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Energy

Energy. What is it? Energy is conserved How do we use it in physics. An Energy Pathway. We need energy Where does it come from? Where does the energy in food come from?. An Energy Pathway. An Energy Pathway. Where does the Energy of the Sun come from?. Energy.

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Energy

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  1. Energy What is it? Energy is conserved How do we use it in physics

  2. An Energy Pathway • We need energy • Where does it come from? • Where does the energy in food come from?

  3. An Energy Pathway

  4. An Energy Pathway • Where does the Energy of the Sun come from?

  5. Energy • Energy can be transformed from one form to another. Nuclear-> Heat and Light Chemical Mechanical • What is conversion rate? • We can account for every bit of energy along the way. ENERGY IS CONSERVED

  6. The Law of Conservation of Energy The total energy of the Universe is unchanged by any physical process. Energy may be converted from one form to another or transferred between bodies. It never disappears. It cannot be created or destroyed.

  7. Does the power generated • affect the speed of the wind? • Would locations behind the • “windmills” have more wind if • the windmills weren’t there? • Yes • No

  8. Energy • Energy has a somewhat abstract nature. Try to be concrete. • Energy is the property of a system that enables it to do work. • What is work?

  9. Work by a Constant Force Work is an energy transfer by the application of a force. For work to be done there must be a nonzero displacement. This is a bit circular. Work = Force x Distance if F and D are parallel. If not use the component of F that is parallel to displacement The unit of work and energy is the joule (J). 1 J = 1 Nm = 1 kg m2/s2.

  10. Is he doing any work against the wall? A) Yes B) No

  11. y F rx rx N  x  w F It is only the force in the direction of the displacement that does work. An FBD for the box at left: The work done by the force F is:

  12. The work done by the normal force N is: The normal force is perpendicular to the displacement. The work done by gravity (w) is: The force of gravity is perpendicular to the displacement.

  13. The net work done on the box is:

  14. Fig. 06.08

  15. In general, the work done by a force F is defined as where F is the magnitude of the force, r is the magnitude of the object’s displacement, and  is the angle between F and r (drawn tail-to-tail).

  16. r y x w Example: A ball is tossed straight up. What is the work done by the force of gravity on the ball as it rises? FBD for rising ball:

  17. y F N F x   w Example: A box of mass m is towed up a frictionless incline at constant speed. The applied force F is parallel to the incline. What is the net work done on the box? An FBD for the box: Apply Newton’s 2nd Law:

  18. Example: What is the net work done on the box in the previous example if the box is not pulled at constant speed? Proceeding as before:

  19. Energy and Work • We defined energy and work • Review: Work can be negative • Machines –help us do work • Kinetic Energy • Potential Energy

  20. r y x w Example: A ball is tossed straight up. What is the work done by the force of gravity on the ball as it rises? FBD for rising ball:

  21. Question A box with mass m1 is being pulled up a rough incline by a rope-pulley-weight system. How many forces are doing work on the box? A) one force B) two forces C) three forces D) four forces E) no forces are doing work Gravity, friction and tension

  22. Machines • Machines help us do work. • They can increase the Force at our disposal. • We still have to do the same amount of work. • Energy is conserved!!

  23. Fig. 06.03

  24. Fig. 06.10

  25. Kinetic Energy • An object that is moving has the ability to do work The faster the ball is moving the more the pins will bounce. The heavier the ball the more the pins will bounce

  26. Kinetic Energy is an object’s translational kinetic energy. This is the energy an object has because of its state of motion. It can be shown that, in general

  27. Example: The extinction of the dinosaurs and the majority of species on Earth in the Cretaceous Period (65 Myr ago) is thought to have been caused by an asteroid striking the Earth near the Yucatan Peninsula. The resulting ejecta caused widespread global climate change. If the mass of the asteroid was 1016 kg (diameter in the range of 4-9 miles) and had a speed of 30.0 km/sec, what was the asteroid’s kinetic energy? This is equivalent to ~109 Megatons of TNT.

  28. Gone with the Wind • 20 mph winds hardly ever do damage • 60 mph almost always do: uproot trees, rip shingles off roofs. Why? • 60 mph winds have 9 times the energy (1/2mv2) and can do 9 times as much (destructive ) work

  29. How much work do the brakes do when your car decreases its speed from 25m/s to 20 m/s? Take m= 1,500 kg ΔK = ½mvf2 - ½mvi2 = ½m(vf2 – vi2 )

  30. Question Compare the kinetic energy of two balls: ball 1: mass m thrown with speed 2v ball 2: mass 2m thrown with speed v A) KE1 = 4KE2 B) KE1 = KE2 C) 2KE1 = KE2 D) KE1 = 2KE2

  31. Question Your brakes can apply a constant force, F, to the wheels of your car. If it takes a distance of 30 m to stop when you are traveling 40 km/hr, what distance is required to stop when you are traveling 120 km/hr? A) 10 m B) 90 m C) 110 m D) 270 m

  32. Potential Energy • Object can store energy because of its position. Examples • A stretched or compressed spring • A drawn bow • Water in an elevated reservoir • Chemical energy because of the position of electrons

  33. Gravitational Potential Energy Objects have gravitational potential energy (PE) because of their elevated position.

  34. Gravitational Potential Energy Objects have gravitational potential energy (GPE) because of their elevated position. Work is done to lift an object and this is equal to the amount of GPE. Lifting an object up to a height h at constant v requires a Force of mg F We can get this back Work = FΔx = mg Δx =mgh =GPE mg This is minus the work done by gravity -Wg

  35. The change in gravitational potential energy (only near the surface of the Earth) is where y is the change in the object’s vertical position with respect to some reference point that you are free to choose.

  36. GPE depends only on h not on how it got there

  37. Example: What is the change in gravitational potential energy of the box if it is placed on the table? The table is 1.0 m tall and the mass of the box is 1.0 kg. First: Choose the reference level at the floor. U = 0 here.

  38. Example continued: Now take the reference level (U = 0) to be on top of the table so that yi = 1.0 m and yf = 0.0 m. The results do not depend on the location of U = 0.

  39. Potential Energy Objects have potential energy because of their location (or configuration). There are potential energies associated with different (but not all!) forces. Such a force is called a conservative force. Friction is not a nonconservative . In general

  40. Mechanical energy Whenever nonconservative forces do no work, the mechanical energy of a system is conserved. That is Ei = Ef or K = U.

  41. Conservation of Mechanical Energy

  42. Conservation of Mechanical Energy

  43. Exam on Monday • Covers chapters 4 & 5 (lectures posted on course website) • Same format as first exam • Equation sheet from Master the Concepts section • Will post answers to Practice exam • First exam: I will add 5 pts to everyone’s grade.

  44. Energy • Energy • Work • Kinetic Energy • Potential Energy • Conservation of Mechanical Energy • K+U = constant • More on Gravitational Potential Energy • Variable forces • Power

  45. Example (text problem 6.28): A cart starts from position 4 with v = 15.0 m/s to the left. Find the speed of the cart at positions 1, 2, and 3. Ignore friction.

  46. 40 m 20 m y=0 Example (text problem 6.84): A roller coaster car is about to roll down a track. Ignore friction and air resistance. m = 988 kg • At what speed does the car reach the top of the loop? • What is the force exerted on the car by the track at the top of the loop?

  47. y x N w Example continued: (b) What is the force exerted on the car by the track at the top of the loop? FBD for the car: Apply Newton’s Second Law:

  48. Example continued: (c) From what minimum height above the bottom of the track can the car be released so that it does not lose contact with the track at the top of the loop?

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