Plan for Today (AP Physics I)

1. Plan for Today (AP Physics I) • Notes/Lecture on Potential Energy

2. One Definition of Energy – the ability to cause change

3. Example • If I take a brick and put it above a students head a small distance • Will it cause a change? • Yes • What if I raise it farther up? • Will it cause more change? • Yes • What kind of energy increased? • Potential energy (PEg)

4. Example • If I pick up a 1 kg brick and move it 1 m, did I do work? • Yes • W = F *x • W = (mg) * h • W = mgh • Is this a form of energy? • How do we know – check the units • PEg = mgh = [kgm/s^2*m) • Yes in joules • Note: h is change in y • Calculation: 1 * 9.8 * 1 = 9.8 J

5. Gravitational Potential Energy • PEg = mgh

6. Example • What if I carry a brick across the room? • Is this a change in potential energy? • No? • Still no • What if I stick the brick out the window? • Is this a change in potential energy? • Yes? • But then how is this possible? • I didn’t do any work – so how do I have a change in potential energy?

7. Let’s draw a picture and calculate this

8. Let’s draw a picture and calculate this

9. Let’s draw a picture and calculate this

10. Let’s draw a picture and calculate this

11. Let’s draw a picture and calculate this

12. Let’s draw a picture and calculate this

13. Let’s draw a picture and calculate this

14. What if we change where we start from?

15. What if we change where we start from?

16. What if we change where we start from?

17. What if we change where we start from?

18. Same Change in potential energy • Individual values depend on zero point

19. For the brick outside the window • Could we look at the radius of the earth? • Hi =6,280,006m • Hf=6,280000m • Still have -58.0 J for change in PE

20. Example • 1 kg brick, 1 m above the ground vs. 6 m above the ground outside • Zero point is the floor • What’s the change in PE from holding it in the classroom to outside the window?

21. Example • What if we had the same example BUT our zero point was the ground outside? • What’s the change in PE?

22. So. . . • Change in PE is the same • Just depends on a zero point (to calculate) • We could use from the center of the Earth

23. Elastic Cord • Could this case a change if I let go? • Yes • So there must be energy • How about now? • More change? • Yes so more energy? • What kind of energy is this? • Elastic potential energy = PEe

24. Elastic Cord With Data • 1 step – 1 m • 20 N of force • 2 steps – 2 m • 40 N • 3 steps – 3 m • 60 N • 4 steps – 4 m • 80 N

25. Hmm data • What do we do with this data? • Graph it!

26. Graph of data • Force on y • Change in length on x • Note: Change in length • Lf – Li!

28. Looking at the graph • What’s the slope of this line? • Change in y over change in x • So F/x • This is K – a spring constant • What are the units for K? • F/x = Newtons/meters = N/m

29. Now • What if we double the elastic cord? • Now it’s a different spring • What does that graph look like? • Steeper line • What does this mean?

31. Summary • Different spring = different k • Stiff spring = big k • Weak spring – small k

32. Looking at the graph • Force and distance • Work is not F * x, because it varies • If we could use that, the graph would look like this:

33. Looking at the graph • Force and distance • Work is not F * x, because it varies • If we could use that, the graph would look like this:

34. Still looking at the graph • So what would work be? • Area under the curve • Area = ½ * b * h • W = ½ x *F • But we need to know in terms of k • Slope = k = F/x • So x * k = F • W = ½ * x * x * k • W = ½ k x^2

35. Elastic Potential Energy • W = ½ x * x * k • W = ½ k x^2 • Are we sure it’s energy? • How do we know? • Look at the units • N/m *m^2 = Nm = kgm/s^2 * m = kgm^2/s^2 = J

36. Elastic Potential Energy • PEe = ½ * k * x^2