Physical Science

1. Motion Linear Motion Rotational Motion Slides subject to change Physical Science

2. Position • Position is the location of an object relative to a reference point. • Change in position is “motion.” I am here, where are you?

3. Speedometer Describe Motion • Average—total distance/total elapsed time • d = distance t = time v = speed • v = d/t • Instantaneous speed Odometer Stopwatch

4. Motion: Drive APU to LAX

5. Average Speed • Average speed equals total distance divided by total travel time. • Odometer reading divided by time. • vavg = v = d/t • APU to LAX, according to Google Maps: • d = 41.2 mi • t = 44 min = 0.73 hr • v = d/t = (41.2 mi)/(0.73 hr) = 56 mi/hr

6. Speed or Velocity? • Speed is a scalar (a magnitude, e.g., 45 mi/hr). Speedometer reading. • Velocity has both magnitude and direction. Average velocity is straight-line distance between the starting point and ending point, with an angle or “heading.” An example would be an airplane that has both speed and heading.

7. Average Velocity • Straight-line distance between APU and LAX is 32.7 mi (as the crow flies, called “displacement”). • Suppose a helicopter can do it in 20 minutes? What is average velocity? • displacement d = 32.7 miles • elapsed time t = 20 min = 0.33 hr • vavg = (32.7 mi) /(0.33 hr) = 98 mi/hr • General heading: 240° (in aviation terms, or southwestward.

8. Compass Headings

9. The Average Speed Formula • From the basic definition of average speed v, • v = d/t • If you know the average speed v and time t, rearrange it and you can calculate the distance. • d = vt • If you know the distance d and speed v you can calculate the time t. • t = d/v

10. Running Track • Inside lane of a running track is usually 400 meters long. It’s the longest common sprint race. • Michael Johnson holds record run in 43.2 seconds. (note top speed in 2012 Olympics 43.94 s) • What was Johnson’s average speed? • d = 400 m • t = 43.2 s • v = d/t = 400/43.2 = 9.26 m/s

11. Average Speed Example • Hillary drives from Azusa to Barstow to Needles, CA. • Average speed Azusa to Barstow 45 mi/hr, and it’s 60 miles. • Average speed Barstow to Needles 75 mi/hr, and it’s 175 miles. • What’s her average speed for the entire trip?

13. Average Speed • Hillary’s average speed for the entire trip. • v = dtot /ttot • Divide trip into two legs. • What’s her total distance dtot? • Leg 1: 60 mi • Leg 2: 175 mi • dtot = d1 + d2 = 60 + 175 = 235 miles

14. Average Speed • What’s the total time ttot? • Leg 1: Azusa to Barstow, • v1 = d1/t1 or rearranged, t1 = d1/v1 • or t1 = 60/45 = 1.33 hrs • Leg 2: Barstow to Needles, • t2 = d2/v2 = 175/75 = 2.33 hrs • ttot = t1 + t2 = 3.66 hr • Overall v = dtot /ttot = (235)/(3.66) = 64 mi/hr

15. Johnson Runs 400-m Track • What is his average velocity? • Displacement d between start and finish = 0 • Time t = 43.2 seconds • velocityavg = d/t = (0)/(43.2) = 0 m/s !! • Seems strange, but it’s based on the definition of “velocity.”

16. Acceleration • Acceleration results from a change in speed or a change in direction. • Average linear acceleration equals change in speed divided by the time for the change to occur. • aavg = (v – v0)/t • v – v0 = change in speed, i.e., final speed minus initial speed. • t = elapsed time 16

17. Acceleration • a = (v – v0)/t • If acceleration a is constant: • Every second, the velocity is changing by the same amount. • Can predict future speed by rearranging: • a = (v – v0)/t • at = v – v0 • v = v0 + at • v is final speed • v0 initial speed • t is elapsed time

18. Top Fuel Dragster • Distance: 0.25 miles (“quarter mile”) • Elapsed time t = 4.5 seconds • Initial speed v0 = 0 mi/hr • Final speed v = 330 mi/hr A race …

19. If Constant Acceleration Formula • v = v0 + at Given • v0 = 0 m/s • v = 330 mi/hr = 148 m/s • t = 4.5 second • 148 = 0 + 4.5a • a = 33 m/s2 • Every second, it’s going 33 m/s faster.

20. Compare to Earth Forces • Top fuel dragster a = 33 m/s2 • An object falls in Earth’s gravity at 9.8 m/s2. • The dragster is accelerating at a rate 3.4 times faster down the track than it would fall. • Driver feels this as a force of 3.4 g’s on his or her back. 20

21. A Real Stock Race Car Acceleration from moment to moment

22. Kingda Ka Six Flags, Jackson, NJ 0 to 128 mi/hr in 3.5 s

23. Free Fall • Assume no air resistance. • Assume acceleration is constant over Earth surface. • a = g = 9.8 m/s2 • Drop something, velocity downward is v = v0 + at, and a = g • Every second, an object in free fall is going 9.8 m/s faster.

