdown

The force doesn’t cause the displacement, but it The force doesn’t cause the displacement, but it hindershinders the displacement the displacement

This is commonly called This is commonly called negative worknegative work

The Meaning of Negative WorkThe Meaning of Negative Work

If you substitute the numerical values into the If you substitute the numerical values into the work equation, you are left with a negative work equation, you are left with a negative answeranswer

W = F*d*cosW = F*d*cosΘΘ W = (40 N)(10 m)(cos 180°)W = (40 N)(10 m)(cos 180°) W = (40 N)(10 m)(-1)W = (40 N)(10 m)(-1) W = -400 JW = -400 J The 10 m displacement is hindered by a 40 N The 10 m displacement is hindered by a 40 N

force causing -400 J worth of workforce causing -400 J worth of work This will be an important concept a little laterThis will be an important concept a little later

Example of WorkExample of Work

You are pushing a very heavy stone block You are pushing a very heavy stone block (200 kg) across the floor. You are exerting (200 kg) across the floor. You are exerting 620 N of force on the stone, and push it a 620 N of force on the stone, and push it a total distance of 20 m in 1 direction before total distance of 20 m in 1 direction before you get tired and stop.you get tired and stop.

How much work did you just do?How much work did you just do?

W = (620 N)(20 m) = 12,400 JW = (620 N)(20 m) = 12,400 J

Work ProblemsWork ProblemsAustin lifts a 200 N box 4 Austin lifts a 200 N box 4 meters. How much work did he meters. How much work did he do?do?

W = (200N)(4m)(cos 0W = (200N)(4m)(cos 0°)°)

W = (200N)(4m)(1)W = (200N)(4m)(1)

W = 800 JW = 800 J

Work ProblemsWork ProblemsCaitlin pushes and pushes on a loaded Caitlin pushes and pushes on a loaded shopping cart for 2 hours with 100 N of shopping cart for 2 hours with 100 N of force. The shopping cart does not force. The shopping cart does not move. How much work did Caitlin do?move. How much work did Caitlin do?

Chase lifts a 100 kg (220 lbs) barbell 2 Chase lifts a 100 kg (220 lbs) barbell 2 meters. How much work did he do?meters. How much work did he do?

Work Done By “Lifting” SomethingWork Done By “Lifting” Something Notice that when we were pushing something Notice that when we were pushing something

along the ground, the work done along the ground, the work done didn’tdidn’t depend depend on the mass.on the mass.

Lifting up something does do work that depends Lifting up something does do work that depends on mass.on mass.

Because of gravity:Because of gravity: Gravity always pulls down with a force equal to m*aGravity always pulls down with a force equal to m*agg, ,

where m is the mass, and awhere m is the mass, and agg = 9.8 m/s = 9.8 m/s22.. So we must exert So we must exert at leastat least that much force to lift that much force to lift

something.something. The more mass something has, The more mass something has,

the more work required to lift it.the more work required to lift it.

Work Done By “Lifting” Work Done By “Lifting” Something Something

Example: Example: A weightlifter lifts a barbell with a A weightlifter lifts a barbell with a mass of 280 kg a total of 2 meters off the floor. mass of 280 kg a total of 2 meters off the floor. What is the What is the minimumminimum amount of work the amount of work the weightlifter did?weightlifter did? The barbell is “pulled” down by gravity with a force of The barbell is “pulled” down by gravity with a force of

(280 kg)(9.8 m/s(280 kg)(9.8 m/s22) = 2,744 N) = 2,744 N So the weightlifter must exert So the weightlifter must exert at leastat least 2,744 N of 2,744 N of

force to lift the barbell at all.force to lift the barbell at all. If that If that minimumminimum force is used, the work done will be: force is used, the work done will be:

W = (2,744 N)(2 m) = 5,488 JW = (2,744 N)(2 m) = 5,488 J

Questions???Questions???