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Introduction to Work

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Where we have been Previously we used Newtons Laws to analyze motion of objects Previously we used Newtons 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?

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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

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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

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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

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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

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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

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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: youre exerting a force, and the rocks location changes (i.e. the world has been changed) Throwing a rock is work: youre exerting a force, and the rocks location changes (i.e. the world has been changed) Pushing on a brick wall is not work: youre exerting a force, but the world doesnt change (the walls position doesnt change). Pushing on a brick wall is not work: youre exerting a force, but the world doesnt change (the walls position doesnt change).

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Work So exerting force alone isnt enough. You have to both exert a force, and make a change. So exerting force alone isnt enough. You have to both exert a force, and make a change. If youre not exerting a force, youre not doing work. If youre not exerting a force, youre 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 youre 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 youre doing work. After the ball leaves your hand, you are no longer exerting force. The ball is still moving, but youre no longer doing work. After the ball leaves your hand, you are no longer exerting force. The ball is still moving, but youre no longer doing work.

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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) (cos Θ) or W = F*d*cosΘ W = Work done (J) F = Force exerted on object (N) F = Force exerted on object (N) d = Displacement of object (m) Θ = Angle between the force and the displacement

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New Unit! The units for work are Nm (Newtons × meters). As we did with Newtons (which are kg m/s 2 ), we will define the Newton-meter to be a new unit. Well call this unit the Joule. The units for work are Nm (Newtons × meters). As we did with Newtons (which are kg m/s 2 ), we will define the Newton-meter to be a new unit. Well 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

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Defining Θ – the angle This is a very specific angle This is a very specific angle Not just any angle - It is the angle between the force and the displacement Not just any angle - It is the angle between the force and the displacement Scenario A: A force acts rightward 0°) upon an object as it is displaced rightward 0°). The force vector and the displacement vector are in the same direction, therefore the angle between F and d is 0 degrees Scenario A: A force acts rightward 0°) upon an object as it is displaced rightward 0°). The force vector and the displacement vector are in the same direction, therefore the angle between 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

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Defining Θ – the angle Scenario B: A force acts leftward 180°) upon an object which is displaced rightward 0°). The force vector and the displacement vector are in the opposite direction, therefore the angle between F and d is 180 degrees Scenario B: A force acts leftward 180°) upon an object which is displaced rightward 0°). The force vector and the displacement vector are in the opposite direction, therefore the angle between F and d is 180 degrees F d Θ = 180 degrees 180° - 0° = 180° Subtract the smaller angle from the larger angle to determine the angle between the vectors

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Defining Θ – the angle Scenario C: A force acts upward 90°) upon an object as it is displaced rightward 0°). The force vector and the displacement vector are at a right angle to each other, therefore the angle between F and d is 90 degrees Scenario C: A force acts upward 90°) upon an object as it is displaced rightward 0°). The force vector and the displacement vector are at a right angle to each other, therefore the angle between F and d is 90 degrees F d Θ = 90 degrees 90° - 0° = 90° Subtract the smaller angle from the larger angle to determine the angle between the vectors

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To Do Work, Forces must CAUSE Displacement Consider scenario C from the previous slide Consider scenario C from the previous slide 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*cosΘ W = F*d*cosΘ W = (20N)(10m)(cos 90°) W = (20N)(10m)(cos 90°) 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

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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 doesnt cause the displacement, but it hinders the displacement The force doesnt cause the displacement, but it hinders the displacement This is commonly called negative work This is commonly called negative work

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The Meaning of Negative Work If you substitute the numerical values into the work equation, you are left with a negative answer If you substitute the numerical values into the work equation, you are left with a negative answer W = F*d*cosΘ W = F*d*cosΘ 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 J W = -400 J The 10 m displacement is hindered by a 40 N force causing -400 J worth of work The 10 m displacement is hindered by a 40 N force causing -400 J worth of work This will be an important concept a little later This will be an important concept a little later

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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

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Work Problems Austin lifts a 200 N box 4 meters. How much work did he do? W = (200N)(4m)(cos 0°) W = (200N)(4m)(1) W = 800 J

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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?

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Work Done By Lifting Something Notice that when we were pushing something along the ground, the work done didnt depend on the mass. Notice that when we were pushing something along the ground, the work done didnt 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.

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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/s 2 ) = 2,744 N The barbell is pulled down by gravity with a force of (280 kg)(9.8 m/s 2 ) = 2,744 N So the weightlifter must exert at least 2,744 N of force to lift the barbell at all. 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: If that minimum force is used, the work done will be: W = (2,744 N)(2 m) = 5,488 J

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