24. Distance • Formula for the distance an object falls (assume it starts from rest, and ignore air friction), with constant acceleration, is d = ½ at2

25. Distance • Drop something, and it falls 2.0 meters. How long does it take? • Given • a = g = 9.8 m/s2 • d = 2.0 m • 2.0 = ½ (9.8)(t2) • then, t2 = 0.408, and t = 0.64 s Formula • d = ½ gt2 25

26. Example • Boy walks off 10-meter diving board to do a “cannonball.” • How long before he hits the water? Given Formula d = 10 m d = ½ gt2 g = 9.8 m/s2 • d = 10 = ½ gt2 = ½ (9.8)(t2) t = 1.4 s 26

27. Example • Boy walks off 10-meter diving board to do a “cannonball.” • How fast is he going when he hits the water? Given Formula a = 9.8 m/s2 a = v/t, or v = at t = 1.4 s • v = (9.8)(1.4) = 13.7 m/s • ≈ 30 mi/hr 27

29. Zepplins • In 1937, Hindenburg captains had a standard way of checking their altimeters. • Over the ocean they would periodically drop a soda bottle and measure how long it took to hit the water. • Suppose t = 8.0 seconds. How high was the air ship, in meters? • d = ½ gt2 = ½ (9.8)(8.0)2 = 314 meters

30. Projectile Motion • Projectile motion problems are best solved by treating horizontal and vertical motion independently. • Gravity only affects vertical motion. • Important • Assume no air resistance. • Horizontal velocity is constant. • Time in flight is the same for both horizontal and vertical.

31. Baseball • If you drop an object from 1.5 m, when will hit the ground? • d = 1.5 = ½ gt2 = ½ (9.8)(t2) • t = 0.55 s. • If you throw a baseball horizontally from height 1.5 m it will also take exactly 0.55 s to hit the ground. • If you fire a bullet exactly level from height 1.5 m it will also take exactly 0.55 s to hit the level ground.

32. Acceleration Same for All? • Do objects of different mass really accelerate at the same rate? • In an atmosphere, object experiences “drag” from air friction and reaches a “terminal velocity” –no more acceleration. • Thus, in an atmosphere, size and mass matter! • No air: . Demonstration on the Moon

33. Circular Motion • Even when traveling at constant speed, an object in uniform circular motion must have an inward acceleration. • Change in velocity (the direction of motion). • When object moves in a circle of radius R with constant speed v, centripetal acceleration ac equals • ac = v2 R

34. Constant Speed • T = period, time to go around once, the period of revolution. • v = distance/time = 2πR/T • A yo-yo does a “round-the-world” in 1.1 s. The yo-yo is 0.80 meters long. What is ac? v = d/t = 2πR/T = 2π(0.8)/1.1 = 4.57 m/s ac = v2/R = (4.57)2/0.80 = 26 m/s2

35. Centripetal Motion • Eurofighter Typhoon centripetal acceleration reaches up to 15 g (150 m/s2). The aircraft can increase its maximum turn acceleration in less than one second.

36. Circular Motion in Jet Fighter • 2-3 g’s: Pilot feels heavy. • 4 g’s: Vision switches to black and white (gray-out). • 5-6 g’s: Oxygen to head stops completely. G-LOC (loss of consciousness). • If g onset > 5 g /s, blackouts can happen instantaneously and without warning. • Takes about 30 seconds for a pilot to act and regain his orientation.

37. Anti-G Suits • The pneumatic "anti-g suit"—five interconnected air chambers cover the lower abdomen, thighs, and lower leg. • If aircraft accelerates between 1.5 to 2.0 g’s the trousers automatically inflate.

38. Maximum g’s? • No more than 9 g’s for few minutes - probable blood vessel damage. • For very short duration, very high accelerations can be supported, although some damage can result. • Col. John Stapp (1910-1999), flight surgeon, USAF, did several experiments, strapping himself to a rocket sled, and determined that 32 g’s was an acceleration “someone could walk away from.”

39. Maximum g’s • Col John Stapp video

40. Maximum g’s • 32 g’s became the acceleration used in the design of fighter jet ejection seats. • Stapp survived 43 g’s, but had eye damage. • Stapp laid engineering groundwork for the use of seatbelts in cars. • First seat belt law was a federal law which took effect on January 1, 1968 (signed by Lyndon Johnson, Stapp was invited).