Unit 1.1 – Mechanics - Kinematics (Student)

8/18/2019 Unit 1.1 – Mechanics - Kinematics (Student)

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[UNIT 1 – PHYSICS ON THE GO – 1.0 MECHANICS]

1.1 KINEMATICS

1. Kinematic equation of motion

2. Motion-related experiments

3. Graphical Method4. Projectile Motion

1. Equation of motion

When acceleration a is constant!

" # u $ at

"2 # u2 $2as

s # ut $% at2

&here u # initial "elocit'

" # final "elocit'

t # time

s # displacement

(xample 1

)o& lon* does it ta+e a car to cross a 3,m &ide intersection after

the li*ht turns *reen if the car accelerates from rest at a constant

2ms-2Solution 1

istin* do&n the +no&n "aria/les!s # 3,m a # 2 ms-2 required t #

0lso since car &as stationar' initial "elocit' u # ,

sin* s # ut $% at2

3, # ,t $ %2t2

t2 # 3,

t # √ 30ince time can onl' /e positi"e

t # 5.46 s

(xample 2

7n desi*nin* an airport for small planes one +ind of airplane that

mi*ht use this airfield must reach a speed /efore ta+eoff of at least28.6 ms-1 1,,+m9h and can accelerate at 2ms-2. a 7f the run&a' is

15,m lon* can this airplane reach the required speed for ta+e off/ 7f not &hat is minimum len*th must the run&a' ha"e

aistin* do&n the +no&n "aria/les!

s # 15,m a # 2 ms-2 required " #

0lso since car &as stationar' initial "elocit' u # ,sin* "2 # u2 $2as

"2 # ,2 $ 2215,

# :,,

" # √ 600 # 24.5 ms-1 ; &hich is


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(b)

istin* do&n the +no&n "aria/les!" # 28.6ms-1 a # 2 ms-2 u # , required s #

sin* "2 # u2 $2assin* 28.62 # ,2 $22s

s # 1?3.2 m

u**ested run&a' len*th # 2,, m

2. Motion Related Expeiment!

=7@K(A-=7M(A (BP(A7M(C=

Exp A

AIM:

=his acti"it' is a/out "elocit' acceleration and deceleration

as

influenced /' forces of friction and *ra"itation.

0nd 'ou &ill /e introduced to a de"ice called a ticker-timer .

0t the end of the acti"it' the learner should /e a/le toD

•

Eescri/e ho& friction compensation happens on a run&a'.• Eescri/e ho& a tic+er-timer &or+s.

• Eescri/e the experimental procedures to measure the

"elocit' of a trolle'.

• 7dentif' tic+er-timer tapes that sho& uniform "elocit' and

those that sho& accelerated motion.

• @alculate "elocit' from a tic+er tape.

• Eetermine acceleration due to *ra"it' usin* a tic+er-timer.

0PP0A0=D

=o set up this acti"it' the follo&in* equipment is neededD =rolle's

run&a's tic+er-timers tic+er tapes and rulers.

PAF@(EA(D

• et up the trolle' to mo"e on a horiontal runa&a' as sho&n

in fi*ure /elo& under the *uidance of 'our teacher. 0 tic+er

tape passin* throu*h the tic+er timer is attached to the

trolle'.

• F/ser"e and descri/e ho& the trolle' mo"es alon* the

runa&a'.

• u**est ho& the trolle' can /e made to mo"es do&n the

run&a' at a constant speed.

• 0s+ 'our teacher to help 'ou produce "arious tapes for

constant "elocit' and accelerated motion.

• (xamine the "arious tapes o/tained


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Figure 1

• Eescri/e the "arious tapes that sho& uniform "elocit' and

those sho&in* accelerated motion.

(xp H

E(=(AM7C7CG I(F@7=J

AFM =)( =7@K(A =0P(

Answer the following questions:

• 7f the frequenc' of the tic+er timer is f &hat is the time

inter"al /et&een t&o successi"e dots.

• 7f frequenc' of the tic+er timer is 5,) &hat is the time

inter"al for the follo&in* casesD

o rom the 1st to the 2nd dot!

o rom the 1st to the 5th

dot!

o rom the 1st to the

1,,th dot!

=he follo&in* examples sho&

"arious tapes each of len*th 6cm

o/tained usin* a tic+er timer offrequenc' 5,).

7n each case find the time inter"al

of the tape and the "elocit' in ms-1.

(xp @

E(=(AM7C7CG

0@@((A0=7FC AFM =)(

=7@K(A =0P(

• et up the experiment and produce a num/er of tic+er tapes usin* a trolle' runnin* on

an inclined run&a'.

• ample tic+er tape

=ape ta+e initial part

of the tape to /e on the

left

Eescri/e in each

case ho&

spacin* /et&een

dots "aries

Eescri/e the

t'pe of

motion

represented

0

H

@

E

(

=ape =ime inter"al Ielocit'

0

H

@

0

=he distance x # 16cm

=he distance ' # 3,cm

Time fo initial inte"al x

o final inte"al #$ t%!

Initial "elo&it#$ u%m!'1 inal "elo&it#$ "%m!'1

Time to &an*e fom

a"ea*e "elo&it# u to a"ea*e

"elo&it# "$ T%!

