physics 504 chapter 8 vectors
TRANSCRIPT
Chapter 8 Vectors
Physics 504
Scalars and Vectors A scalar quantity has a size and unit.
E.g. 16 N (Newtons) A vector quantity has a size, unit and direction.
E.g. 5 km/h [N] (North)
Distance and Displacement
Distance travelled depends on position.
Distance is a scalar quantity.
It is always positive. E.g. d = 5 km
Distance and Displacement
Displacement depends on the new position compared to the old position.
Displacement is a vector quantity.
E.g. Δd or đ = 5 km North
Exam QuestionThe following graph represents the trail followed by a hiker going from A to F (A –> B –> C –> D –> E –> F). One centimetre represents 100 metres.
A
B C
DE
F
What is the displacement of the hiker?
A) 1 700 m
B)
700 m
C)
500 m
D)
200 m
The Cardinal Points
Cardinal Points II Never Eat Slimey Worms ½ way between North [N] andWest [W] is NorthWest [NW]
½ way between NW and N is NNW
Trigonometric Direction [East] = 0° [North] = 90° [West] = 180° [South] = 270°
Cardinal and Degrees [N 45 ° E] means you start at North and turn 45 ° East.
It is also known as NE. Or as 45 °
Vector Addition We can show vectors as arrows in diagrams.
We add vectors tip to tail. Vector Ả +Vector B = Vector B + Vector Ả The result of adding two or more vectors is
the RESULTANT VECTOR. Vectors are written with little arrows on
top.
Vector Diagrams
Vector Subtraction To subtract a vector from another, you add the opposite.
Vector A – Vector B = Vector A + (-Vector B)
Activity Page 189, Q 1 – 6 Page 192, Q 1 – 3 Page 195, Q 1 – 4 Page 197, Q. 1 - 2
Multiplying Vectors Multiplying vectors only changes magnitude not direction (if positive).
ā = (1,2); 3 ā = (3,6) đ = 5 km 45°; 2đ = 10 km 45°
Vector Division It is just like vector multiplication, but with a fraction.
N.B. multiplying by a negative ř = (3,2); - ř = (-3,-2) Ŝ = 2 m [N]; -ŝ = 2m [S]
x-Component of a Vector ā-hyp opp Θ y-part
adj x – parts Cos θ = adj/hyp = x/ā Thus, x = ā cos θ
y-Component of a Vector ā-hyp opp Θ y-part
adj x – parts sin θ = opp/hyp = x/ā Thus, y = ā sin θ
Addition of Vectors: Component Method
Add the x-components of the vectors together.
Add the y-components of the vectors together.
Add the total x vector to the total y vector tip to tail.
Tools for Solving You can use diagrams; Pythagoras c2 = a2 + b2;
Sine Law Cosine Law SOHCAHTOA
Summary Some motions can be seen easily; other motions must be observed using other senses or devices.
The trajectory is the path of a moving object.
Summary Vector quantities have magnitude and direction.
Scalar quantities only have magnitude.
Displacement, or change in position, is a vector quantity.
Summary Distance, the path length, is a scalar quantity.
Add vectors tip to tail. Page 199, Q 1 - 5
Activity Design an Amazing Race