Transcript Vectors and Scalars

Vectors and Scalars
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
• Vector – a quantity that requires both
magnitude (size) and direction.
– Displacement, force, and velocity
• 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.
• Vector quantities can be represented by
either letter symbols with arrows above
them or with bold letters.
d or d
• Scalars are simply italicized.
• 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 west
– 50 mi at 45o east of north
• Using a scale of 1.0 cm = 50 km, draw the
displacement vector 275 km at 45o north
of west.
• Using a scale of ¼ in = 20 mi, draw the
displacement vector 150 mi at 22o east of
south.
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.
• To solve a vector addition problem such as one for
displacement.
1. Choose a suitable scale and calculate the scale length of each
vector.
2. Draw a north-south reference line. Graph paper can be used.
3. 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.
4. Draw the sum, or the resultant vector, from the initial end of the
first vector to the terminal end of the last vector.
5. 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.
• Find the resultant displacement of an
airplane that flies 20 mi due east, then 30
mi due north, then 10 mi at 60o west of
south.
• Find the resultant of the displacements
150 km due west, then 200 km due east,
and then 125 km due south.