Introduction to Work

Where we have been Previously we used Newton’s Laws to analyze motion of objects Previously we used Newton’s Laws to analyze motion of objects Force and mass information were used to determine acceleration of an object (F=ma) Force and mass information were used to determine acceleration of an object (F=ma) We could use the acceleration to determine information about velocity or displacement We could use the acceleration to determine information about velocity or 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 going Now we will take a new approach to looking at motion Now we will take a new approach to looking at motion We will now look at work and power in relation to motion We will now look at work and power in relation to motion Today we will focus on “work” Today we will focus on “work”

Definition of “work” The everyday definition of “work” and the one that we use in physics are quite different from each other The everyday definition of “work” and the one that we use in physics are quite different from each other When most people think about “work”, they think of the job that they have When most people think about “work”, they think of the job that they have Although it is possible that you are doing the physics definition of work while at your job, it is not always the case Although it is possible that you are doing the physics definition of work while at your job, it is not always the case

Physics Definition of “Work” Like so many other things in physics, we have to use an exact definition to really explain what “work” is Like so many other things in physics, we have to use an exact definition to really explain what “work” is PHYSICS DEFINITION PHYSICS DEFINITION Work happens when a force causes an object to move through a displacement Work happens when a force causes an object to move through a displacement When a force acts upon an object to cause a displacement of the object, it is said that WORK has been done upon the object When a force acts upon an object to cause a displacement of the object, it is said that WORK has been done upon the object

Work There are three key ingredients to work There are three key ingredients to work Force Force Displacement Displacement Cause Cause In order for a force to qualify as having done “work” on an object, there must be a displacement and the force must cause the displacement In order for a force to qualify as having done “work” on an object, there must be a displacement and the force must cause the displacement

Everyday Examples of “Work” There are several good examples of work which can be observed in everyday life There are several good examples of work which can be observed in everyday life A horse pulling a plow through a field A horse pulling a plow through a field A person pushing a shopping cart A person pushing a shopping cart A student lifting a backpack onto her shoulder A student lifting a backpack onto her shoulder A weightlifter lifting a barbell above his head A weightlifter lifting a barbell above his head In each case described here there is a force exerted upon an object to cause that object to be displaced In each case described here there is a force exerted upon an object to cause that object to be displaced

Work Work – Exerting force in a way that makes a change in the world. Work – Exerting force in a way that makes a change in the world. Throwing a rock is work: you’re exerting a force, and the rock’s location changes (i.e. “the world has been changed”) Throwing a rock is work: you’re exerting a force, and the rock’s location changes (i.e. “the world has been changed”) Pushing on a brick wall is not work: you’re exerting a force, but “the world doesn’t change” (the wall’s position doesn’t change). Pushing on a brick wall is not work: you’re exerting a force, but “the world doesn’t change” (the wall’s position doesn’t change).

Work So exerting force alone isn’t enough. You have to both exert a force, and make a change. So exerting force alone isn’t enough. You have to both exert a force, and make a change. If you’re not exerting a force, you’re not doing work. If you’re not exerting a force, you’re not doing work. Example: Throwing a ball. Example: Throwing a ball. While you are “throwing the ball” (as opposed to just holding it) you are exerting a force on the ball. And the ball is moving. So you’re doing work. While you are “throwing the ball” (as opposed to just holding it) you are exerting a force on the ball. And the ball is moving. So you’re doing work. After the ball leaves your hand, you are no longer exerting force. The ball is still moving, but you’re no longer doing work. After the ball leaves your hand, you are no longer exerting force. The ball is still moving, but you’re no longer doing work.

Work So, mathematically, we define work as “exerting a force that causes a displacement”: So, mathematically, we define work as “exerting a force that causes a displacement”: (Work) = (Force exerted) (Displacement of object) or W = F*d W = Work done (J) F = Force exerted on object (N) F = Force exerted on object (N) d = Displacement of object (m)

New Unit! The units for work are Nm (newton × meter). As we did with newton (which are kg m/s 2 ), we will “define” the newton-meter to be a new unit. We’ll call this unit the joule. The units for work are Nm (newton × meter). As we did with newton (which are kg m/s 2 ), we will “define” the newton-meter to be a new unit. We’ll call this unit the joule. Abbreviation for joule: J Abbreviation for joule: J So, 1 Nm = 1 J So, 1 Nm = 1 J Example: 1 joule = work done to lift a ¼ lb hamburger (1 N) 1 meter Example: 1 joule = work done to lift a ¼ lb hamburger (1 N) 1 meter

Rules for Work If the force and displacement are in the same direction – the work done is POSITIVE If the force and displacement are in the same direction – the work done is POSITIVE If the force and displacement are in opposite directions – the work done is NEGATIVE If the force and displacement are in opposite directions – the work done is NEGATIVE If the force and displacement are perpendicular – the work done is equal to ZERO If the force and displacement are perpendicular – the work done is equal to ZERO

To Do Work, Forces must CAUSE Displacement The situation is similar to a waiter who carried a tray full of meals with one arm (F=20N) straight across a room (d=10m) at constant speed The situation is similar to a waiter who carried a tray full of meals with one arm (F=20N) straight across a room (d=10m) at constant speed W = F*d W = F*d W = (20N)(10m) **but the force and displacement are perpendicular!** W = (20N)(10m) **but the force and displacement are perpendicular!** W = 0J W = 0J The waiter does not do work The waiter does not do work upon the tray as he carries it across the room

The Meaning of Negative Work On occasion, a force acts upon a moving object to hinder a displacement On occasion, a force acts upon a moving object to hinder a displacement A car skidding to a stop on a roadway surface A car skidding to a stop on a roadway surface A baseball player sliding to a stop on the infield dirt A baseball player sliding to a stop on the infield dirt In such cases the force acts in the direction opposite the objects motion in order to slow it down In such cases the force acts in the direction opposite the objects motion in order to slow it down The force doesn’t cause the displacement, but it opposes the displacement The force doesn’t cause the displacement, but it opposes the displacement This results in negative work This results in negative work

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

Work Problems Austin lifts a 200 N box 4 meters. How much work did he do? W = (200N)(4m) W = (200N)(4m) W = 800 J

Caitlin pushes and pushes on a loaded shopping cart for 2 hours with 100 N of force. The shopping cart does not move. How much work did Caitlin do? Chase lifts a 100 kg (220 lbs) barbell 2 meters. How much work did he do?

Work Done By “Lifting” Something Notice that when we were pushing something along the ground, the work done didn’t depend on the mass. Notice that when we were pushing something along the ground, the work done didn’t depend on the mass. Lifting up something does do work that depends on mass. Lifting up something does do work that depends on mass. Because of gravity: Because of gravity: Gravity always pulls down with a force equal to m*a g, where m is the mass, and a g = 9.8 m/s 2. Gravity always pulls down with a force equal to m*a g, where m is the mass, and a g = 9.8 m/s 2. So we must exert at least that much force to lift something. So we must exert at least that much force to lift something. The more mass something has, The more mass something has, the more work required to lift it.

Work Done By “Lifting” Something Example: A weightlifter lifts a barbell with a mass of 280 kg a total of 2 meters off the floor. What is the minimum amount of work the weightlifter did? Example: A weightlifter lifts a barbell with a mass of 280 kg a total of 2 meters off the floor. What is the minimum amount of work the weightlifter did? –The barbell is “pulled” down by gravity with a force of (280 kg)(9.8 m/s2) = 2,744 N –So the weightlifter must exert at least 2,744 N of force to lift the barbell at all. --If that minimum force is used, the work done will be: W = (2,744 N)(2 m) = 5,488 J

Questions???