1. Work

2. Based on these examples, how do you define work?
What do you think?
List five examples of things you have done in the last year that you would consider work.
Based on these examples, how do you define work?
When asking students to express their ideas, you might try one of the following methods.
(1) You could ask them to write their answers in their notebook and then discuss them.
(2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups.
The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally.
Likely answers are: homework, babysitting, jobs, studying physics, and so on. After listening and discussing, let the students know that in physics, the definition of work is much more precise and many things that they consider work will not fit that definition. In physics, work produces a change in energy. Work is defined in terms of force and displacement on the next slide.

3. Work
In physics, work is the magnitude of the force (F) times the magnitude of the displacement (d) in the same direction as the force.
W = Fd
Units are sometimes confusing. It would be a good idea to show students that 1 J = 1 N•m = 1 kg•m2/s2 at this time. Give them a chance to figure it out for themselves from the definition of a newton (F=ma). This is important because they will later learn that kinetic energy and potential energy are measured in joules as well, and the equations lead to kg•m2/s2. Students need to understand the fundamental SI units behind all of the derived units such as newtons, joules, watts and so on.

4. Units of Work force x distance = work N x m = N·m
1 N·m = 1 joule = 1 J
You perform ≈1 J of work when you lift a 100-gram apple from the floor to your table top

5. Work
Pushing this car is work because F and d are in the same direction.
Why aren’t the following tasks considered work?
A student holds a heavy chair at arm’s length for several minutes.
A student carries a bucket of water along a horizontal path while walking at a constant velocity.
In the first case, no work is done because the object does not move (d = 0).
In the second case, no work is done because the distance moved is not in the direction of the force (the force is vertically upward while the distance is horizontal). There is no component of the force in the horizontal direction.

6. Work How would you calculate the work in this case?
What is the component of F in the direction of d?
F cos 
If the angle is 90°, what is the component of F in the direction of d?
F cos 90° = 0
If the angle is 0°, what is the component of F in the direction of d?
F cos 0° = F
Discussion of the component of F along the direction of d should lead to the equation on the next slide.

7. Net Work Done By a Constant Net Force
Students should already have deduced this equation from the last slide.

8. Work is a Scalar
In which direction (+ or ) is the x-component of F in each case? F F F F
Show students that the two diagrams on the left show force and distance in opposite directions, while those on the right show force and distance in the same direction.
Ask the angle between the force and distance in the top left diagram. It looks like it is roughly 135°. Point out to them that the cos(135°) is a negative number.
The angle on the top right is about 45° (cos is +).
The angle on the bottom left is about 225° (cos is -).
The angle on the bottom right is about 315° (cos is +).
For the bottom pictures, it will be harder for students to determine the angle unless they draw the force and distance starting at a common point.

9. Classroom Practice Problem
A 20.0 kg suitcase is raised 3.0 m above a platform. How much work is done on the suitcase?
Answer: 590 J
Students may use the mass instead of the weight (20.0 kg x 9.81 m/s2). This is a good time to remind them that mass and weight are different although related quantities.

10. Now what do you think?
Based on the physics definition, list five examples of things you have done in the last year that you would consider work.
Students should now select answers that show a force moving an object in the direction of the force.

11. Work and Kinetic Energy

12. Kinetic Energy Since then or
Show students the steps and substitutions needed to derive the final equation for work. Make sure they see the use of F = ma in the first equation and the substitution for ax from the 2nd equation into the third equation. Help students see the transformation of the 3rd equation into the 4th equation.
Have them note that calculating the work no longer requires knowledge of the force but, instead, can be determined by the effect of the force or the change in velocity.
Mention that a name has been given to the quantity 1/2 mv2 . It is called kinetic energy. So, work is the change in KE. Then show them the next slide, which introduces the kinetic energy equation.

13. Work - Kinetic Energy Theorem
KE is the work an object can do if the speed changes.
Wnet is positive if the speed increases.
Discuss the many examples of moving objects doing work on other objects. For example, a moving baseball bat does work on a ball as it exerts a force on the ball, and the ball moves a distance in the direction of the force. Conversely, the ball does work on the bat as it exerts a force opposite to the direction the bat is moving. Work has a negative value in this case. A change in speed for an object allows it to do work on its environment.

