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

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

2. Roller Coaster Project: Read handout 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?
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3. 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 loop (radius of 10 m) and then descends back to the ground.
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4. Compare to others:
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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?

5. 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)
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6. A professional design team would like your help on their roller coaster design
Start with the side view. (p349). 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 through E, moves into 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

7. 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, or changing direction)
1. Which parts of the Terminator Express give the most thrills?
2. What kind of motion is responsible for the most thrills?
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8. Energy and Work ppt
Use a computer to find this ppt file on my website.
teacher.sanjuan.edu/webpages/pdifilippo
click on physics
click on Energy in Roller Coasters
Click on file: Energy and Work ppt
Answer all the questions on the handout.
Then use the link on the last slide to Build Your Own Roller Coaster (you must be in slideshow mode for the link to work)
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 (p ) 1-5, 10 Get another stamp when Finished
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9. Nitro
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What happens to you when you first get on a roller coaster? From the time you step on until you get to the top of the first big hill…What happens first on every roller coaster? Why?

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

11. What effects the speed of the ball at the bottom of the ramp?

12. Mass of the marble
Hypothesis:
Data
Summary:
Type of marble
Velocity

13. Height of the ramp (angle of the ramp)
Hypothesis:
Will 2X the height result in 2x the velocity?
Data
Summary:
height
velocity
1 brick (6.5 cm)
2 bricks (13.0 cm)
3 bricks (19.5 cm)

14. Length of the ramp Hypothesis:
Will 2x the length result in 2X the velocity?
Data
Summary:
length
velocity
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15. Conclusions: What can you do to make the marble speed up?
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16. Conclusions: What can you do to make the marble speed up?
1. Increase the length of the ramp 2. Increase the angle of the ramp 3. Increase the height of the ramp (The velocity is related to the square of the height of the ramp!)
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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
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18. 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 (a roller coaster at the top of the first hill)
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

19. 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

20. 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
Aside: Earth is just another big ball:
Obeys Newton’s laws
* Force on superball by earth countered by force on earth
* Earth accelerates towards dropped ball (F = ma)
- tiny, tiny acceleration
* Tries to continue in straight line, but deflected by Sun
- acceleration changes direction of velocity vector
Included in conservation laws
* Dropped ball appears to get momentum out of nowhere
- but earth’s motion towards ball counters with same momentum
* Energy conservation must include huge input from sun
- the activity around us gets its energy from the sun

21. 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

22. 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

23. 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

24. 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

25. 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. =
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0 m

26. Energy Conversion/Conservation Example
P.E. = 98 J
K.E. = 0 J
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

27. Get a stamp when finished Notebook check and extra credit!
Finish for next time:
p59
Read Active Physics p
Answer CU (p367) 1-5
CDP 9-2
Get a stamp when finished
Notebook check and extra credit!

28. Phet: Adventures in Energy Skate Park
Use a computer and open the phet sim: Energy Skate Park ons/sims.php?sim=Energy_Skate_Park Complete the document Adventures in Energy Skate Park Get a stamp when finished
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29. Relay…only one person can write at a time
Welcome back!
Let’s review…
Generate ideas…What words/ phrases can you use to describe a roller coaster
Relay…only one person can write at a time
No one can take another turn until everyone has had a turn
The team with the most recorded wins

30. Now generate ideas for our Energy Model
Double your score!
Turn your paper over
Now generate ideas for our Energy Model
What PHYSICS have we learned about roller coasters? How do roller coasters work?
Use full sentences this time!

31. Review the Energy model Driving question: How do roller coasters work?p
Energy comes from doing work

32. Energy model Driving question: How do roller coasters work?
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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!

