Objectives Distinguish between vector and scalar quantities Add vectors graphically Scalar a quantity that can be completely described by a number called its magnitude and a unit Ex length temperature and volume ID: 395547
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Slide1
Vectors and Scalars
Objectives
:
Distinguish between vector and scalar quantities
Add vectors graphicallySlide2
Scalar
– a quantity that can be completely described by a number (called its magnitude) and a unit.
Ex: length, temperature, and volume
Vector
– a quantity that requires both magnitude (size) and direction.
Displacement, force, and velocitySlide3
Displacement
– the net change in position of an object; or the direct
distance
and
direction
it moves.
Examples: 15 mi NE, 10 meters upward
It does not contain any information about the path an objects moves.
How can an object change position but have a displacement of zero? Give an example.Slide4
Vector quantities can be represented by either letter symbols with arrows above them or with bold letters.
d
or
dScalars are simply italicized.Slide5
Vectors are drawn as arrows
in the correct direction
and the magnitude is indicated by the length.
An appropriate scale is selected, e.g. 1.0 cm = 25 mi.
Draw vectors for the following displacements using the scale above:125 mi west50 mi at 45o
east of northSlide6
Using a scale of 1.0 cm = 50 km, draw the displacement vector 275 km at 45
o
north of west.
Using a scale of ¼ in = 20 mi, draw the displacement vector 150 mi at 22
o east of south.Slide7
Graphical Addition of Vectors
Any given displacement can be the result of many different combinations of displacements.
For example, there is more than one way to get to the cafeteria.
Resultant vector
– the sum of a set of vectors.Slide8
To solve a vector addition problem such as one for displacement.
Choose a suitable scale and calculate the scale length of each vector.
Draw a north-south reference line. Graph paper can be used.
Using a ruler and protractor, draw the first vector and then draw the
other vectors so that the initial end of each vector is placed at the terminal end of the previous vector.
Draw the sum, or the resultant vector, from the initial end of the first vector to the terminal end of the last vector.
Measure the length of the resultant and use the scale to find the magnitude of the vector. Use a protractor to measure the angle of the resultant.Slide9
Find the resultant displacement of an airplane that flies 20 mi due east, then 30 mi due north, then 10 mi at 60
o
west of south.Slide10
Find the resultant of the displacements 150 km due west, then 200 km due east, and then 125 km due south.