14. Classroom Practice Problems
A 6.00 kg cat runs after a mouse at 10.0 m/s. What is the cat’s kinetic energy?
Answer: 3.00 x 102 J or 300. J
Suppose the above cat accelerated to a speed of 12.0 m/s while chasing the mouse. How much work was done on the cat to produce this change in speed?
Answer: 1.32 x 102 J or 132 J
For the second problem, students should just use the change in KE (432 J – 300 J = 132 J).
Sometimes they make the mistake of thinking that they can use the change in speed (2 m/s) in the equation for KE and end up with an answer of 12 J for the work done. This does not work because ( )2 is not equal to ( ).

15. Conservation of Mechanical Energy

16. What do you think?
Imagine two students standing side by side at the top of a water slide. One steps off of the platform, falling directly into the water below. The other student goes down the slide. Assuming the slide is frictionless, which student strikes the water with a greater speed?
Explain your reasoning.
Would your answer change if the slide were not frictionless? If so, how?
When asking students to express their ideas, you might try one of the following methods.
(1) You could ask them to write their answers in their notebook and then discuss them.
(2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups.
The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally.
A variety of answers are possible. Encourage them to explain their ideas so you can better understand the answer they chose. Remind the students that friction is not a consideration. Water slides are not truly frictionless, so they might want to imagine an air hockey table as a slide. Students will find out later in the lesson that, in the absence of friction, the speeds would be the same. The only difference would be the direction each is traveling at impact.

17. What do you think?
What is meant when scientists say a quantity is conserved?
Describe examples of quantities that are conserved.
Are they always conserved? If not, why?
Students may be familiar with conservation of mass as a conservation law. Try to get them to explain what it means for something to be “conserved.” There are many ways to describe conservation but students often struggle. They may say that they know what it means but they can’t figure out how to say it or write it. These questions should be a good exercise for them to express their ideas in writing.
Conservation may be expressed as “no change in the quantity” or “before = after” or “the total always stays the same.”

18. Mechanical Energy (ME)
ME = KE + PEg + PEelastic
Kinetic Energy
Elastic Potential Energy
Gravitational Potential Energy
Hooke’s Law
Discuss ME as a useful tool for studying motion. Do not tell students yet that ME is conserved. They will determine this from the coming slides and calculations.
As an example. toss a ball in the air and talk about the potential energy and kinetic energy as it rises and falls. As another example. show students a pendulum and talk about the PE and the KE changing as it swings.

19. Mechanical Energy (ME)
ME = KE + PEg + PEelastic
Does not include the many other types of energy, such as thermal energy, chemical potential energy, and others
ME is not a new form of energy.
Just a combination of KE and PE
Discuss ME as a useful tool for studying motion. Do not tell students yet that ME is conserved. They will determine this from the coming slides and calculations.
As an example. toss a ball in the air and talk about the potential energy and kinetic energy as it rises and falls. As another example. show students a pendulum and talk about the PE and the KE changing as it swings.

20. Classroom Practice Problems
A 1.00 kg book is dropped from a height of 2.00 m. Assume no air resistance.
Calculate the PE and the KE at the instant the book is released.
Answer: PE = 19.6 J, KE = 0 J
Students should use PE = mgh to get the PE at each point.
To calculate the KE they need to first find the velocity. The easiest way to get v2 is using vf2 = 2gy. (Note that the initial velocity is zero, so it was eliminated from the equation). After getting the velocity, use the equation KE = 1/2 mv2.
After making these calculations, show students the chart on the next slide.

21. Classroom Practice Problems
A 1.00 kg book is dropped from a height of 2.00 m. Assume no air resistance.
Calculate the KE and PE when the book has fallen 1.0 m. (Hint: you will need an equation from Chapter 2.)
Answer: PE = 9.81 J, KE = 9.81 J
Students should use PE = mgh to get the PE at each point.
To calculate the KE they need to first find the velocity. The easiest way to get v2 is using vf2 = 2gy. (Note that the initial velocity is zero, so it was eliminated from the equation). After getting the velocity, use the equation KE = 1/2 mv2.
After making these calculations, show students the chart on the next slide.

22. Classroom Practice Problems
A 1.00 kg book is dropped from a height of 2.00 m. Assume no air resistance.
Calculate the KE and PE just before the book hits the ground
Answer: PE = 0 J, KE = 19.6 J
Students should use PE = mgh to get the PE at each point.
To calculate the KE they need to first find the velocity. The easiest way to get v2 is using vf2 = 2gy. (Note that the initial velocity is zero, so it was eliminated from the equation). After getting the velocity, use the equation KE = 1/2 mv2.
After making these calculations, show students the chart on the next slide.