33. PtoGo (p370) 1. For which track is the speed of the car the greatest at the bottom? Why? (assume no friction)
B A
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34. PtoGo (p370)
2. State the Law of Conservation of energy as it applies to roller coasters. Include in your statement GPE, KE, mgh, and ½ mv2
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35. p62 PtoGo (p370) 3.) Enlarged on handout Mass = 200 kg g = 10 m/s2
Position/height
GPE = mgh
KE = 1/2mv2
Total energy =
GPE + KE
Top (30m)
Not moving
(200)(10)(30)
= 60,000 J
Bottom (7.5 m)
Moving fast
Top (15 m)
Moving slow
Bottom (5 m)
moving
End (0 m)
Stopped/not moving

36. PtoGo (p370) 3.) p69 Mass = 200 kg g = 10 m/s2 Position/height
GPE = mgh
KE = 1/2mv2
GPE + KE
Top (30m)
(200)(10)(30)
= 60,000 J
(½)(200)(0)
= 0 J
60,
Bottom (0 m)
(200)(10)(0)
60,000 – 0
60,000 J
Halfway down
(200)(10)(15)
= 30,000 J
60,000-30,000
¾ way down
(200)(10)(7.5)
= 45,000 J
60, ,000
=15,000 J

37. make an energy bar chart on your paper (PtoGo (p370) #4)4.
Finish PtoGo (p370) #5-10
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38. Next time, come prepared to answer the following questions about your project: partner’s name, materials you will use to build your coaster, intensity of ride (mild, medium, or
high), target group of riders, theme/decorations,
top and side views

39. Finish PtoGo (p370) #5-10 Get your work stamped
Energy Quiz #1 Thursday
Finish PtoGo (p370) #5-10
Get your work stamped
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40. How many G’s can you take? Apparent Weight
Ride the roller coaster. What changes do you feel as the coaster moves?
What is a G-Force?

41. Weight (or not to weight!)
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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

42. 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

43. Calculate the weight:
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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

44. What happens to your weight on an elevator?
Stays the same
Goes up
Goes down
Explain:
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45. P418 #4
Acceleration
(up, down, zero)
Scale reading
(larger, smaller, same)
Explanation
A. Elevator at rest on top floor
Zero
same
B. Elevator starts moving down
C. Elevator moves down at constant speed
D. Elevator comes to rest on the bottom floor
E. Elevator is at rest on the bottom floor
F. Elevator begins to move up up
larger
G. Elevator moves up at constant speed
H. Elevator comes to rest on the top floor
I. Elevator at rest on the top floor
zero

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 (p ) 4-9
CU (p415) 1-5 Get stamps when you are finished!
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47. Check your Answers:
PtoGo (p ) 5-9
CU (p415) 1-5
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
5.) Down 6.) Up 7.) Down =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)

48. p61 Add to our energy model
10. Apparent weight is the net force acting on you in the direction of earth 11. This g-force (weight) can be compared to gravity (10 m/s2 = 1g) 12. A safe roller coaster ride can have up to 5 g’s. Astronauts and fighter pilots experience up to 10 g’s.

49. Where does a Popper toy Get it’s energy?
Turn a popper toy inside out and PLACE it on the table. Observe what happens.
Once again compress the popper and DROP it onto the table. Observe what happens.
Record in your notebook and answer the following:
1.) What propelled the popper into the air?
2.) Will dropping the popper from greater heights make the popper jump higher? Explain.
3.) Describe where the popper got the energy to move upward and downward through the air.

50. 1.) What propelled the popper into the air?
When the popper abruptly returns to its original shape, its elastic potential energy is transformed into kinetic energy and then gravitational potential energy

51. p67
2.) Will dropping the popper from greater heights make the popper jump higher? Explain.
Yes, the popper has more gravitational potential energy when it is dropped from a greater height. This results in a greater energy transformation.

52. 3.) Describe where the popper got the energy to move upward and downward through the air.
The popper’s source of energy is the work done (provided by the elastic potential energy) to deform it and the work done to elevate it against earth’s gravity (gravitational potential energy)
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53. Active Physics p380-381) 1-13 1.) p67 Position above table EPE (J)
KE (J)
GPE (J)=mgh
Mass = 4.16g
Total energy= EPE + KE + GPE
At rest on table
h= 0 m 25
Just after popping
At peak
h= 0.60 m
½ way up
h= 0.30 m
h= (?)
h=(?)

