Roller Coasters: Measures of Effort & Motion; Conservation Laws

1. Roller Coasters: Measures of Effort & Motion; Conservation Laws

2. Who likes to ride a roller coaster?! • Black Hole 2000 • California Screamin’ • Bizzarro • Nitro • Medusa • Space mountain • Splash mountain • Big Thunder Railroad

3. Roller Coaster Project: need to know list. In groups of 3-4 make a list for each of these on a piece of paper • What do you want to know about the project? • What physics stuff will you need to learn?

4. Investigation 1 (pp348-349):Velocity and acceleration: The big Thrill • Sketch a roller coaster with a first hill of 15 m that quickly descends to 6 m and then turns to the right in a big circle (radius of 10 m) and then descends back to the ground. P 46

5. Compare to others: p46 • Copy the different sketches from 2 other people seated around you. • Circle the sketch you like the best 1.Which sketch is the best way to show a hill? 2.Which sketch is the best way to show a loop? 3.What other characteristics make the best sketch?

6. Two views: now create 2 views of the same coaster. • Side view (if you were standing on the ground looking at the coaster • Top View (if you were above the coaster in a balloon looking straight down) p46

7. A professional design team would like your help on their roller coaster design • Start with the side view. Move your finger along the track as I read a description to you: The Terminator Express Roller Coaster car begins from the loading platform at A and then rises along the lift. It reaches the top of hilltop #1 at B and then makes its first drop. It then goes into a vertical loop at C. This clothoid loop (it has a big radius at the bottom and a small radius at the top) allows the riders to be safely upside down. The coaster then goes along the track starting at E, moves through the backcurve to F, rises over hilltop #2 at G, and then swings into a horizontal loop at I. The brakes are applied after the loop, and the roller coaster comes to a stop at J. • Now move your finger along the top view as I read the description to you

8. A professional design team would like your help on their roller coaster design • Label each part of the track with the kind of motion: at rest, constant motion, acceleration (either speeding up, or slowing down) • Which parts of the Terminator Express give the most thrills? • What kind of motion is responsible for the most thrills? p47

9. Energy and Work ppt p48 • Use a computer to find this ppt file on my website. • Answer all the questions on the handout. • Then use the link on the last slide to Build Your Own Roller Coaster • Draw your successful coaster (both a top view and a side view) and Get a stamp from your teacher before you shut down your computer. • Now answer PtoGo (p358-359) 1-5, 10

10. What happens first on every roller coaster? Why? p49

11. Investigation #2 (p360-363)Which roller coaster track will give the bigger thrill? Why? p49

12. What effects the speed of the ball at the bottom of the ramp? p49

13. Angle of the ramp • Hypothesis: • Data • Summary:

14. Height of the ramp • Hypothesis: Will 2X the height result in 2x the velocity? • Data • Summary:

15. Length of the ramp • Hypothesis: Will 2x the length result in 2X the velocity? • Data • Summary:

16. Height of the ramp • Hypothesis: Will 2X the height result in 2x the velocity? • Data • Summary: • The velocity is related the square of the height of the ramp!

17. Work, defined • Work carries a specific meaning in physics • Simple form: work = force  distance W = F· d • Work can be done by you, as well as on you • Are you the pusher or the pushee • Work is a measure of expended energy • Work makes you tired • Machines make work easy (ramps, levers, etc.) • Apply less force over larger distance for same work

18. Working at an advantage • Often we’re limited by the amount of force we can apply. • Putting “full weight” into wrench is limited by your mg • Ramps, levers, pulleys, etc. all allow you to do the same amount of work, but by applying a smaller force over a larger distance Work = ForceDistance = ForceDistance

19. Larger Force Small Force Short Distance Long Distance M Ramps Exert a smaller force over a larger distance to achieve the same change in gravitational potential energy (height raised)

20. Gravitational Potential Energy • Gravitational Potential Energy near the surface of the Earth: • DW = mg Dh  Work = Force Distance m Dh m

21. How much work? • To lift 100 kg 1 m? W = Fd =mgd = • To push 100 kg up a 10m ramp to a height of 1 m? W = Fd = mgd = Why is it easier to push something up a ramp than lift it to the same height?

