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Physical Science

- Motion
- Linear Motion
- Rotational Motion
- Slides subject to change

Position

- Position is the location of an object relative to

a reference point. - Change in position is motion.

I am here, where are you?

Describe Motion

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

- Averagetotal distance/total elapsed time

Odometer

Stopwatch

Motion Drive APU to LAX

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

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.

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.

Compass Headings

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

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

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

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

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.

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

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

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.

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

Kingda Ka Six Flags, Jackson, NJ 0 to 128 mi/hr

in 3.5 s

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.

Distance

- Formula for the distance an object falls (assume

it starts from rest, and ignore air friction),

with constant acceleration, is - d ½ at2

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

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.

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.

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

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

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

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.

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.

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.

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.

Maximum gs

- Col John Stapp video

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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