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1. Energy Modeling Unit VII

2. Whiteboard the Lab Results: • Sketch the graph for your spring • Identify the color of your spring • Just the straight line (no points) • Label each axis with their proper units • Write the equation for your spring • Replace y and x with the actual variables from the graph • Include units for the slope and y-intercept • Write down what you think each of the following represent • slope • the y –intercept represent about the spring. • The Area between your line and the displacement (stretch) axis

3. Warm-up Question The equation for a spring is: FT = (25N/m) Δd + 2.5N Determine the following: a)The tension force (FT ) required to stretch the spring 0.50 m. b) The amount of mass you would need to hang from the spring to stretch it 0.50m

4. 50 45 F (N) 40 35 30 25 20 15 10 5 0 0.5 1 1.4 0 Δd(m) Spring-Force Lab Results

5. 50 F = (25N/m) Δd + 2.5N 45 F (N) 40 35 30 25 20 15 10 5 0 0.5 1 0 Δd (m) How much mass needs to be added to the red spring to stretch it approximately 0.50 m? F = (25 N/m) (0.50 m) + 2.5N = 12.5 N +2.5N = 15.0 N FT = 15.0 N = Fg = mass (10N/kg) mass = 0.150 kg =150 g

6. Hooke’s Law for Springs • “k” = spring constant (strength of spring) • Ideal springs have no preload (F0). • Any amount of force on a spring causes it to stretch. General Equation:

7. Effort to Stretch Spring • The energy to stretch a spring involves the combination of… • The force of tension in the spring (FT) • The displacement or stretch of the spring (Δx) • How do we represent this force-stretch combination? … or the combination of two values in general?

8. Review: finding displacement (Δd) • If you are moving your displacement depends on 2 things… • How fast you are traveling • How much time you are traveling at that speed • We found this graphically by finding the area under the curve of a velocity versus time graph. During Constant Velocity: During Acceleration: Δd = (½)•bh = 9m Δd = (2m/s)•6s = 12m

9. 50 45 FT(N) 40 35 30 25 20 15 10 5 0 0.5 1 0 Δd (m) Representing Effort to stretch a spring: Effort to stretch spring = area under FTvs. stretch (Δd) graph Effort =

10. Finding Effort Mathematically • The effort exerted to stretch a spring can be used to do things (launch a projectile, etc…) • We can say that ENERGY is stored in a stretched or compressed spring. Energy stored In a Spring (Eel) = Area under The graph

11. Energy Stored in a Spring (Eel) Eel = Elastic Energy k= Spring Constant Δd= displacement or stretch Joules (J) are the standard units for ENERGY  A calorie is also a unit of energy.

12. Money Analogy for Energy • Use a whiteboard to illustrate how money (\$) is used and moves in our society: • Consider the following questions? • How is \$ moved or is transferred in society? • What can you do with \$? • Where is \$ stored when it is not being transferred? • How do individuals get \$? • Etc... Be creative! (school appropriate and legal)

13. Important Ideas about Money • \$ is transferred between people • You get \$ by working • \$ gives you the ability to do things • \$ is stored in different places (banks, pockets, etc…) • The flow of money can be cyclic

14. Analogy for Energy • Spring – our system, something that can store energy. • A spring is like a bank, a place where \$ can be stored. • Energy – gives you the ability to do things / change things. • Energy is like \$, which gives you the ability to do things in society. • It cannot be created or destroyed, just transferred from one place to another. • “Working” – transferring energy from one system to another. • Working = transferring \$ from one person to another(losing and gaining \$)

15. Energy (\$) Storage Accounts • Elastic Energy Account (Eel)–you can store energy in an elastic material by working on it (apply a force over some displacement) • Gravitational Energy Account (Eg) – you can store energy in the Earth’s gravitational field by increasing the distance between the earth and an object. • Kinetic Energy Account (Ek) – the energy stored in moving objects. • Internal Energy Account (Eint) – the energy stored in the random motion of atoms in a system. Measured by change in temperatures.

16. Energy Bar Charts (LOL) • A visual way to account for the energy in a system. Where the energy is being stored and any transfers, into or out of the system (bank)

17. Final Initial Worksheet 3a (Problem #1) v1 • Define the system as… Spring + Cart + Earth • NO FRICTION Spring + Cart + Earth

18. Final Initial Worksheet 3a (Problem #1) v2 • Define the system as… Spring + Cart + Earth • WITH FRICTION Spring + Cart + Earth

19. Final Initial Worksheet 3a (Problem #1) v3 • Define the system as… Cart + Earth • NO FRICTION Cart + Earth + work is done on the cart by the spring

20. Final Initial Worksheet 3a (Problem #1) v4 • Define the system as… the Spring • NO FRICTION Spring • Work is done • on the spring by • the cart

21. Kinetic Energy Account: • What visually tells us that an object has more or less kinetic energy (Ek)? • Its velocity or speed • …so the kinetic energy an object has depends on its velocity.