22. Ramp Example • Ramp 10 m long and 1 m high • Push 100 kg all the way up ramp • Would require mg = 980 N (220 lb) of force to lift directly (brute strength) • Work done is (980 N)(1 m) = 980 N·m in direct lift • Extend over 10 m, and only 98 N (22 lb) is needed • Something we can actually provide • Excludes frictional forces/losses 1 m

23. Work Examples “Worked” Out • How much work does it take to lift a 30 kg suitcase onto the table, 1 meter high? W = (30 kg)  (9.8 m/s2)  (1 m) = 294 J • Unit of work (energy) is the N·m, or Joule (J) • One Joule is 0.239 calories, or 0.000239 Calories (food) • Pushing a crate 10 m across a floor with a force of 250 N requires 2,500 J (2.5 kJ) of work • Gravity does 20 J of work on a 1 kg (10 N) book that it has pulled off a 2 meter shelf

24. Work is Exchange of Energy • Energy is the capacity to do work • Two main categories of energy • Kinetic Energy: Energy of motion • A moving baseball can do work • A falling anvil can do work • Potential Energy: Stored (latent) capacity to do work • Gravitational potential energy (perched on cliff) • Mechanical potential energy (like in compressed spring) • Chemical potential energy (stored in bonds) • Nuclear potential energy (in nuclear bonds) • Energy can be converted between types

25. Conversion of Energy • Falling object converts gravitational potential energy into kinetic energy • Friction converts kinetic energy into vibrational (thermal) energy • makes things hot (rub your hands together) • irretrievable energy • Doing work on something changes that object’s energy by amount of work done, transferring energy from the agent doing the work

26. Energy is Conserved! • The total energy (in all forms) in a “closed” system remains constant • This is one of nature’s “conservation laws” • Conservation applies to: • Energy (includes mass via E = mc2) • Momentum • Angular Momentum • Electric Charge • Conservation laws are fundamental in physics, and stem from symmetries in our space and time • Emmy Noether formulated this deep connection • cedar.evansville.edu/~ck6/bstud/noether.html

27. Energy Conservation Demonstrated • Roller coaster car lifted to initial height (energy in) takes work • This work converts gravitational potential energy at the top • GPE converts to kinetic energy as it drops and picks up speed • Fastest at bottom of track (no GPE left!) • Re-converts kinetic energy back into potential as it climbs the next hill

28. Potential energy • Potential energy (PE or GPE) is stored energy caused by gravity pulling an object downward • An object gets to this position because work was done to get it up there • Work = Force x distance = (mass)(gravity)(distance) • PE = (mass)(gravity)(height) • Example: a 1.5 kg ball raised 1 meter above the table has PE = (1.5)(10)(1) = 15 Joules of energy

29. Kinetic Energy • The kinetic energy for a mass in motion is K.E. = ½mv2 • Example: 1 kg at 10 m/s has 50 J of kinetic energy • Ball dropped from rest at a height h (P.E. = mgh) hits the ground with speed v. Expect ½mv2 = mgh • h = ½gt2 • v = gt v2 = g2t2 • mgh = mg(½gt2) = ½mg2t2 = ½mv2 sure enough • Ball has converted its available gravitational potential energy into kinetic energy: the energy of motion

30. Kinetic Energy, cont. • Kinetic energy is proportional to v2… • Watch out for fast things! • Damage to car in collision is proportional to v2 • Trauma to head from falling anvil is proportional to v2, or to mgh (how high it started from) • Hurricane with 120 m.p.h. packs four times the punch of gale with 60 m.p.h. winds

31. Energy Conversion/Conservation Example P.E. = 98 J K.E. = 0 J 8 m P.E. = K.E. = 6 m P.E. = K.E. = 4 m P.E. = K.E. = 2 m P.E. = K.E. = 0 m

32. Energy Conversion/Conservation Example P.E. = 98 J K.E. = 0 J 10 m • Drop 1 kg ball from 10 m • starts out with mgh = (1 kg)(9.8 m/s2)(10 m) = 98 J of gravitational potential energy • halfway down (5 m from floor), has given up half its potential energy (49 J) to kinetic energy • ½mv2 = 49 J  v2 = 98 m2/s2  v  10 m/s • at floor (0 m), all potential energy is given up to kinetic energy • ½mv2 = 98 J  v2 = 196 m2/s2  v = 14 m/s 8 m P.E. = 73.5 J K.E. = 24.5 J 6 m P.E. = 49 J K.E. = 49 J 4 m P.E. = 24.5 J K.E. = 73.5 J 2 m P.E. = 0 J K.E. = 98 J 0 m