A&&eleation$ a H

=he distance x # 14cm

=he distance ' # 24cm

Time$ t Initial "elo&it#$ u inal "elo&it#$ " Time$ T A&&eleation$ a


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• Eiscuss ho& to choose the inter"al for the initial and final

"elocities on the accelerated tape.

• Eiscuss &h' the initial dots could /e i*nored cut off.

• @alculate initial and final "elocities on the accelerated tapes.

• Eiscuss ho& to o/tain the time ta+en to chan*e from initial

to final "elocit'.

• @alculate acceleration on the accelerated tapes.

@alculate acceleration for the tapes /elo& in the steps *i"en. =a+e

frequenc' f # 5,)


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(xp EE(=(AM7C7CG 0@@((A0=7FC E( =F GA0I7=J 7CG

=)( =7@K(A =7M(A

• Eiscuss the set up of the experiment.

Figure 2

• et up the experiment as sho&n in dia*ram and produce a

num/er of tic+er tapes.

• se the method of findin* acceleration from a/o"e to

determine the acceleration due to

*ra"it'.

Ae"ie& 'our understandin*

=he follo&in* examples sho& "arious

tapes each of len*th 6cm *ot usin* a tic+er

timer of frequenc' 5,).

7n each case find the time inter"al and the

time inter"al of the tape and the "elocit' inms-1.

=ime for initial inter"al x or

final inter"al ' t9s

7nitial "elocit' u

inal "elocit' "

=ime to chan*e from a"era*e"elocit' u to a"era*e "elocit'

" =9s

0cceleration a

=ape =ime inter"al Ielocit'

0

H

@


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7@= 0PP7@0=7FC

Alternatie experiment: !sing "ight #ates

+etch an alternati"e for (xp 0 usin* li*ht *ates. a/el

appropriatel'.

1$ tate the difference major difference of the apparatus set-up of

the a/o"e &ith that of Figure 1%

=rac+

Eisplacement


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=ime

2 Eescri/e &h' one method is /etter than the other.

LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL



3 (xplain &h' a stop&atch is not used instead.

LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL +.,api&al Metod

What si*nificance of the slope and area under the *raph of thefollo&in*D

7. Eisplacement-time *raph

0 1 2 3 40

5

10

t

s

Gradient # ,∴ Ielocit' # ,


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0 1 2 3 4

0

5

10

t

s

Gradient is increasin* linearl'∴ Ielocit' # increasin* linearl'

0 1 2 3 4

0

2

4

6

8

10

t

s

Gradient increasin* exponentiall'

∴ Ielocit' increasin* exponentiall'

77. Ielocit'-time *raph

0 1 2 3 4

0

5

10

t

v

Gradient # ,∴ 0cceleration # ,

0rea under the *raph # displacement

0 1 2 3 40

5

10

t

v


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Gradient increasin*∴ 0cceleration increasin*

0rea under the *raph # displacement

777. 0cceleration-time *raph

0 1 2 3 4

0

5

10

t

a

@onstant acceleration

4. Projectile Motion

F/jects mo"in* freel' under the influence of *ra"it'.

0t time t # , x, # ', #,

Iertical @omponent! When t#, "', # ,.

=a+in* up&ard as positi"e then a' # #*

0ppl'in* " # u $ at ! "' # -*t

0ppl'in* s # ut $1

2 at2 ! s' #

−1

2 *t2

)oriontal @omponent!

Co other force actin*! # , a #,

" # "x, "x remains constantN

0ppl'in* s # ut $1

2 at2 ! sx # "x,t


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Iertical @omponent!

When t#, " # "', &hich *raduall' decreases until..

hi*hest point &here "' # , and

increases do&n&ard direction /ecomin* more ne*ati"e.

)oriontal @omponent!

"' remains constant

Eoes the /all on the left fall faster than the /all on the ri*ht


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(xample 1

0 /all is +ic+ed at an an*le θ0=37o

&ith a "elocit' of 2, ms-1.

7*norin* air resistance and assumin* /all lea"es at *round le"el.@alculate D

a the maximum hei*ht

/ the time of tra"el /efore the /all hits the *round

c ho& far a&a' it hits the *round

d the "elocit' "ector at the maximum hei*hte the acceleration "ector at maximum hei*ht.

Aesol"in* intial "elocit' into componentsD"x, # ", cos 38

o # 1: ms-1

"', # ", sin 38o # 12 ms-1

a 0t hi*hest point "' # ,

t #v

y 0

g #

12

9.80 # 1.22 s

0ppl'in* ' # "'ot -1

2 *t2

# 121.22 -1

2 ?.6,1.222

# 8.35 m

/ @onsider '#,

0ppl'in* ' # "'ot -1

2 *t2

, # 12t -1

2?.6t2

actorin* the equation

4.?5t O 12N t # ,

=&o solutions t # , s corresponds to initial point ',N

and t # 2.45 s total tra"el time of /allN

c Kno&n that t # 2.45 s ta+en to tra"el from F to H.

sx # "x,t

# 1: 2.45 # 3?.2 m

d " # "x, $ "',ince no "ertical component

" # "xp # 1: ms-1-

e 0cceleration is constant throu*hout fli*ht.

∴a # ?.6, ms

-2


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Unit 1.1 – Mechanics - Kinematics (Student)

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