Chapter 3

1. Chapter 3 Energy (Spring 09)

2. Especially college students What 4-letter word in the English language upsets more people than any other?

3. Work is defined as being the product of a force and the distance the force moves in the direction of the force. Movement must happen in the direction of the force. The force and the motion cannot be perpendicular. No work is done in holding something. No work is done in carrying something parallel to the ground. No work is done in doing physical science homework unless a pencil or pen is pushed along the paper. Work

4. Work = force x distance moved W = F • d (put on formula sheet) What work is done when a force of 10 N is used to push an object 3 m? Note that the weight or mass of the object is not important, only the force necessary to move it. Work

5. 1 joule = 1 newton • 1 meter A joule is the work done in pushing with a force of one newton for a distance of one meter. James Prescott Joule was an English brew-master. We will hear more of him later. 3q The joule

6. Work = force x distance When we lift something, the force necessary to lift it is the weight of the object w=mg (force) Therefore, the work necessary to raise an object a height h is W=mgh (formula sheet) = work h is the height the object is raised (or lowered). The weight is w=mg, don’t confuse weight and work. Weight is a force that can do work. Work against gravity

7. Calculate the amount of work for a 100 kg person to climb stairs that are 10 m high. • Data • W=? • m=100 kg • h=10 m

8. How fast can you work? • Power is the rate of doing work. • Power = work/time Formula sheet! If 30 joules of work is done in 6 seconds, what is the power?

9. One watt is one joule per second. Watt = joule/sec 5 watts = 5 w Units of power

10. What is my power if my mass is 70 kg and I can climb stairs that are 10 m high in 3 seconds? One horsepower is 746 watts so 2286 W is 3.1 horsepower. This calculation is necessary for your pre-lab next week (measure your horsepower). Note that this says nothing about how steep the stairs are, only their height. 2q

11. Energy is the ability (capacity) to do work. Energy comes in many forms: Heat energy Chemical energy Food Gasoline Dynamite Potential energy Kinetic energy If I have a lot of energy I can do a lot of work.

12. Potential energy is energy due to the position of an object. Examples of potential energy include: A compressed spring A nail near a magnet A car on a hill Gravitational potential energy Potential energy

13. Energy = work done To have one joule of energy, I must do 1 joule of work to raise the object. The units of work are also joules. The force of gravity is mass times the acceleration of gravity W = mg Gravitational Potential Energy

14. P.E. = Work = force • distance W = f • d f = Weight = W = mg d = distance = height = h P.E. = mgh (Formula for gravitational potential energy) This applies only on the surface of the Earth. Gravitational P.E. (cont)

15. What is the P.E. of a 20 kg block, 2 m above the floor? Gravitational P.E. (cont)

16. Kinetic energy is the energy something has because it is moving. Energy of motion K.E. = ½ mv2 Where m = mass of the object v = velocity of the object Kinetic Energy

17. What is the K.E. of a 70 kg person running 10 m/s? Kinetic energy

18. Energy – the ability to do work Potential energy P.E. = mgh Kinetic energy K.E. = ½ mv2 Energy – a review

19. Conservation of Energy Energy may be changed from one type to another but the total amount of energy remains the same.

20. Total energy is always conserved We will be especially interested in situations in which mechanical energy is conserved This means no energy is given to heat or friction When mechanical energy is conserved, the sum of the potential and the kinetic energies will remain constant. There are many types of problems we can solve using this knowledge. This will be the idea that will be worth more points on the next two tests than any other topic. More on conservation of energy

21. 100% P.E at the top 90% P.E. 10%K.E. 80% P.E. 20%K.E 70% P.E. 30%K.E 60% P.E. 40%K.E 50% P.E. 50%K.E half way down 40% P.E. 60%K.E 30% P.E. 70%K.E 20% P.E. 80%K.E 10% P.E. 90%K.E . 100%K.E at the bottom Energy conservation- Changing P.E. to K.E. and K.E. to P.E. - - - - Case 1: A falling object

22. At the top – All P.E. 1/3 of the way from the top 2/3 P.E., 1/3 K.E. Half way down ½ K.E., ½ P.E. 1/3 of the way from the bottom, 1/3 P.E., 2/3 K.E. At the bottom – All K.E. P.E. to K.E. and K.E. to P.E.

23. You will be asked to add one additional step in the solution of these problems. That step is the principle. In the principle you must give the state of the energy of the system in its initial state and its final state. For this problem the principle is: Potential Energyis changed to Kinetic Energy. mgh = ½ mv2

24. Potential to Kinetic • What is the velocity of an object after falling 10m? • v=? • h= 10m • Initial state = Potential energy • Final state = kinetic energy • Principle P.E. = K.E. • mgh = ½ mv2 3q

25. Kinetic to Potential • How high will an arrow go that is shot straight into the air with an initial velocity of 100 m/s? • h = ?, v = 100 m/s • Initial state = kinetic energy • In this problem the arrow has already been shot and is moving with a velocity of 100 m/s. • But it is still at zero height. • final state = potential energy • ½ mv2=mgh • Solve the equation for h 3q

26. Work to Kinetic energy Work to Potential energy Kinetic energy to work Potential energy to work The energy can be used to do work or work can be used to give energy.

