Building the Ancient Pyramids…

1. Building the Ancient Pyramids…

2. Located on the Giza Plateau, the Great Pyramid (or Pyramid of Khufu) is truly marvelous • How did the ancient Egyptians build it?

3. Some Stats • Constructed from approximately 2580-2560 BCE • The world’s tallest structure (480 ft, now 460ft) for over 3000 years • The pyramid contains 2 million blocks, each weighing 1.5 tons • Some materials were transported over 500 miles to the construction site • A truly massive undertaking (no pun intended…)

4. Let’s focus on how the blocks were transported to their actual locations on the pyramid • The pyramid has a height of 480 ft • How did they transport massive stones to such heights?

5. Masters of Simple Machines • The Egyptians were smart enough to realize the practical value of simple machines • A machine is a device which can multiply or change the directions of forces • The primary machine used by Egyptians was the ramp, or inclined plane

6. What does the ramp do for us (think back to the lab…) • It reduces the amount of necessary force to transport an object from one location to the other

7. Egyptian Ramps

8. Some Numbers • The force necessary to lift a 1.5 ton block straight up in the air is about 14,000N • The force required to push it up a ramp inclined at 15° is 3500N • The ramp reduces the amount of force necessary to move the block

9. Mechanical Advantage • Without the machine, we’d need 14000N to move the block • With the machine, we need 3500N • The ratio of these two forces is called Mechanical Advantage (MA) • In this case, our MA is 14000N/3500N, which equals 4

10. Which Force Goes Where? • MA = Output Force/Input Force • Input Force is the force we apply, using our machine • Output Force is the force we’d need without the machine (or the effective force we get with the machine)

11. Other Simple Machines • Pulleys • Levers • Screws

12. Pulley Demo • What is the Mechanical Advantage of this pulley system?

13. A Choice of MA • You have the choice of using four simple machines to achieve a task. Machine 1 has a MA of 1.2; Machine 2, 0.5; Machine 3, 4.5; Machine 4, 1 • Which would you choose? • Why?

14. Which machine would do more harm than good?

15. The Catch • Using the ramps, the Egyptians needed less force to push the blocks up the ramp • What was the tradeoff? • They had to move the stones further than they would have by lifting them straight up

16. Think Back to the Lab • What did you notice about the values in the far right column in your data table? • They should have been constant • What does Force x distance represent? • Work

17. Work • We’re all familiar with work • Love it, hate it, we all have to do it • Scientific work however, is a bit different • Work = Force x Displacement

18. Units? • There’s a better way to talk about work than Newtons x meters • To better deal with work, we define a new unit, called a Joule (J)

19. Find the work done by a 10N force that moves an object 30m • 300J

20. Direction Matters • Imagine two situations: • In situation 1, you pick a book up off the ground and lift it up 1m • In situation 2, you walk for 5 miles with the book already in your hand • In which situation do you do more work on the book?

21. One can only do work on an object if the force is in the direction of motion, or against it • The entire force does not have to be in that direction; a piece of a force can also do work on an object

22. A Better Definition • Work = Force x Distance x cos q • W = Fd cos q • **Note: F and d represent magnitudes, not vectors • q is the angle between the force vector and your direction of motion

23. In an airport, a traveler pulls her luggage across the ground with a 20N force, which is at an angle of 35 with the horizontal • If she moves the suitcase 10m, calculate the work done by her pull • What is the work done by friction?

24. Machine Efficiency • In an ideal machine, the work you do with the machine = the work you would do without the machine • In reality, these values are never the same

25. Why? • Think about an Egyptian worker pushing a stone up the ramp • Which other forces does the worker experience? • Friction • He’s got to push a little harder than he would without friction, which results in more work

26. The ratio of the work we get out of the machine to the work we put into the machine is called efficiency • In an ideal machine, it is always 1 • In reality, it is always less than 1

27. Efficiency = Output work/Input work • If we multiply this number by 100, we can represent efficiency by a %

28. Input vs. Output • Using 40N of force, I push a 80kg object 5m up a ramp. Assuming the object starts on the ground and ends 2m high

29. Give the input and out work, respectively: • 1. 80J, 40J • 2. 160J, 200J • 3. 200J, 160J • 4. 40J, 80J

30. In a rope/pulley system, a 4kg mass is raised vertically 0.2m. To accomplish this, a 25N horizontal force is applied over a distance of 0.4m • What is this pulley’s efficiency? • 78-80%

31. + and - Work • So what happens when your angle = 180, and work is negative? • Work is a scalar, so the + and – do not represent direction • They give us some indication of the energy gain or loss of a system

32. What is Energy? • Scientifically, energy gives us the ability to do work • Like work, it has units of Joules

33. Suppose I do 40J of work on an object; what is this object’s change in energy? • (use a – sign if it loses energy…) • Bonus: What if it does 40J of work on me?

34. Work/Energy Theorem • A fancy way of saying what we already know: doing + work on an object gives it energy and doing – work on an object takes energy away

35. Energy Types • Kinetic • Potential • Radiant • Like work, energy is a scalar quantity

36. Kinetic Energy • Kinetic Energy (KE) is energy associated with motion

37. How Much KE? • We calculate an object’s kinetic energy by the equation: • KE = ½ (mass) x (speed)2 • The 2 may not seem important to you, but it explains everything from why baseball players cork bats to why comets are more dangerous than asteroids

38. An elephant (1) and mouse (2) both have the same amount of Kinetic Energy. Which is moving faster? Do they have the same amount of momentum?

39. Assume the elephant from the previous problem (m=1500kg) is running at 10m/s. How much kinetic energy does this elephant have while running?

40. Two objects (A and B) have the same mass, but object A is moving 3 times as fast as object B. What is the ratio KEA/ KEB?

41. Corking Bats and Dangerous Asteroids • The 2 may not seem important to you, but it explains everything from why baseball players cork bats to why comets are more dangerous than asteroids

43. Potential Energy • Potential is “stored” energy that has the potential to do work • A stretched rubber band, a compressed spring, TNT, a nucleus, and a rock on the edge of a cliff all have potential energy

44. Gravitational Potential Energy • Gravitational Potential energy is the potential energy of an object due to its position • GPE = weight x height = mgh

45. So… • The higher an object relative to the ground, the more gravitational potential energy it has…

46. Imagine 3 objects, A, B, and C. Object A is located 2m above the ground; object two has ½ the mass of A and is also 2m off the ground; Object C has ¼ the mass of A and is located 10m off the ground. Rank the GPE of these objects in increasing order • 1. A, B, C 2. B, C, A • 3. B, A, C 4. C, A, B • 5. A, C, B

47. An astronaut in full space gear climbs a vertical ladder on Earth (1). Later, she makes the same climb on the moon (2). In which location does her GPE change less?

48. A 10kg object is lifted from the floor to a shelf, 2m off the ground. What is the change in this object’s GPE? Bonus: How much work did it take to get the object up to the ledge?

49. Elastic Potential Energy • The energy stored in a stretched spring • Depends upon the amount the spring is stretched/compressed, the type of spring

50. Chemical Potential Energy • A combustion reaction releases a large amount of energy… • What is this energy’s origin? • From the chemical bonds between atoms