1. Objectives: The students will be able to: Solve problems using the law of conservation of energy. Solve problems using the law of conservation of energy. Analyze collisions to find the change in kinetic energy. Analyze collisions to find the change in kinetic energy.

2. An object has the MOST kinetic energy when it’s movement is the GREATEST. When an object has the LEAST potential energy, it has the MOST kinetic energy.

3. A water bottle is knocked off a desk. When does the bottle have the MOST kinetic energy? A. At the top of the fall. B. In the middle of the fall. C. At the bottom of the fall.

4. It has the most kinetic energy when its movement and speed are greatest, which is at the bottom of the fall right before it hits the ground. When an object has the LEAST potential energy is when it has the MOST kinetic energy.

5. Roller Coasters When does the train on this roller coaster have the MOST potential energy? AT THE VERY TOP! The HIGHER the train is lifted by the motor, the MORE potential energy is produced. At the top of the hill the train has a huge amount of potential energy, but it has very little kinetic energy.

6. As the train accelerates down the hill the potential energy is converted into kinetic energy. There is very little potential energy at the bottom of the hill, but there is a great amount of kinetic energy.

7. When does the train on this roller coaster have the MOST kinetic energy? (When is it moving the fastest?) (When does it have the LEAST potential energy???) At the bottom of the tallest hill!

8. The Conservation of Mechanical Energy

9. THE PRINCIPLE OF CONSERVATION OF MECHANICAL ENERGY The total mechanical energy (E = KE + PE) of an object remains constant as the object moves, provided that the net work done by external non-conservative forces is zero.

10. Conservation of Mechanical Energy If friction and wind resistance are ignored, a bobsled run illustrates how kinetic and potential energy can be interconverted, while the total mechanical energy remains constant.

11. Mechanical Energy and Its Conservation If there are no nonconservative forces, the sum of the changes in the kinetic energy and in the potential energy is zero – the kinetic and potential energy changes are equal but opposite in sign. This allows us to define the total mechanical energy: And its conservation: (6-12b)

12. Problem Solving Using Conservation of Mechanical Energy In the image on the left, the total mechanical energy is: The energy buckets (right) show how the energy moves from all potential to all kinetic.

13. Problem Solving Using Conservation of Mechanical Energy If there is no friction, the speed of a roller coaster will depend only on its height compared to its starting height.

14. Rollercoaster Example Loss in height corresponds to a gain in speed as total energy is conserved.

15. Skier Example #1 When the skier loses his total mechanical energy, work is done on the snow and the snow gains the energy.

16. A Daredevil Motorcyclist A motorcyclist is trying to leap across the canyon shown in the Figure above by driving horizontally off the cliff at a speed of 38.0 m/s. Ignoring air resistance, find the speed with which the cycle strikes the ground on the other side. Now use a kinematic and vector approach to solve this.

17. Roller Coaster (Ideal) The Magnum XL-200 at Cedar Point Park In Sandusky, Ohio. The ride includes a vertical drop that accelerates the cart to a speed of 34 m/s (76 mi/hr) at the bottom of the dip. Assume that the coaster has a speed of nearly zero as it crests the top of the hill. Neglecting friction and other non- conservative forces, determine the approximate height of the peak. Hint: Use the energy approach.

18. Non-conservative Forces for the Roller Coaster Example In the roller coaster example, we ignored non-conservative forces, such as friction. In reality, however, such forces are present when the roller coaster descends.

19. Energy in a Roller Coaster Ride 1.Go to the following site: http://www.pbslearningmedia.org/resource/hew06.sci.phys.maf.rollercoaster/energy-in-a- roller-coaster-ride/ http://www.pbslearningmedia.org/resource/hew06.sci.phys.maf.rollercoaster/energy-in-a- roller-coaster-ride/ 2.Run the animation and observe the relationship between kinetic and potential energy at each position. 3.Stop the roller coaster and at each position and describe on a sheet of paper the relationship between kinetic and potential energy using the pie chart. Then explain in detail why that relationship exists based on the information given in the animation. 4.Now you will design your own roller coaster. Go to the following site: http://www.learner.org/interactives/parkphysics/coaster/ http://www.learner.org/interactives/parkphysics/coaster/ 5.Follow the directions on how to build your roller coaster. Think through each step carefully and the physics behind each step. 6.When you are finished you, will get an analysis of your design. On the back of the paper you used for the previous activity, explain why your steps were successful in terms of energy or why you were not successful and what needs to be done in order to improve your design.

20. Conservation of Energy Problem Starting from rest, a child zooms down a frictionless slide from an initial height of 3 m. What is her speed at the bottom of the slide? (Assume she has a mass of 25 kg)

21. Conservation of Energy Problem h i = 3mm = 25kgv i = 0 m/s h f = 0mv f = ? Slide is frictionless  Mechanical energy is conserved Slide is frictionless  Mechanical energy is conserved Kinetic energy & potential energy = only forms of energy present Kinetic energy & potential energy = only forms of energy present KE = ½ mv 2 PE g = mgh KE = ½ mv 2 PE g = mgh Final gravitational potential energy = zero (Bottom of the slide)  PE gf = 0 Final gravitational potential energy = zero (Bottom of the slide)  PE gf = 0 Initial gravitational potential energy  Top of the slide  PE gi = mgh i  (25kg)(9.8m/s 2 )(3m) = 736 J Initial gravitational potential energy  Top of the slide  PE gi = mgh i  (25kg)(9.8m/s 2 )(3m) = 736 J

22. Conservation of Energy Problem h i = 3mm = 25kgv i = 0 m/s h f = 0mv f = ? Initial Kinetic Energy = 0, because child starts at rest Initial Kinetic Energy = 0, because child starts at rest KE i = 0 KE i = 0 Final Kinetic Energy Final Kinetic Energy KE f = ½ mv 2  ½ (25kg)v 2 f KE f = ½ mv 2  ½ (25kg)v 2 f ME i = ME f ME i = ME f PE i + KE i = PE f + Ke f 736 J + 0 J = 0 J + (1/2)(25kg)(v 2 f ) v f = 7.67 m/s

23. Elaboration Energy Transfer 11-3 Transparency Conservation of Energy Concept Development Page Conservation of Energy Lab Practice Problems p.297 #s 15, 17 Practice Problems p.300 #s 19, 21 Section Review p.301 #s 24, 27, 28 Page 308 & 309 #s 73, 74, 77

24. Closure Kahoot 11.2