Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Eigenstate thermalization hypothesis wikipedia , lookup
Internal energy wikipedia , lookup
Hunting oscillation wikipedia , lookup
Mass versus weight wikipedia , lookup
Relativistic mechanics wikipedia , lookup
Work (thermodynamics) wikipedia , lookup
Roller Coasters: Measures of Effort & Motion; Conservation Laws Who likes to ride a roller coaster?! Black Hole 2000 California Screamin’ Bizzarro Nitro Medusa Space mountain Splash mountain Big Thunder Railroad 1 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? 2 P 54 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. P 55 3 p55 Compare to others: 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? 4 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) p56 5 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 6 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? p56 7 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 (p358-359) 1-5, 10 Get 8 another stamp when Finished p57 Nitro p58 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? 9 Investigation #2 (p360-363) Which roller coaster track will give the bigger thrill? Why? p58 10 What effects the speed of the ball at the bottom of the ramp? p58 11 Mass of the marble Hypothesis: Data Type of marble Summary: 12 Velocity Height of the ramp (angle of the ramp) Hypothesis: Will 2X the height result in 2x the velocity? Data height 1 brick (6.5 cm) 2 bricks (13.0 cm) 3 bricks (19.5 cm) Summary: 13 velocity Length of the ramp Hypothesis: Will 2x the length result in 2X the velocity? Data length velocity Summary: p58 14 Conclusions: What can you do to make the marble speed up? 1. 2. 3. p58 15 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!) p58 16 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 p58 17 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 18 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 19 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 20 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 21 next hill Potential energy Potential energy (PE or GPE) is stored energy caused by 22 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 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 23 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 24 Energy Conversion/Conservation Example P.E. = 98 J K.E. = 0 J 8m P.E. = K.E. = 6m P.E. = K.E. = 4m 2m 0m 25 P.E. = K.E. = P.E. = K.E. = p59 Energy Conversion/Conservation Example 10 m 8m P.E. = 98 J K.E. = 0 J starts out with mgh = (1 kg)(9.8 m/s2)(10 m) = 98 P.E. = 73.5 J K.E. = 24.5 J 6m P.E. = 49 J K.E. = 49 J 4m 2m 0m 26 Drop 1 kg ball from 10 m 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 P.E. = 24.5 J K.E. = 73.5 J P.E. = 0 J K.E. = 98 J ½mv2 = 98 J v2 = 196 m2/s2 v = 14 m/s Finish for next time: p59 Read Active Physics p363-367 Answer CU (p367) 1-5 CDP 9-2 Get a stamp when finished Notebook check and extra credit! 27 Phet: Adventures in Energy Skate Park Use a computer and open the phet sim: Energy Skate Park http://phet.colorado.edu/new/simulati ons/sims.php?sim=Energy_Skate_Park Complete the document Adventures in Energy Skate Park Get a stamp when finished 28 p60 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 29 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! 30 Review the Energy model Driving question: How do roller coasters work? Energy comes from doing work 31 p Energy model Driving question: How do roller coasters work? p61 1. Energy comes from doing work 2. Gravitational Potential Energy (GPE) is the same as PE 3. Potential Energy (PE) is stored energy (must be higher than the ground) 4. Kinetic Energy (KE) is energy in motion 5. Energy can be converted from one form to another 6. The total energy is always the same (Law of conservation of energy) 7. PE=mgh= (mass)(gravity)(height) 8. KE=1/2 mv2=(1/2)(mass)(velocity)2 9. Twice the velocity means four times as much KE! 32 PtoGo (p370) 1. For which track is the speed of the car the greatest at the bottom? Why? (assume no friction) B A p62 33 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 p62 34 p62 PtoGo (p370) 3.) Enlarged Mass = 200 kg g = 10 m/s2 Position/height GPE = mgh 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 35 on handout End (0 m) Stopped/not moving KE = 1/2mv2 Total energy = GPE + KE PtoGo (p370) p69 3.) Mass = 200 kg 36 g = 10 m/s2 Position/height GPE = mgh KE = 1/2mv2 GPE + KE Top (30m) (200)(10)(30) = 60,000 J (½)(200)(0) =0J 60,000 + 0 = 60,000 J Bottom (0 m) (200)(10)(0) =0J 60,000 – 0 = 60,000 J 60,000 J Halfway down (200)(10)(15) = 30,000 J 60,000-30,000 = 30,000 J 60,000 J ¾ way down (200)(10)(7.5) = 45,000 J 60,000 -45,000 60,000 J =15,000 J make an energy bar chart on your paper (PtoGo (p370) #4) 4. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 GPE KE GPE + KE A 37 B C D E Finish PtoGo (p370) #5-10 p62 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 38 Energy Quiz #1 Thursday Finish PtoGo (p370) #5-10 39 Get your work stamped p62 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? 40 p64 Weight (or not to weight!) p64 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 41 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 42 Calculate the weight: 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 43 p64 What happens to your weight on an elevator? Stays the same Goes up Goes down Explain: p64 44 P418 #4 Acceleration (up, down, zero) A. Elevator at rest on Zero top floor Scale reading Explanation (larger, smaller, same) 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 zero same G. Elevator moves up at constant speed H. Elevator comes to rest on the top floor 45 I. Elevator at rest on the top floor 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) 4-9 CU (p415) 1-5 Get stamps when you are finished! p65 46 Check your Answers: PtoGo (p418-419) 5-9 5.) Down 6.) Up 7.) Down 10-1.5=8.5 W=(50)(8.5)=42.5N 8.) rest W=(50)(10)=500N UpW=(50)(10+2)=600N Constant speed =(50)(10)=500N 9.) (in your own words) 47 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 Add to our energy model p61 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. 