Physical Science

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Physical Science

• Motion
• Linear Motion
• Rotational Motion
• Slides subject to change

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Position

• Position is the location of an object relative to
  a reference point.
• Change in position is motion.

I am here, where are you?
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Describe Motion

• d distance t time v speed
• v d/t
• Instantaneous speed

• Averagetotal distance/total elapsed time

Odometer
Stopwatch
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Motion Drive APU to LAX
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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

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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.

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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.

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Compass Headings
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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

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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

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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?

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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

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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

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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.

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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

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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

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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
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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.

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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.

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A Real Stock Race Car
Acceleration from moment to moment
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Kingda Ka Six Flags, Jackson, NJ 0 to 128 mi/hr
in 3.5 s
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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.

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Distance

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

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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

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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

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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

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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

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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.

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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.

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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
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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

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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

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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.

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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.

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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.

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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.

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Maximum gs

• Col John Stapp video

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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).

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