motion speed acceleration velocity

8/17/2019 Motion Speed Acceleration Velocity

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Speed, velocity,

acceleration & Newton

Micro-World Macro-WorldLecture 2


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speed

speed = v =

distance traveled

elapsed time

50km

v = 50km

1 hr = 50km/hr

Hawaii Kai Haleiwa

In one hor

This is the averagespeed over 1 hour.For shorter timeintervals it can be

higher or lower.


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instantaneous speed

Instantaneous

speed = here

! here

"peed determined #or ver$ short time intervals

vistantaneos =distance traveled!very short" time

km

%m %m


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Earth’s motion around the Sun

r=1#5$1011m

% =distance

elapsed time = r $ '#1( $ 1#5 $ 1011m

')5 days $ ( hr/day=

1year

=*#( $ 1011 m

+)0 hr =

*#( $ 1011 m

+#) $10' hr

= 1#1$10+

m/hr = 1#1$105

km/hr ≈

11& %m'hr

*#(

+#= $ 1011-' m/hr

= 1

- ( % m


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Tip of a watch’s minute hand (HW!!)

% = distanceelapsed time = r $ '#1( $ 1cm)0 min $ )0 s/min=1hr

=)#+ cm

')00 s=

)#+ cm

'# ) $10's= 1#$10-' cm/s

= 1#$10-5 m/s

r = 1

c m

= 1 - 2

m


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Scalars and Vectors

Simple nm.ers

Speed v

emperatre T

Nm.er direction

%elocity v

relative positions r

2orce 2

3cceleration a

4i.rary

r

5 a m

p s

5 e n t e

r


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Velocity = speed direction

r=1#5$1011m

) months laterspeed = same

di##erent direction

v

velocit$ is a *vector+, a uantit$ that has bothmagnitude and direction

Length o# the arrow = speedirection o# arrow same asdirection o# the motion


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cceleration ( chan"es in #)

acceleration = change in velocit$elapsed time

a =

change in v elapsed time


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han6e in % = 100km/hr

7lapsed time = ' sec

*This bab$ goes #rom to1%m'hr in onl$ ( seconds+

a =chan6e in velapsed time

= 100km/hr ' s = '' km/hr s10' m

')00 s

='#)$10's

=''$10'm

'#)$10' s$s = *#1 m/s


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$ifferent ways to chan"e V

v v

ar speeds p

v

ar slows p

v

s c r e e c h !

a

a


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ccelerations (continued)

v

5 ar t r nsv

In all three cases, v chan6es#here8ore these are all e$amples o8 accelerations

a


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a % v on a hot wheels track


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Free Fall


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(#*m

t=0 v0=0

t=1s v1=9

vav6 = disttime

(#*m1 s= = (#*m/s

vav6

= v0 v1

0 v1

=

v1

=

v1 = vav6 = *#+ m/s

%1 = *#+ m/s


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&ree'fall acceleration

acceleration =chan6e in velocity

elapsed time

a =*#+m/s

1s= *#+ m/s

/.0m's

1s

This is called the *acceleration due to gravit$+ and given the special s$mbol,

g=/.0m's2

In this class g≈

1 m's2

will be close enough #or us

g


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&ree fall from "reater hei"hts

%0 = 0

t = 0s

%1 = 10m/s

t = 1s

5m

% = 0m/s

t = s

%' = '0m/s

t = 's

%( = (0m/s

t = (s

15m

5m

'5m

5m

0m

(5m

+0m

otal

distance

1

6t


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pward toss

%( = 0t = (s

%' = 10m/st = 's

5m

% = 0m/st = s

%1 = '0m/s

t = 1s

%0 = (0m/st = 0

15m

5m

'5m

5m

)0m

'5m

0m

otal

hei6ht

+0m

6t1

v0t


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"imple rule #or #ree #alla%a, proectile motion

When Earth’s gravity is the only forceinvolved:

actual height = height for no gravity 3gt2


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Hori*ontal tosst = 0s

t = 1s

5m

t = s t = 's t = (s

0m

(5m

+0m


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upward toss

t = 0s

t = 1s

5m

t = s

t = 'st = (s

0m

(5m+0m


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Shoot the monkeycommnistdead white

4uropean male


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%ery 8ast hori:ontal toss

t = 0st = 1s

$= +km

5m

t = s

$=1)km

t = 's

$=(km

0m (5m

%=+km/s


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+r,ital motion is free fall


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3rti8icial satellite

a = 6

v = + km/s


25/53

Turnin" car

5n obect #ree to slide on the dashboard&tries to #ollow a straight line path


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-ewton’s . laws of motion

Isaac Newton 1)( --- 1


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le/ander 0ope1

6ature and nature7s laws la$ hid in the night

8od said& *Let 6ewton be&+ and all was light.


