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## Physical Science

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Title: Physical Science

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

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
Describe Motion
• d distance t time v speed
• v d/t
• Instantaneous speed
• Averagetotal distance/total elapsed time

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).
• 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
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. Its 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 Johnsons 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 its
60 miles.
• Average speed Barstow to Needles 75 mi/hr, and
its 175 miles.
• Whats her average speed for the entire trip?

12
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13
Average Speed
• Hillarys average speed for the entire trip.
• v dtot /ttot
• Divide trip into two legs.
• Whats her total distance dtot?
• Leg 1 60 mi
• Leg 2 175 mi
• dtot d1 d2 60 175 235 miles

14
Average Speed
• Whats 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 its 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
• Given
• v0 0 m/s
• v 330 mi/hr 148 m/s
• t 4.5 second
• 148 0 4.5a
• a 33 m/s2
• Formula
• v v0 at
• Every second, its going 33 m/s faster.

20
Compare to Earth Forces
• Top fuel dragster a 33 m/s2
• An object falls in Earths 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 gs 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
28
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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 2pR/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 2pR/T 2p(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 gs Pilot feels heavy.
• 4 gs Vision switches to black and white
(gray-out).
• 5-6 gs Oxygen to head stops completely. G-LOC
(loss of consciousness).
• If g onset gt 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 gs
the trousers automatically inflate.

38
Maximum gs?
• No more than 9 gs 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 gs was
an acceleration someone could walk away from.

39
Maximum gs
• Col John Stapp video

40
Maximum gs
• 32 gs became the acceleration used in the design
of fighter jet ejection seats.
• Stapp survived 43 gs, 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).

41
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