6B - Vectors
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Transcript of 6B - Vectors
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8/17/2019 6B - Vectors
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Physical Quantities, Units and MeasurementPhysical Quantities, Units and Measurement
T H E M E O N E : M E A S U R E M E N T
C h a p t e r 1
Scalar & Vector Quantities
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1.4 Scalars and Vectors
• Scalar quantities are quantities that havemagnitude only. Two examples are shown elow!
Measuring Mass Measuring Temperature
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1.4 Scalars and Vectors
• Scalar quantities are added or sutracted y usingsimple arithmetic.
"xample! # $g plus % $g gives the answer 1& $g
' (
# $g
% $g
1& $g
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1.4 Scalars and Vectors
• Vector quantities are quantities that have othmagnitude and direction
Magnitude ( 1&& )
*irection ( +et
- orce Arrgh
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1.4 Scalars and Vectors
• "xamples o scalars and vectors
/calars 0ectors
distance displacement
speed velocity
mass weight
time acceleration
pressure orce
energy momentum
volume
density
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Vectors
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Vector Addition
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1.4 Scalars and Vectors
Adding Vectors using Gra!ical Met!od• Parallel vectors can e added arithmetically
)
# )
% ) # )
)
)
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1.4 Scalars and Vectors
Adding Vectors using Gra!ical Met!od• )on2parallel vectors are added y graphical
means using the parallelogram law3 0ectors can e represented graphically y arrows
3 The length o the arrow represents the magnitude o the
vector
3 The direction o the arrow represents the direction o the
vector
3 The magnitude and direction o the resultant vector can e
ound using an accurate scale drawing
4.& cm &.& )*irection ( right
≡
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• The arallelogra" la# o$ %ector addition statesthat i two vectors acting at a point are
represented y the sides o a parallelogram
drawn rom that point, their resultant isrepresented y the diagonal which passes through
that point o the parallelogram
1.4 Scalars and Vectors
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1.4 Scalars and Vectors
Head&to&tail Met!od 'Alternati%e "et!od(• To add vectors A and B
3 place the starting point o B at the ending point o A
3 The vector sum or resultant R is the vector 5oining the
starting point o vector A to the ending point o B3 Conversely, R can also e otained y placing the
starting point o - at the ending point o 6
3 )ow the resultant is represented y the vector 5oining
the starting point o 6 to the ending point o -
• /ee next slide
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1.4 Scalars and Vectors
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C h a p t e r 1Vectors: Graphical method
• A light aircraft is flying with a velocity relative to
the air of 200kmh! in a direction due north"
#here is a wind $lowing from a direction of %00
north of west at 0kmh!
"• 'alculate the velocity of the aircraft relative to
the ground"
• Ans: vmag ( !)*kmh!+ vdirection ( 22
0 east of north
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Vector Su$traction
A ,- (
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'omponents of Vectors• A num$er of vectors which are added together to
give a single resultant are called the
components of the resultant"
•."g /etermine the components of the velocityvector !0 ms 1 %0°"
• 3 ( ")4+ y ( 54
1
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esolution of Vectors
• #he sum of two or more vectors is a single
vector called the resultant" #hey are drawn from
the tail of the first vector to the head of the last
vector"
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."g!• esolve the vector $elow into its
components"
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."g 2• esolve the vector $elow into its
components
• x coordinate = 2 ×sin(60°) =
y coordinate = 2 ×cos(60°) = 2(½)=1
1
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."g %• A cruise sails at %0kmh! in a north
easterly direction 6Ѳ = 450)" 7hat is its
speed in an easterly direction8 6Give ans
in ms to 2s"f"9"
• Ans: 2!kmh! ( 5" ms
1
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1. /calar quantities are quantities that only havemagnitudes
. 0ector quantities are quantities that have oth
magnitude and direction
7. Parallel vectors can e added arithmetically#. )on2parallel vectors are added y graphical
means using the parallelogram law
5" #he direction or angle of a vector is always
measured from the horiontal"*" #rigonometric functions and the ;ythagorean
#heorem are used to calculate the magnitude and
direction of resultant vectors"
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• ?@
'A?@ #>A to get the direction"
•
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