Grade 10 Science - Unit 3 – Physics
Vectors in Physics
Related Scalar and Vector Quantities in Physics
Scalar Quantity
Vector Quantity
Position
d
5 km
2 m/s
9.8 m/s
2
Distance
Displacement
?d
?d
Speed
Velocity
v
v
Acceleration
Acceleration
a
a
5 km [S]
2 m/s [N]
2
9.8 m/s [E]
Scalar – A quantity that has a number and unit – called magnitude and offers ONE
piece of information
Examples of scalar quantities
? Time – 1 s, 24 h
? Distance – 12 m, 500 km
? Speed – 120 km/h, 50 m/s
? Money - $10.00
? Mass – 27 kg
? Counting objects – 2 pens, 31 students
Scalar symbols include t, d, v, a
Vector – A quantity that has a number, unit AND direction = magnitude + direction, TWO pieces
of information
Ways of representing direction
? North, South, East, West, SE, NW
? Left, Right, Up, Down, Forward, Backward
? Positive or Negative Signs
Note: State magnitude followed by direction in these type of brackets [ ]
Examples of vector quantities
? Position – 350 km [W], 100 m [W 30O N]
? Velocity – 120 km/h [N], 12 m/s [up]
? Acceleration – 9.81 m/s2 [down]
Adding Vectors
Head-to-Tail Method
The head-to-tail method involves drawing a vector to scale beginning at a designated starting
position -- where the head of this vector ends the tail of the next vector begins (thus, head-to-tail
method). The process is repeated for all vectors to be added. Once all vectors have been added
head-to-tail, the resultant is drawn from the tail of the first vector to the head of the last vector;
i.e., from start to finish. Once the resultant is drawn, its length can be measured and converted to
real units using the given scale.
The direction of the resultant can be determined by using a protractor and measuring its
counterclockwise angle of rotation from due East.
Problem - Find the Resultant Vector for the following vectors.
O
O
O
25 m, 45 + 25 m, 300 = 15 m, 210
Scale 1 cm = 5 m
The vectors should look like the vectors below, BUT drawn to scale.
O
The Resultant Vector is 22 m, 310 .
Adding Vectors – Practice
Task / Practice
Use the Head-to-Tail Method to determine the Resultant Vector for the following data/
O
O
1.
3.0 m, 45 and 5.0 m, 135
2.
5.0 km, 45 and 2.0 km, 180
3.
6.0 m/s, 225 and 2.0 m/s, 90
4.
4.0 m/s, 135 and 4.0 m/s, 315
5.
3.0 km, 45 and 5.0 km, 135 and 2.0 km, 60
6.
2.0 m, 315 and 5.0 m, 180 and 2.0 m, 60
7.
2.5 m/s, 45 and 5.0 m/s, 270 and 5.0 m/s, 330
O
Scale 1 cm = 1 m
O
O
O
O
O
O
Scale 1 cm = 1 km
O
O
Scale 1 cm = 10 m/s
Scale 1 cm = 1 m/s
O
O
O
Scale 1 cm = 1 km
O
O
Scale 1 cm = 1 m
O
Scale 1 cm = 2 m/s
Vector Direction
The direction of a vector is often expressed as a counterclockwise angle of rotation of the vector
O
about its "tail" from due East. Using this convention, a vector with a direction of 40 is a vector
O
which has been rotated 40 in a counterclockwise direction relative to due east. A vector with a
O
O
direction of 240 degrees is a vector which has been rotated 240 degrees in a counterclockwise
relative to due east (See Diagram).
Questions
1.
Given the SCALE: 1 cm = 10 m/s, determine the magnitude and direction of this vector.
Direction =
Magnitude =
2.
Given the SCALE: 1 cm = 50 km/hr, determine the magnitude and direction of this vector.
Direction =
Magnitude =
3.
Given the SCALE: 1 cm = 10 m/s, determine the magnitude and direction of this vector.
Direction =
Magnitude =
4.
Given the SCALE: 1 cm = 50 km/hr, determine the magnitude and direction of this vector.
Direction =
Magnitude =
5.
Given the SCALE: 1 cm = 10 m/s, determine the magnitude and direction of this vector.
Direction =
Magnitude =