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2st 3aw1 3aw of 4nertia

5 bod$ at rest tends to sta$ atrest& a bod$ in motion tends to%eep moving along at a constantspeed and in a straight-line

path unless inter#ered with b$some e9ternal #orces.


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e/ample


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5otorcycle crash dummy


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nother e/ample(watch the ladder)


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2nd Law, F=ma

T he acceleration o# a bod$ is directl$proportional to the net #orce acting on

it and inversel$ proportional to itsmass.The direction o# the accelerationis in the direction o# the applied #orce


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$irectly proportional to &orce

a

Small 8orceSmall acceleration

a

4ar6e 8orce

4ar6e acceleration


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in#ersely proportional to mass

aa

4ar6e mass

Small acceleration

small mass

4ar6e acceleration

;owlin6

.all

;each

.all


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*Inertial+ mass

*Inertial+ mass& mi& is the resistance tochanges in the state o# motion

:bects with large mi are hard to get moving;! once started& hard

to stop


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nits a"ain! (we cant a#oid them!)

Mass, basic unit = 1%ilogram = 1%g

mass o# 1 liter ;1.1 uarts< o# water

This muchwater

1cm

1cm

1cm


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-et force

Tip-to-tail method#or adding vector

"lide tail o# one to tipo# the other ;%eepdirections #i9ed<

6et #orce is the vector#rom the tail o# the 1st to

the tip o# the 2nd. ; inthis case


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Tip-to-tail method

"lide tail o# one to tipo# the other ;%eepdirections #i9ed<

6et #orce pointsdown the hill


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6ewton7s 2nd law F=ma

a ∝ F

a ∝ 1'm

a is proportional to F,

direction o# a

= direction o# F,

a ∝ F

a is inversel$proportional to m,

a ∝ F'mcombine,

set proportionalit$constant = 1, a = F'm

multipl$both sides

b$

m

W i ht & f it


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Wei"ht = &orce of "ra#ity

a = 6<

;owlin6

.allm

;each

.all

a = 621 = ma2 =


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Wei"ht is proportional to mass

Newton>s nd law 2=ma

I8 6ravity is the only 8orce 2 = ? a = 6

? = m6weight

*gravitational+mass

accelerationdue to gravit$


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wo different aspects o8 mass

Weight, W = m g Force o# gravit$ isproportional to*gravitational+ mass

a = F

m

Inertia> resistanceto changes in stateis proportional to*inertial+ massmi

mgg

6ewton7s 2nd law,

49perimentshows, mg = mi


43/53

nits of &orce

F=ma

%gm

s2

?nit o# #orce, 1 6ewton = 16 = 1 %g m's2

1 pound =1lb = @.A 6

What is your mass6


44/53

What is your mass6

Weight = #orce o#

4arth7s gravit$ on $ou

W=mg

W

a=g

F=ma

m=Wg

"uppose I

ump o##a tble


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Mass ! weight

Bonvert to 6ewtons,

W = 0A %g 9 /.0m's2 = 0(( 6

%g m's2?nits o# 6 =

Cg# =*%ilogram #orce+ = /.0 6

* w

e i g h t +

= 0 A

% g

%g is a unit o# mass& not #orce

* m $ w

e i g h t +


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6ewton7(rd Law, action-reaction

Whenever one obect e9erts a #orce on asecond obect& the second obecte9erts an eual in magnitude but

opposite in direction #orce on the #irst.

action, I push

on the canoe

reaction, thecanoe pushes

me #orward


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ActionReaction


48/53

I push on the bus

F

v=


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Dut I accelerate

6ewton,

The bus e9erted an *eual but opposite+ #orce on me.

v


50/53

Loo% again

F

-F

5ll #orces come in pairs

This #orce causes meto accelerate bac%wards

This #orce tries to accel.the bus #orward


51/53

5ir-#illed balloon

action, balloonpushes on air

reaction, airpushes on balloon

il


52/53

recoilaction, gun e9erts

#orce F2 on bulletma%ing it accelerate

reaction, eual butpposite #orce on the gun F1

Eroduces a recoil

7 k t l i


53/53

7ocket propulsion

action, roc%et enginepushes e9haust

gasses out the rear

reaction, roc%etgets pushed

in the opposite

direction

motion speed acceleration velocity

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