22. Studying Kinetic Energy (Ek & V) Ek(J) Ek (J) V(m/s) • If we pull the cart back, what kind of energy is stored in the system? • Where does the energy go when you release the car and the spring has lost all its stored energy? ? 0 0 V(m/s) Motion Sensor Δx m = 0.291kg

23. Kinetic Energy (Ek) • The energy stored in moving objects. • Depends on the mass and velocity of an object. • Kinetic energy increases as mass increases. • Kinetic energy increases when velocity increases.

24. Energy Review • What is energy? • The ability to do something • Gained or lost through “working” (W=FΔx) • How or where can energy be stored? • In a stretched spring or elastic material (Eel = 1/2k(Δx)2) • In a moving object (Ek = 1/2mV2) • By raising an object off the ground (Eg =?) • In the motion of atoms or molecules (Eint)

25. Gravitational Energy (Eg) Account • To be above the ground something has to do work ON the car to give it some Eg: F =_____ h Fg = mg Eg = g = 10N/kg

26. Whiteboard Problem • How high should the cart be placed so that it will have a velocity of 1m/s when it goes through the photogate? (Photogate) m = 0.291kg h = ? h = 0m

27. Solving Other Problems • Changing gravitational energy to kinetic energy is useful for solving many different types of problems. Freefall Straight Ramps Curved Ramps Pendulums 1 1 1 1 h 2 2 2 2 The speeds will be the same, but the directions different!

28. Final Initial WK3a Problem #2 20m • What is the car’s velocity halfway up the loop? m = 500kg k = 8000N/m Δx = 5m h = 0m h = 10m V = ? Cart Spring Earth

29. WK3a Problem #8 Initial: Final: • How much force did Super Man use when stopping the train? m = 100,000kg V = 22.7m/s or 50mi/hr Δx = 50m V = 0m/s F = ? Train Superman

30. Whiteboard Problem • You are driving along at 22.7m/s (50mph) on a wet country road late at night when a deer jumps out 20m in front of your car. If you immediately slam on your breaks how fast will you be going when you hit the deer? The car’s mass is 1500kg and the coefficient of kinetic friction is 0.6

31. v = 0 5 height (m) m = 20 kg v = ? 0 WK3b Answers #1 & 2 1. Δx = 2m 2. V = 9.5m/s 100J 100J Cart + Earth + Spring 1000J 900J Cart + Earth 100J

32. Initial Final m = 500 g v = 0 k = 100 0 x = 0.30 m Initial Final WK3b Answers #3 & 4 3. h = 0.9m 4. Δx = 0.03m Block + Earth + Spring 4.5J 4.5J Bullet + Earth 1,531J ? ? W = -1,531J

33. Unit VII WK3b Answers • 5. a. discuss b. c. Working by engine = work done by friction = 1000J d. Since the Fengine> fk then the box will accelerate: a = 0.5m/s2 • 6. Δx = 20m • 7. b. Fx = 86.6N  W = 866J c. the box is accelerating because Fx > fk d. Working by friction = 675J e. discuss

34. Δx=0.35m Unit VII WK4 Answers F=? • 1.a. b. F = 180N • 2. a. Eg = 6000J b. Ek = Eg = 6000J c. V = 14.14m/s d. V = 20m/s or 1.4 times more e. htotal = 40m or 30m higher than the original height • 3. V = 16.5m/s • 4. V = 33m/s, twice the original velocity Ek = W ball -W done by glove on ball h=10m

35. Unit VII WK4 Answers W=Ek V=0m/s V=? • 5. Vbullet = 967m/s • 6. a. Eint = 1106J b. See notes Δx=0.85m 1200J Child Slide Earth 94J Eg=mgh Ek=1/2mV2

36. WK4 Problem #6 • A 24kg child descends a 5.0m high slide and reaches the ground with a speed of 2.8m/s. • How much energy was dissipated due to friction in the process? • Do a pie chart analysis of the final state, using accurate % of the pie to represent the amount Eint in the process.

37. Power • One of the events in the “World’s Strongest Man” competition is called Atlas Stones. Five stones are placed at the base of five platforms. • Strength or power is judged by the time it takes to complete the task. Units: J/s = Watts …also measured in units of horsepower (746W = 1hp)

38. PHHS Strong Student Competition • Find the total work done / energy exerted and the amount of time to do it.