Vectors and Scalars

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Vectors and Scalars
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Vector and Scalar Quantities Scalar quantities
have magnitude only. Vector quantities have
magnitude and direction. Note By definition,
all base quantities have no direction and so are
scalar.
Vectors Scalars





Vectors Scalars
Displacement Distance
Velocity Speed
Weight Mass
Acceleration Time
Force Energy
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Vector Arrows A Vector is often represented using
a straight arrow. The length of the arrow
represents its magnitude, its direction
represents the direction of the vector. E.g. A
Force of 15N at an angle 30 to the
horizontal It can have a vertical and
horizontal component
15 sin30 15 cos30
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Vector Addition Vectors can be added using a
graphical method or by adding perpendicular
components. Graphical method (Link)
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Example
R a b
a
b


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Example
R a b
a
b


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Example
a
b
-

R a (- b)
-b
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Vector addition using components Any vector can
be resolved into two perpendicular components.
Often these may be horizontal and vertical. If
more than one vector are being added together,
the parallel components may be added. E.g. Two
forces act on a body as shown. What is the
resultant force?
For the 40N force Vertical component 40
sin60 34.6N Horizontal component 40 cos60
20.0N
For the 50N force Vertical component 50
sin30 (-) 25.0N Horizontal component 50
cos30 43.3N
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E.g. Two forces act on a body as shown. What is
the resultant force?
For the 40N force Vertical component 40
sin60 34.6N Horizontal component 40 cos60
20.0N
For the 50N force Vertical component 50
sin30 25.0N Horizontal component 50 cos30
43.3N
Resultant Vertical force 34.6 - 25.0
19.6N Horizontal component 20.0 43.3
63.3N
Calculate resultant using pythagoras Resultant
force v (19.62 63.32) 66.2 N Now
calculate the angle from the horizontal
19.6N
63.3N
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