23. Table of Values for the Falling Book
h (m)
PE(J)
KE(J)
ME(J)
19.6
0.5
14.7
4.9
1.0
9.8
1.5
2.0
Mention the following to the students:
(1) KE and PE change during the fall but ME remains the same (it is conserved).
(2) You might ask students what values would change if air resistance was considered. The KE values would be smaller and the ME would gradually decrease, so ME would not be conserved.
(3) No consideration was given to the path the book took to the floor, only its position. Therefore, the result would be the same even if it slid down a ramp (as long as the ramp was frictionless).

24. Conservation of Mechanical Energy
MEi = MEf
Initial ME = Final ME
The sum of KE and PE remains constant.
One type of energy changes into another type.
For the falling book, the PE of the book changed into KE as it fell.
As a ball rolls up a hill, KE is changed into PE.
Conservation of energy provides an easier method of solving some problems. For example, go back to the table created for the falling book, and point out the fact that they never needed to calculate the velocity. If they know the PE, then the KE is simply (19.6 J - PE).

25. PEmax = mgh
KE = 0
PE = mgh
PE + KE = PEmax
PE = mgh
PE + KE = PEmax
PE = 0
KE = PEmax

26. Conservation of Energy
Acceleration does not have to be constant.
ME is not conserved if friction is present.
If friction is negligible, conservation of ME is reasonably accurate.
A pendulum as it swings back and forth a few times
Previously, in Chapter 2, the equations developed required that acceleration be constant. That is not the case for conservation of ME.
The example with friction provides an opportunity to point out that even though ME may not be conserved, energy in general is conserved. With friction, the material becomes warmer due to the contact between the surfaces, which causes the speed of the vibrating molecules to increase.

27. Conservation of Energy
Consider a child going down a slide with friction.
What happens to the ME as he slides down?
Answer: It is not conserved but, instead, becomes less and less.
What happens to the “lost” energy?
Answer: It is converted into nonmechanical energy (thermal energy).
Previously, in Chapter 2, the equations developed required that acceleration be constant. That is not the case for conservation of ME.
The example with friction provides an opportunity to point out that even though ME may not be conserved, energy in general is conserved. With friction, the material becomes warmer due to the contact between the surfaces, which causes the speed of the vibrating molecules to increase.

28. Problem Solving Process
Draw a sketch
Identify: KEi, PEi, KEf, and PEf
Include both gravitational and elastic PE, as needed
Apply the equation: (KE + PE)i = (KE + PE)f
Solve for required quantity
Mass, speed, distance, height, etc.

29. Nonconservative Forces
A force is nonconservative if the work it does on an object depends on the path taken by the object between its final and starting points.
Examples of nonconservative forces
kinetic friction, air drag, propulsive forces

30. Friction as a Nonconservative Force
The friction force is transformed from the kinetic energy of the object into a type of energy associated with temperature
The objects are warmer than they were before the movement
Internal Energy is the term used for the energy associated with an object’s temperature

31. Friction Depends on the Path
The blue path is shorter than the red path
The work required is less on the blue path than on the red path
Friction depends on the path and so is a non-conservative force

32. Nonconservative Forces with Energy Considerations
When nonconservative forces are present, the total mechanical energy of the system is not constant
The work done by all nonconservative forces acting on parts of a system equals the change in the mechanical energy of the system

33. Nonconservative Forces and Energy
In equation form:
The energy can either cross a boundary or the energy is transformed into a form of non-mechanical energy such as thermal energy

34. Now what do you think?
Imagine two students standing side by side at the top of a water slide. One steps off of the platform, falling directly into the water below. The other student goes down the slide. Assuming the slide is frictionless, which student strikes the water with a greater speed?
Explain your reasoning.
Would your answer change if the slide were not frictionless? If so, how?
Both strike at the same speed. One hits the water vertically, while the other slides in nearly horizontally. The PE lost is the same for both and, therefore, the KE gained is the same as well.
With friction, the student falling straight down would be moving faster, because energy is not conserved for the student on the slide. Some of the lost PE is converted into thermal energy

35. Now what do you think?
What is meant when scientists say a quantity is “conserved”?
Describe examples of quantities that are conserved.
Are they always conserved? If not, why?
Conserved means that the quantity does not change. The quantity neither increases nor decreases. Common examples are the conservation of mass and the conservation of energy. Mechanical energy is considered to be conserved in cases where friction is negligible. If friction is significant, mechanical energy is not conserved.