54. Active Physics P to Go (p380-381) 1-132.

55. Finish PtoGo (p ) 1-11
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56. Section 7 Investigation (p420-424)
1.) What makes you go in a circle?
Demo air puck
Water demo
Active Physics Section 7 Investigation p420
What do you think?
2.) Why don’t you fall out of a roller coaster when it goes upside down in a loop?
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57. Section 7 Investigation (p420-424)
Why don’t you fall out of a roller coaster when it goes upside down in a loop?
Do Active Physics
Section 7 Investigation (p )
Part A: Moving in Curves (10 minutes only!) steps 1-4
Part B: How much force is required? (10 more minutes!)
Record answers in your notebook
Share out
Answer CU (p429 (1-5)
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58. 1.) Objects want to travel in straight paths
Diagram of centripetal force on a roller coaster
Active Physics Section 7 Investigation (p ) Part A: Moving in Curves Steps 1-4
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1.) Objects want to travel in straight paths
2.) To make a curve you must apply a force towards the direction you want the object to travel
3.) 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

59. keep the string parallel to the floor! Get a stamp when finished
Active Physics Section 7 Investigation (p ) Part B: How much force is required?
You have 10 minutes to follow the directions and record as many answers as you can (do at least 1-4)
keep the string parallel to the floor!
Get a stamp when finished
Then we will share out…tomorrow
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60. Part B (force and speed)
1a.) Centripetal force acts toward the center of the circle (your fingers have to exert force to keep the stopper flying in a circle. If you let go, the stopper would fly away in a straight line) 1b. As you twirl the stopper at larger speeds, your fingers tighten up to supply a larger force (higher speeds require more centripetal force).

61. Part B (force and mass)
2a. As the mass (number) of the stoppers on the end of the string increases, you must supply a bigger (centripetal) force. 2b. If you change more than 1 variable, you will not know what causes the change. Therefore, you must change only one variable, the mass. 2c. As the mass increases, the centripetal force required also increases.

62. Part B (Force and radius of circle)
3a. As you twirl the stopper in a smaller circle, you tighten your fingers to supply a larger (centripetal) force. 3b. You must hold the mass and the speed of the stopper constant in order to compare how changes in length affect the required force.

63. Part B (force and vertical circles)
4b. The force your finger provide (centripetal force) is less when the stopper is at the top of the vertical circle, and larger when it is at the bottom. 4c. As the speed of the stopper decreases, the string will eventually go slack, indicating that the string is no longer exerting a force on the stopper. Then the stopper will no longer travel on a circular path and your fingers will not be providing any force to the string.

64. Part B
5a. As the speed of a roller coaster increases, a larger centripetal force is required to keep it moving in a circle at a constant speed. 5b. As the mass of a roller coaster increases, a larger centripetal force is required to keep it moving in a circle at a constant speed. 5c. As the radius of the curve of the roller coaster decreases, a larger force is required. If the radius increases, the required force is smaller.

65. Part B
6a.A very high speed would require a very large force. 6b. If there were zero speed, there would be no force required. If you were going very slowly, a very small force would be required.

66. Part B
7a. (diagram) 7b. The velocity vectors should be tangent to the circle at each position. 7c. The centripetal force vectors should always point toward the center of the circle.

67. Part B
8a. The gravitational force is always downward. At the bottom of the loop, the normal force due to the track acting on the car will be upward. FN Fg

68. Part B
9a. The gravitational force vector should be pointing down. 9b. The force of the track (normal force) should be pointing up, opposite the gravitational force vector. 9c. The force of the track pointing up (normal force vector) should be larger than the weight (gravity vector) force acting down

69. Part B
10. The normal force at the bottom must be larger than the weight to provide a net force upward toward the center of the circle.

70. Part B
11a. The force required to keep the roller coaster moving in a circle would be very large. At the top of the loop for a roller coaster going very fast, most of the downward force is provided by the track. For a person sitting in a roller coaster car, the downward force would be provided by the seat. Depending on the speed of the roller coaster, at the top of the loop, the riders may either feel that they weigh more than the normal or less. In either case, the seat is pressing down on the rider to accelerate the rider toward the center of the circle.

71. Part B
11b. The roller coaster goes slower at the top of the loop than at the bottom, and at the top of the loop the weight contributes to the force toward the center. This means that the loop does not have to supply as much force at the top as it would at the bottom. Therefore, the track would not have to be constructed to withstand as much force at the top as at the bottom.

