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

We could use the acceleration to We could use the acceleration to determine information about velocity determine information about velocity or displacementor displacement• Did 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 We will now look at work and power in relation to motionin relation 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 everyday definition of “work” and the one that we use in physics are the one that we use in physics are quite different from each otherquite different 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 Although it is possible that you are doing the physics definition of work doing the physics definition of work while at your job, it is not always the while at your job, it is not always the casecase

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

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

PHYSICS DEFINITIONPHYSICS DEFINITION• Work happens when a force causes Work happens when a force causes

an object to move through a an object to move through a displacementdisplacement

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

WorkWork

There are three key ingredients to workThere are three key ingredients to work• ForceForce• DisplacementDisplacement• CauseCause

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 done “work” on an object, there must be a displacement and the force must be a displacement and the force must causecause the displacement the 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 life• A horse pulling a plow through a fieldA horse pulling a plow through a field• A person pushing a shopping cartA person pushing a shopping cart• A student lifting a backpack onto her shoulderA student lifting a backpack onto her shoulder• A 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 – Exerting force in a way that makes a change in the world.makes a change in the world.• Throwing a rock is Throwing a rock is workwork: you’re exerting : you’re exerting

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

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

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

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

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

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

a force that causes a displacement”:a force 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). As we did with Newtons (which are meters). As we did with Newtons (which are kg m/skg m/s22), we will “define” the Newton-meter ), we will “define” the Newton-meter to be a new unit. We’ll call this unit the to be a new unit. 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 Example: 1 joule = work done to lift a ¼ lb hamburger (1 N) 1 meterlift a ¼ lb hamburger (1 N) 1 meter

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

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

between the force and the between the force and the displacementdisplacement

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 . The force vector and the displacement vector are in force vector and the displacement vector are in the same direction, therefore the angle between the same direction, therefore the angle between F and d is 0 degreesF 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 an object which is displaced upon an object which is displaced rightward (@ 0rightward (@ 0°)°) . The force vector and . The force vector and the displacement vector are in the the displacement vector are in the opposite direction, therefore the angle 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 an object as it is displaced rightward upon an object as it is displaced rightward (@ 0(@ 0°)°) . The force vector and the . The force vector and the displacement vector are at a right angle to displacement vector are at a right angle to each other, therefore the angle between F each other, therefore the angle between F and d is 90 degreesand 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 Consider scenario C from the previous slideslide

The situation is similar to a waiter who The situation is similar to a waiter who carried a tray full of meals with one arm carried a tray full of meals with one arm (F=20N) straight across a room (d=10m) (F=20N) straight across a room (d=10m) at constant speedat 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 to On occasion, a force acts upon a moving object to

hinder a displacementhinder 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 A baseball player sliding to a stop on the infield

dirtdirt 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 If you substitute the numerical values into the work equation, you are left with a the work equation, you are left with a negative answernegative answer

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 The 10 m displacement is hindered by a 40

N force causing -400 J worth of workN force causing -400 J worth of work This will be an important concept a little This will be an important concept a little

laterlater

Example of WorkExample of Work

You are pushing a very heavy stone You are pushing a very heavy stone block (200 kg) across the floor. You block (200 kg) across the floor. You are exerting 620 N of force on the are exerting 620 N of force on the stone, and push it a total distance of stone, and push it a total distance of 20 m in 1 direction before you get 20 m in 1 direction before you get tired and stop.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 meters. How much work did he do?did he 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 Caitlin pushes and pushes on a loaded shopping cart for 2 hours loaded shopping cart for 2 hours with 100 N of force. The with 100 N of force. The shopping cart does not move. shopping cart does not move. How much work did Caitlin do?How much work did Caitlin do?

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

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

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

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

Because of gravity:Because of gravity:• Gravity always pulls down with a force equal to Gravity always pulls down with a force equal to

m*am*agg, where m is the mass, and a, where 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 that much force to

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

force of (280 kg)(9.8 m/sforce of (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 2,744 N

of force to lift the barbell at all.of force to lift the barbell at all.• If that If that minimumminimum force is used, the work done force is used, the work done

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

Questions???Questions???