33. Finish for next time: p50 • Read Active Physics p363-367 • Answer CU (p367) 1-5 • Answer PtoGo (p370) 1-3 • CDP 9-2

34. Review the Energy model p51 • Energy comes from doing work

35. Review the Energy model p51 • Energy comes from doing work • Gravitational Potential Energy (GPE) is the same as PE • Potential Energy (PE) is stored energy (must be higher than the ground) • Kinetic Energy (KE) is energy in motion • Energy can be converted from one form to another • The total energy is always the same (Law of conservation of energy) • PE=mgh= (mass)(gravity)(height) • KE=1/2 mv2=(1/2)(mass)(velocity)2 • Twice the velocity means four times as much KE!

36. PtoGo (p370) 1-3 p50 3.)

37. PtoGo (p370) 1-3 p50 3.)

38. Now let’s make an energy bar chart(PtoGo (p370) #4) 4. Finish PtoGo (p370) #4-10 p51

39. Phet: Adventures in Energy Skate Park Use a computer and open the phetsim: Energy Skate Park http://phet.colorado.edu/new/simulations/sims.php?sim=Energy_Skate_Park Complete the document Adventures in Energy Skate Park Then finish PtoGo (p370) #4-10 p52

40. p Energy “rules”!List 3 rules that you used to complete the worksheet last time: Share out. What other “rules” were shared by your classmates?

41. Apparent Weight p55 • Ride the roller coaster. What changes do you feel as the coaster moves? • What is a G-Force?

42. Weight (or not to weight!) p55 • What is weight? How is it measured? • What will your weight be if you stand with one foot on each of two bathroom scales? Explain

43. What is weight? How is it measured? Weight is a force and force is equal to mass times acceleration (newton’s second law…) weight = mass x acceleration • What will your weight be if you stand with one foot on each of two bathroom scales? Explain ½ of the force will be on each scale, therefore each scale will read ½ of that measured on one scale, But THE TOTAL WEIGHT WILL BE THE SAME

44. Calculate the weight: p55 1.) A football player with mass of 100 kg 2.) a student with mass of 42.5 kg 3.) an adult with mass 60 kg

45. What happens to your weight on an elevator? • Stays the same • Goes up • Goes down Explain: p55

46. Explain how your weight changes (this is called apparent weight) • Objects travelling at constant velocity have no net force acting upon them (therefore the force of their weight is equal and opposite to some other force) • Apparent weight is the net force acting on you in the direction of earth • If you are accelerating less than g=10 m/s2 then you “weigh” less • If you are accelerating more than g=10m/s2 then you “weigh” more • If no acceleration (constant speed) then you weigh the same (F=ma) • Remember: air resistance is ignored to make the problems easier! Now finish PtoGo (p418-419) 5-9 CU (p415) 1-5 Get stamps when you are finished! p56

48. Check your Answers: PtoGo (p418-419) 5-9 CU (p415) 1-5 5.) Down 6.) Up 7.) Down 10-1.5=8.5 W=(50)(8.5)=42.5N 8.) rest W=(50)(10)=500N Up W=(50)(10+2)=600N Constant speed =(50)(10)=500N 9.) (in your own words) 1.) At constant speed the sum of the forces is zero. 2.) apparent weight is more when going up 3.) Going up gives you more weight because there is more force acting on you. 4.) in free fall there is zero force 5.) air resistance slows things down

49. Why don’t you fall out of a roller coaster when it goes upside down in a loop? • Do Active Physics Section 7 Investigation (p420-424) • Part A: Moving in Curves (10 minutes only!) • Part B: How much force is required? (10 more minutes!) • Record answers in your notebook • Share out • Answer CU (p429 (1-5) p57

50. Diagram of centripetal force on a roller coaster Active Physics Section 7 Investigation (p420-424)Part A: Moving in Curves • Objects want to travel in straight paths • To make a curve you must apply a force towards the direction you want the object to travel • As soon as you stop applying the force the object will again continue on a straight path #4 (your diagram should look something like the diagram to the right) • tutorial