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
Work can be positive or negative but does not have a direction.
What is the angle between F and d 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. 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.

10. 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.

11. 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.

12. Kinetic and Potential Energy

13. What do you think? You have no doubt heard the term kinetic energy.
What is it?
What factors affect the kinetic energy of an object and in what way?
You have no doubt heard the term potential energy.
What factors affect the potential energy of an object and in what way?
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.
Kinetic energy comments will likely center around the velocity and probably not mention the mass of the object. Students may mention the different types of potential energy (gravitational, electrostatic, elastic, etc). Listen to ideas about these topics and then begin the lecture/discussion.

14. What are the SI units for KE?
Kinetic Energy
What are the SI units for KE?
kg•m2/s2 or N•m or J
Ask students to determine the units from the equation before showing this on the slide. Have them see that, since N are kg•m/s2, the units of N•m are equivalent to kg•m2/s2.

15. 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.

16. 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.

17. 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 ( ).

18. Potential Energy
Energy associated with an object’s potential to move due to an interaction with its environment
A book held above the desk
An arrow ready to be released from the bow
Some types of PE:
Gravitational
Elastic
Electromagnetic
Chemical
Hold a book above the desk. The book has the potential to move due to an interaction with Earth (gravity).
Stretch a rubber band with a wad of paper held in it like a sling shot. The paper has the potential to move due to an interaction with its environment (the rubber band).

19. Gravitational Potential Energy
What are the SI units?
kg•m2/s2 or N•m or J
The height (h) depends on the “zero level” chosen where PEg = 0.
g = 9.80 m/s2 if h is positive
This equation comes from W = Fd = (ma)d = mgh, so PEg is simply the work done in lifting an object.
To help students understand the fact that the zero level is arbitrary, hold a book over the desk and ask them what they would use for h in order to calculate the PE. Then, maintaining the book at the same height, move it over the floor and ask the students once again what value they would use for h.
Point out that, in general, our primary concern in physics involves changes in PE, not the actual amount of PE. The change in PE is always the same regardless of what zero level is assigned. Generally, the zero level is assigned to the lowest point the object will reach. For example, the desk if the book is held over the desk, and the floor if the book is held over the floor.

20. Elastic Potential Energy
The energy available for use in deformed elastic objects
Rubber bands, springs in trampolines, pole-vault poles, muscles
For springs, the distance compressed or stretched = x
Point out that x in the diagram is the “Distance compressed.” This will be used in the equation for elastic potential energy (slide 10).
Discuss the transfer of the elastic potential energy to the block when the deformed spring returns to its original configuration.

21. Spring Constant (k)
Click below to watch the Visual Concept.
Visual Concept
The spring constant (k) depends on the stiffness of the spring.
Stiffer springs have higher k values.
Measured in N/m
Force in newtons needed to stretch a spring 1.0 meters

22. Elastic Potential Energy
PEelastic = kx2
k = the spring constant (N/m)
x = the distance the spring is stretched (m)
What are the SI Units for PEelastic?
Joules (J) (N·m)
The joule is the SI unit for any form of energy
Help students find the SI units as N•m or Kg•m2/s2 or J.
Now would be a good time to remind them that work, KE, and PE are all measured in joules (kg•m2/s2).

23. Classroom Practice Problems
When a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table.
What is the gravitational potential energy associated with the mass relative to the table?
Answer: 9.81 J
What is the spring’s elastic potential energy if the spring constant is N/m?
Answer: 2.00 J
Point out to students that the zero level is at the table for gravitational PE. Also, they must use meters, not centimeters, in order to have joules as units in the final answers.

24. Now what do you think? What is kinetic energy?
What factors affect the kinetic energy of an object and in what way?
How are work and kinetic energy related?
What is potential energy?
What factors affect the gravitational potential energy of an object and in what way?
What factors affect the elastic potential energy of an object and in what way?
Mass and KE are directly proportional. KE is directly proportional to the velocity squared.
The net work done on an object equals the change in kinetic energy.
Factors affecting gravitational PE are mass, acceleration due to gravity, and height above the zero level. All are directly related.
Factors affecting elastic PE are the spring constant (directly related) and the displacement from equilibrium position (directly related to the displacement squared).