vectors.pptx

7/25/2019 vectors.pptx

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Ch 3 Working with Vectors

To describe motion correctly, we have toknow relative to what does the objectmove.

Consider a passenger walking on a movingbus. The bus moves 80 m in 10 s. Duringthat time the passenger walks m !rom theback o! the bus to the !ront.

The velocity o! the bus relative to the road is" #.......#..The velocity o! the passenger relative to the bus is"

####...The velocity o! the passenger relative to the road is"

####...

8,0 m$s0, m$s

8, m$s


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Vb= 8m/s


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Vb= 8m/s


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Vb= 8m/s


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Vb= 8m/s


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Vp= 0,5 m/s


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vp= 0,5 m/svb= 8 m/s

vres= vb+ vp ?


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vp= 0,5 m/s

vb= 8 m/s

(vres)2= (vb)

2+ (vp)2

= 64 + 0,25

= 64,25

vres= 8,02 m/s


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%calar

&ector

' scalar is a (uantity speci)ed

only by its magnitude, like

mass, energy.

' vector is a (uantity which isspeci)ed by both magnitude

and direction, like !orce.


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Displacement, 2 km, 45 Velocity, 60 km/h, N

Force, 12 N, down

2km

some more e!amples o" #ectors$

V = 1000 km/h, S

W = 50 N, down


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%!ample 1

A

B

A B

R A B

%!ample 2

A B

A

BR A B

%!ample &

A B

A

B

R A B

'ddin( and s)*tractin( o" #ectors$


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A

B

Determine$

R A BR A B

AB

R A B A

B

B

( )A B= +

R

'ddin( as opposed to s)*tractin(


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A

B

R A B

+he arallelo(ram method$

R


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R

y x

Rx

yR

R R Rx y

R Rx cos

sinyR R =

-plittin( a #ector into components$

1tan

y

x

R

R

=


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Rx

yR

-plittin( a #ector into components$

The two components Rxand Rywill have

the same e*ect as the original vector R.


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%plit the !ollowing !orce into twoperpendicular components such that#

cosmg

sinmg

one component is perpendicular tothe incline plane, and

the other component is parallel to

the incline plane.

mg


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cosmg

sinmg


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! "#er$ge #e%ocit&

distance coveredAve speed =time taken

peed is a sca!ar "#antit$, b#t ve!ocit$ isa vector % &avin' sie and direction

disp!acementAve ve!ocit$ =time taken


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!3 'nst$nt$neo(s #e%ocit&

0

instantaneo#s ve!ocit$ = !imt

xv

t

=

r

x

tt1

t2

x1

x2 ) xave v

t=

r


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!) "cce%er$tion

c&an'e in ve!ocit$Ave acce!eration =time interva!

vat

=

r

0

instantaneo#s acce!eration = !imt

vat

=

r


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*(estions+

*s t&e o!!oin' statement tr#e or a!se? If the velocity of an object is zero, then the acceleration must also be zero.

-an a stationar$ car be acce!eratin'?

.&at is t&e acce!eration o a car movin'at a constant 100 km/& a!on' a strai'&troad?


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*s t&e direction o t&e disp!acement,ve!ocit$ and acce!eration a!a$s t&esame?

.&at is t&e direction o t&e disp!acement,ve!ocit$ and acce!eration o a car t&atcomes to a stop d#e to its brakes?

*(estions+

2 7 F f lli bj t


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2-7 Free falling objects

+ravitational acceleration, g"

' body close to the earths sur!acee-periences an acceleration calledgravitational acceleration g// with asie o! ,8m$s2 and in a directionpointing to the centre o! the earth.

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vectors.pptx