Introduction to Work

1. Introduction to Work

2. Where we have been • 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) • We could use the acceleration to determine information about velocity or displacement • Did the object speed up or slow down? • How far did the object travel?

3. Where we are going • Now we will take a new approach to looking at motion • We will now look at work and power in relation to motion • Today we will focus on “work”

4. Definition of “work” • 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 • Although it is possible that you are doing the physics definition of work while at your job, it is not always the case

5. Physics Definition of “Work” • Like so many other things in physics, we have to use an exact definition to really explain what “work” is • PHYSICS DEFINITION • 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

6. Work • There are three key ingredients to work • Force • Displacement • 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

7. Everyday Examples of “Work” • There are several good examples of work which can be observed in everyday life • A horse pulling a plow through a field • A person pushing a shopping cart • A student lifting a backpack onto her shoulder • 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

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

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

10. Work • 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) d = Displacement of object (m)

11. New Unit! • The units for work are Nm (newton × meter). As we did with newton (which are kg m/s2), we will “define” the newton-meter to be a new unit. We’ll call this unit the joule. • Abbreviation for joule:J • So, 1 Nm = 1 J • Example: 1 joule = work done to lift a ¼ lb hamburger (1 N) 1 meter

12. 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 opposite directions – the work done is NEGATIVE • If the force and displacement are perpendicular – the work done is equal to ZERO

13. 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 • W = F*d • W = (20N)(10m) **but the force and displacement are perpendicular!** • W = 0J • The waiter does not do work upon the tray as he carries it across the room

14. The Meaning of Negative Work • On occasion, a force acts upon a moving object to hinder a displacement • A car skidding to a stop on a roadway surface • 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 • The force doesn’t cause the displacement, but it opposes the displacement • This results in negative work

15. 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. • How much work did you just do? • W = (620 N)(20 m) = 12,400 J

16. 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

17. Work Problems 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?

18. Work Done By “Lifting” Something • 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. • Because of gravity: • Gravity always pulls down with a force equal to m*ag, where m is the mass, and ag = 9.8 m/s2. • So we must exert at least that much force to lift something. • The more mass something has, the more work required to lift it.

19. 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? • 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

20. Questions???