72. Summary of forces in a circle
p69
Draw a large circle. Draw vectors and label the forces of gravity, normal force, and centripetal force in 4 places (top, bottom, left, right)
force diagram for circular motion top
left right
FC = Fg + FN
Fg is the same everyplace
FN is the normal force of
the track pushing back on
the cart = the apparent weight
bottom

73. What is the apparent weight at the top? The bottom?
Draw a force diagram for a fast-moving roller coaster using the values in the chart below:
Centripetal force
Weight due to gravity
Normal force
Top of loop
1000 N
4000 N
Bottom of loop
10,000 N
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What is the apparent weight at the top? The bottom?

74. What is the apparent weight at the top? The bottom?
Draw a force diagram for a slow-moving roller coaster using the values in the chart below:
Centripetal force
Weight due to gravity
Normal force
Top of loop
1000 N
1100 N
Bottom of loop
7100 N
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What is the apparent weight at the top? The bottom?

75. Fc = mv2/r Fc = Fg + FN How do you calculate Fc?
p69
Fc = Fg + FN
1.) What is the centripetal force of a roller coaster if the mass is 10 kg and if the normal force is 25 N?
How do you find the speed in a loop?
Fc = mv2/r
r = radius
2.) How fast is a 200 kg roller coaster going if the radius of the loop is 200 m and the centripetal force is 100 N?

76. 3.) Why don’t you fall out of a roller coaster when it goes upside down in a loop? 4.) So what keeps the roller coaster car on the track, and why is a clothoid loop better than a circular loop?
Clothoid loop: Larger radius at the bottom, smaller radius at the top. Larger radius means smaller acceleration
At the top of a small circle the normal force is smaller and as speed decreases Fc becomes less and less. At the same point FN = 0 leaving a small gap between the car and the track. So Fc must be greater than Fg to keep the car moving in a circle.
At the bottom a small radius would contribute to greater acceleration, beyond what a human body can withstand (4g’s = 40 m/s2). So to slow down the car a larger radius is needed (leading to the clothoid shape instead of a simple circle).
Finish CU (p429) 1-5 and PtoGo (p ) only
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77. Loop-the-Loop: summary
video
In the loop-the-loop (like in a roller coaster), the velocity at the top of the loop must be enough to keep the train on the track:
v2/r > g
Works out that train must start ½r higher than top of loop to stay on track, ignoring frictional losses
After watching the video, read over your notes from last time and record 4 things you learned about loops in roller coasters (write this at the end of the handout on the lines provided)
Share out ½r r

78. Energy Model update
13. An object moving in a curved path must have a force pointing toward the center of a circle, or it will continue in a straight path. This force is called centripetal force. 14. The normal force is the force that pushes back on an object and is equal to the apparent weight 15. Centripetal force Fc = mv2/r 16. Centripetal acceleration ac = v2/r 17. For objects travelling in a circular path at a constant speed, the centripetal acceleration and force are always perpendicular to the object’s velocity
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79. Energy Quiz #2 tomorrow Roller Coaster Design due tomorrow
Finish p70 from yesterday
Complete this problem
Do PtoGo (p ) 3-11
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Mass of car = 200 kg g=10 m/s2
Position of car= height (m)
GPE=mgh
KE=1/2mv2
GPE+KE= total energy
How fast is the car going?
Top (30 m)
Bottom (0 m)
Halfway down
7.5 m

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

81. Friday
1.) QUIZ! You may use your notebooks, but no phones! 2.) Finish p Get stamps when done! ________________________________________________ 3.) Turn in My Roller Coaster Plan (one per team) 5.) NRG SK8TR. Use a computer to complete handout. Get a stamp when finished. This is page )Extra credit due Monday before school (when we return) HAVE A GREAT WEEK!

82. What do you need to do to pass this class? The Main Event…
Welcome Back! p
What do you need to do to pass this class?
The Main Event…
What is “the main event”?
Describe at least 3 things other students do to distract from the “main event”
Describe at least 3 things you do/allow to distract you from the “main event”
What are you doing/can you do in physics to demonstrate the “main event”?