48 p67 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. 49 1.) What propelled the popper into the air? When the popper 50 abruptly returns to its original shape, its elastic potential energy is transformed into kinetic energy and then gravitational potential energy 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. 51 p67 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) p67 52 p67 Active Physics p380-381) 1-13 1.) Position above table EPE (J) At rest on table h= 0 m 25 Just after popping h= 0 m At peak h= 0.60 m ½ way up h= 0.30 m h= (?) h=(?) 53 KE (J) GPE (J)=mgh Mass = 4.16g Total energy= EPE + KE + GPE Active Physics P to Go (p380-381) 1-13 2. p67 30 25 20 EPE KE GPE total 15 10 5 0 At rest 54 just after popping at peak 1/2 way up 3/4 way up p68 Finish PtoGo (p380-381) 1-11 55 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? p68 56 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!) steps 1-4 Part B: How much force is required? (10 more minutes!) Record answers in your notebook Share out p68 Answer CU (p429 (1-5) 57 Diagram of centripetal force on a roller coaster Active Physics Section 7 Investigation (p420-421) Part A: Moving in Curves Steps 1-4 p68 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 58 Active Physics Section 7 Investigation (p422-424) 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 59 p68 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). 60 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 61 increases. 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. 62 Part B (force and vertical circles) 63 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. 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. 64 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. 65 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. 66 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 67 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 68 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. 69 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. 70 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. 71 p69 Summary of forces in a circle 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 72 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 1000 N 10,000 N p69 73 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 1000 N 7100 N p69 What is the apparent weight at the top? The bottom? 74 How do you calculate Fc? p69 F c = 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 = 2 mv /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? 75 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 (p433-435) 10-14 only 76 p70 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 ½r r 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 77 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 p61 always perpendicular to the object’s velocity 78 Energy Quiz #2 tomorrow Roller Coaster Design due tomorrow Finish p70 from yesterday p71 Complete this problem Mass of car = 200 kg Position of car= height (m) g=10 m/s2 GPE=mgh KE=1/2mv2 GPE+KE= total energy Top (30 m) Bottom (0 m) Halfway down 7.5 m 79 Do PtoGo (p380-381) 3-11 How fast is the car going? 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? 80 Friday 1.) QUIZ! You may use your notebooks, but no phones! 2.) Finish p70-72. 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 73. 6.)Extra credit due Monday before school (when we return) HAVE A GREAT WEEK! 81 Welcome Back! p What do you need to do to pass this class? The Main Event… 82 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”? 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 83 Section 8 Work and Power: Getting to the top (p436-438) #2-4 Use equipment to fill in the chart below Distance (cm along ramp) Force (in Newtons) Now make a line graph of your data (put a graph stamp in your notebook!) 30 cm 40 cm 50 cm force 60 cm 70 cm 80 cm 90 cm 100 cm 84 110 cm p75 Distance (cm) p75 Sample data work force vs distance 1.6 Distance x Force = 30 1.43 40 1.07 50 0.86 60 0.72 0.8 70 0.61 0.6 80 0.54 0.4 90 0.48 100 0.43 110 0.39 1.4 1.2 1 force vs distance 0.2 0 0 100 200 Average work 85 Calculate the amount of work for each data point and then the average work As a CLASS discuss/record sample data/graph p75 #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 86 Energy Quiz #2 corrections 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 = Force Distance Distance Mechanical advantage is a ratio of the force required (or the distance the force is applied over) 87 p76 Ramps Exert a smaller force over a larger distance to achieve the same change in gravitational potential energy (height raised) Larger Force Short Distance M 88 Small Force Long Distance p76 Gravitational Potential Energy Gravitational Potential Energy near the surface of the Earth: Work = Force Distance DW = mg Dh m Dh m p76 89 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 P76 90 How much work? p76 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? 91 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 1m Extend over 10 m, and only 98 N (22 lb) is needed Something we can actually provide Excludes frictional forces/losses p76 92 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! 93 Energy model: 94 p61 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 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 (p446-447) #2-6 and Energy at the Amusement Park Get a stamp when finished 95 p77 PtoGo (p446-447) #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.) 200000 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)… p82 96 Section 9 Force and Energy: Different insights (p448-450) p78 What do you see? What do you think? Draw your concept map in your notebook. Just do #1-5 Roller Coasters Energy Forces and Interactions 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 97 Concept map example 98 Section 10 Safety is required, but thrills are desired (p458460) What do you see? p79 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 (p456-457) #1,2,6,7 Get stamps when finished Notebook check and UNIT TEST NEXT TIME! Review/practice test posted on my website 99