27. Work to energy and energy to work • A 3 kg hammer moving 10 m/s hits a nail and drives it 2 cm into a board. What was the force on the nail? • m = 3 kg v = 10 m/s d = 2 cm = 0.02 m F=? • A falling hammer (K.E.) drives a nail (work)(force x distance) • Principle K.E. = work • ½ mv2=F·d 3q

28. How fast will a 5 kg rocket be traveling if its motor has a force of 2000 n and it operates for 500 m horizontally? • v=?, m=5kg, F=2000N, d=500m • Principle: work = K.E. • F·d=½ mv2 • v=? • m=5kg • F = 2000 n • d = 500 m

29. Work to energy and energy to work • A 3 kg hammer moving 10 m/s hits a nail and drives it 2 cm. What was the force on the nail? • m = 3 kg v = 10 m/s d = 2 cm = 0.02 m F=? • A falling hammer (K.E.) drives a nail (work)(force x distance) • Principle K.E. = work • ½ mv2=F·d

30. How fast will a 5 kg rocket be traveling if its motor has a force of 2000 n and it operates for 500 m? • v=?, m=5kg, F=2000N, d=500m • Principle: work = K.E. • F·d=½ mv2 • v=? • m=5kg • F = 2000 n • d = 500 m

31. Two types: Linear momentum and angular momentum Linear momentum = mass times velocity In the absence of outside forces, the total momentum of a group of objects remains unchanged (even if the objects collide). Useful when objects collide or when they separate (boy jumping from wagon, etc) Angular momentum = radius x mass x velocity Useful for systems, such as planets, comets, etc We will only do calculations with linear momentum. Conservation of momentum

32. m1 is the mass of object one. v1i is the initial velocity of object one. m2 is the mass of object two. v2i is the initial velocity of object two. v1f is the final velocity of object one. v2f is the final velocity of object two. m1 v1i + m2 v2i = m1 v1f + m2 v2f momentum before collision = momentum after m1 v1i m2 v2i This needs to go on your formula sheet!

33. Example one A 500 kg car traveling 20 m/s collides head-on with a 2000 kg truck traveling 10 m/s in the opposite direction. The two stick together after the collision. What is the direction and velocity of the two after the collision? DATA This minus sign is very important

34. General equation m1 v1i + m2 v2i = m1 v1f + m2 v2f In our special case (v1f = v2f = vf ) m1 v1i + m2 v2i = (m1 + m2)vf 500 kg•20 m/s+ 2000 kg•(-10 m/s)=(500+2000)kg•vf 10,000 kg m/s-20,000 kg m/s = 2500 kg • vf -10,000 kg m/s = 2500 kg • vf vf = -10,000 kg m/s 2500 kg vf = -4 m/s Direction is that of the truck

35. A 70 kg man stands on a 20 kg boat in the water and jumps with a velocity of 5 m/s. What is the recoil velocity of the boat? Another momentum example

36. General equation m1 v1i + m2 v2i = m1 v1f + m2 v2f In our special case (v1i = v2i = 0 ) 0 =m1 v1f + m2 v2f - m1 v1f = m2 v2f -70 kg•5 m/s = 20 kg•vf vf = -350 kg m/s 20 kg vf = -17.5 m/s Direction is opposite the way the man jumped. The minus sign tells us the direction.

37. A colorless, odorless liquid that is in most substances. When a substance burns the caloric in it is given off as heat This theory explained heat until the 18th century. Caloric

38. An American who fled the U.S. in 1773 because of British sympathies. Became a military consultant (mercenary) Took the name of Count Rumford Made cannon Discovered that heat is a form of energy Set up the first public school for the children of his workers. Benjamin Thompson

39. An rich English beer maker who liked to do science experiments. James Prescott Joule showed how many joules (unit of energy) were in a calorie (unit of heat). 1 calorie = 4.2 joules (put on formula sheet) 1 calorie is the amount of heat necessary to raise the temperature of one gram of water one degree Celsius. James Prescott Joule

40. Didn’t like grade school very well Got a doctor’s degree in physics but couldn’t get a job teaching (even in high school) so took a job in the post office (taking care of patents). Takes his girl friend on a trip and she gets pregnant. Child is taken by girl’s relatives, and is not heard of later Writes three papers in physics journals in 1905 that profoundly change three major areas of physics. Becomes most famous scientist of 20th century Guess who

41. Theory of Brownian motion Theory of photons Theory of relativity Two postulates of special relativity The speed of light is always measured to be the same even when two systems are moving with respect to one another. The laws of physics apply in systems that are moving with respect to one another. Albert Einstein

42. The special theory that we have already discussed does not apply to systems that are accelerated or in a gravitational field. The general theory applies to accelerated systems or systems in a gravitational field. The most significant result of the general theory we will note is that gravity affects light. Light is bent by gravity (stars) We can see this when there is an eclipse of the sun. General Theory of Relativity

43. E = Energy m = mass c = speed of light = 3 x 108 m/s (formula sheet) c2 = 9 x 1016 m2/s2 What energy is obtained when 7 grams is changed to mass Data: m = 7 grams = 0.007 kg E = mc2

44. The Energy Problem Energy is necessary for our life style. We are running out of the energy sources we use the most.

45. The cheapest The easiest to use The most convenient The worst for the environment (Global warming and acid rain) Supplies will become limited in our lifetime. Fossil Fuels

46. Natural gas 3-4¢ Coal 4-5¢ Wind 4-5¢ Geothermal 3-8¢ Hydropower 4-10¢ Biomass 6-8¢ Nuclear 10-15¢ Solar thermal 10-15 ¢ Photovoltaics 20-30¢ Energy Costs per kilowatt hour of electricity

48. Burns without pollution H2 + O2 H2O Could be used in cars and distributed at filling stations Car manufacturers are designing hydrogen cars Solar generated hydrogen

49. Cars without engines Each wheel has an electric motor that drives it Skateboard concept All electronic steering, brakes Tops plug-in to the fuel cell base.