83. Section 8 Work and Power: Getting to the top (p436-438)
What do you see?
What do you think?
Does it take more energy to pull the RC up a steep
incline than a gentle incline?
Why is it more difficult to walk up a steep incline
than a gentle incline?
As a CLASS discuss/record #1
As a lab group, go to your assigned lab bench and collect the data, then return to your table to make the graph (20 minutes total)
P75

84. Section 8 Work and Power: Getting to the top (p436-438)
#2-4 Use equipment to fill in the chart below
Now make a line graph
of your data (put a graph
stamp in your notebook!)
Distance (cm along ramp)
Force
(in Newtons)
30 cm
40 cm
50 cm
60 cm
70 cm
80 cm
90 cm
100 cm
110 cm
force
Distance (cm)

85. Sample data p75 Calculate the amount of work for each data point
Distance x
Force =
work 30
1.43 40
1.07 50
0.86 60
0.72 70
0.61 80
0.54 90
0.48
100
0.43
110
0.39
Average work
Calculate the amount of work for each data point
and then the average work

86. As a CLASS discuss/record sample data/graph
#5: As the ramp gets steeper, the force required to get the car to the top is __________
#6 As the ramp gets steeper the amount of work ____
#7: What is the average work needed to move the car up the ramp?
#8: Does it take more energy/work to pull a roller coaster up a gradual ramp or a steep ramp? Explain.
Ppt notes (handout)
Complete CDP 9-1 and get a stamp
Energy Quiz #2 corrections

87. 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
Mechanical advantage is a ratio of the force required (or the distance the force is
applied over)
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88. Ramps
Exert a smaller force over a larger distance to achieve the same change in gravitational potential energy (height raised) M
Larger Force Small Force
Short Distance Long Distance
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89. Gravitational Potential Energy
Gravitational Potential Energy near the surface of the Earth:
DW = mg  Dh 
Work =
Force
Distance m Dh m
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90. 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 calories, or 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
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91. How much work?
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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?

92. 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
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93. Power
Power is simply energy exchanged per unit time, or how fast you get work done (Watts = Joules/sec)
One horsepower = 745 W
Perform 100 J of work in 1 s, and call it 100 W
Run upstairs, raising your 70 kg (700 N) mass 3 m (2,100 J) in 3 seconds  700 W output!
Shuttle puts out a few GW (gigawatts, or 109 W) of power!

94. Energy model:
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18.) Work = distance x force (and is equal to the amount of PE at the top) Work is measured in newton meters =joules 19.) The amount of work is dependent on how high you must move an object, not the path that you take to get it there (gradual slopes require the same work as steep slopes) 20.)Power = work/time. Power is measured in joules/second = watts

95. Section 9 Force and Energy: Different insights (p448-450)
Together: Read /Answer p449 (6-9)
Individually: Read p 441 and answer CU (p442) 1-5
Then do PtoGo (p ) #2-6 and Energy at the Amusement Park
Get a stamp when finished

96. PtoGo (p ) #2-6 Answers
2a.) no work (because the displacement is horizontal, not vertical) b.) 30 J c.) 3000 J d.) 350 J 3. Conserve energy can also mean don’t waste energy 4. The force to lift the cart up the incline would have changed, so the total work would have changed. The cart’s GPE at the top of the ramp would be larger. The work in all the trials would be the same. 5a.) J b.) 1333 watts 6.) The motor does positive work on the roller coaster to bring it to its highest point. As the coaster goes down the hill, gravity does the work to increase the KE (as the GPE decreases)…
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97. Section 9 Force and Energy: Different insights (p448-450)
What do you see? What do you think?
Draw your concept map in your notebook. Just do #1-5
Go back to your Energy Model and highlight the important terms.
Add at least 20 terms from your Energy Model to your concept map
Get a stamp when finished
Roller Coasters
Forces and
Interactions
Energy

98. Concept map example

99. Section 10 Safety is required, but thrills are desired (p458-460)
What do you see?
What do you think?
Does the knowledge that people can get hurt or die on a roller coaster change the thrill of the ride?
Would your answer change if you found out that one-half of all roller coaster rides ended in the death of its passengers?
As a class, discuss/record #1-6
Read p464. Answer CU (p464) 1-4
CU (p453) 1-5/PtoGo (p ) #1,2,6,7
Get stamps when finished
Notebook check and UNIT TEST NEXT TIME!
Review/practice test posted on my website