1. VECTORS

2. Do you remember the difference between a scalar and a vector?
Scalars are quantities which are fully described by a
magnitude alone.
Vectors are quantities which are fully described by both a
magnitude and
a direction.

3. Intro to Vectors Warm-up
A bear walks one mile south, then one mile west, and finally walks one mile north. After his brisk walk, the bear ends back where he started.
What color is the bear???

4. Vector Representation
1. The length of the line represents the
magnitude and the arrow indicates the
direction.
2. The magnitude and direction of the vector is clearly labeled.

5. Vector Addition

6. Easy Adding…

7. Resultant Vectors
The resultant is the vector sum of two or more vectors.

8. Vector Addition
Graphical Method

9. Vector Addition: Head to Tail Method or (tip to tail)
Select an appropriate scale (e.g., 1 cm = 5 km)
Draw and label 1st vector to scale.
*The tail of each consecutive vector begins at the head of the most recent vector*
Draw and label 2nd vector to scale starting at the head of the 1st vector.
Draw the resultant vector (the summative result of the addition of the given vectors) by connecting the tail of the 1st vector to the head of the 2nd vector. (initial to final pt.)
Determine the magnitude and direction of the resultant vector by using a protractor, ruler, and the indicated scale; then label the resultant vector.

12. Scaling!!!
The magnitude of a vector in a scaled vector diagram is depicted by the length of the arrow. The arrow is drawn precisely to length in accordance with a chosen scale.

13. Compass Coordinate System
Use the same scale for all vector magnitudes
Δx = 30 m @ 20º E of N
V = 20 30º W of N
a = 10 40º W of S
F = 50 N @ 10º S of E N W E
To Draw direction:
Ex. 20º E of N: Start w/ North and go 20° East S

14. All these planes have the same reading on their speedometer
All these planes have the same reading on their speedometer. (plane speed not speed with respect to the ground (actual speed)

15. A B C

16. Velocity Vectors = = B. Headwind Tailwind (against the wind)
120 km/h
20 km/h
80 km/h
100 km/h = =
100 km/h
20km/h
B. Headwind
(against the wind)
Tailwind
(with the wind)

17. Velocity Vectors C. 90º crosswind Resultant
Using a ruler and your scale, you can determine the magnitude of the resultant vector. Or you could use the Pythagorean Theorem.
Then using a protractor, you can measure the direction of the resultant vector. Or you could use trigonometry to solve for the angle.
Resultant
80 km/h
100 km/h
60 km/h

18. The Parallelogram Method
Find the resultant force vector of the two forces below.
25 N due East, 45 N due South
25 N, East
Decide on
a scale!!!
51 N
59º S of E
51 N
31º E of S
45 N, South

19. An airplane is flying 200mph at 50o N of E. Wind velocity
is 50 mph due S. What is the velocity of the plane? N
180o 0o
Scale: 50 mph = 1 inch
270o

20. An airplane is flying 200mph at 50o N of E. Wind velocity
is 50 mph due S. What is the velocity of the plane? N W E
Scale: 50 mph = 1 inch S

21. An airplane is flying 200mph at 50o N of E. Wind velocity
is 50 mph due S. What is the velocity of the plane? N
50 mph
200 mph W E
VR = 165 mph @ 40° N of E
Scale: 50 mph = 1 inch S

22. 700 m/s @35 degrees E of N; 1000 m/s @ 30 degrees N of W
2. Find the resultant velocity vector of the two velocity vectors below.
700 degrees E of N; degrees N of W V2 Vr V1

23. Vector Addition
Component Method

24. In what direction is the leash pulling on the dog?

25. Breaking Down Vectors into Components

26. What would happen to the upward and rightward Forces if the Force on the chain were smaller?

27. Breaking Down Vectors into Components

28. Breaking Down Vectors into Components

29. Breaking Down Vectors into Components

30. Breaking Down Vectors into Components

31. Adding Component Vectors

32. Adding Component Vectors

33. Adding Component Vectors

35. Warm Up sohcahtoa 24.99 N 34.90º N of W VR=? V2 V1
1) Find the resultant Magnitude:__________
of the two vectors Direction:___________
Vector #1 = 20.5 N West
Vector #2 = 14.3 N North
Vector Diagram
34.90º N of W V2 V1
VR=?

36. Warm Up sohcahtoa + - + - 115.8 m South (-) 227.2 m East (+) V2 V1 Vr
2) Find the component of the
resultant = 255m 27º South of East
Vector # 1 _______ Direction__________
Vector # 2________ Direction__________
Vector Diagram:
115.8 m
South (-)
227.2 m
East (+)
Conventions: V2 V1 + Vr - + -

37. Vector Addition: The Method of Components
Practice: Find FR = Fnet =?
200 N due South, N at 40º N of W
Skip
Draw vector diagram. (Draw axis)
Resolve vectors into components using trig:
Vadj = V cos θ Vopp = V sin θ
3. Sum x and y components:
ΣVxi ΣVyi
Redraw!! Determine resultant vector using Pythagorean’s Theorem and trig:
Magnitude= √(Σ Vxi)² + (Σ Vyi)²
Direction Action: θ = tan-1(opp/adj)
Answer: Fnet = N @ ˚ W of S

38. Solve using the components method!!
An airplane flies at an engine speed of 100 m/s at 50º W of S into a wind of 30 m/s at 200 E of N. What is the airplane’s resultant velocity?
Solve using the components method!!
How far has the plane traveled after 1 hr??
Answer: ˚ S of W
miles per 1 hour

39. You Try!!!
A motor boat traveling 4.0 m/s, East encounters a current traveling 3.0 m/s, North.
a. What is the resultant velocity of the motor boat?
b. If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore?
c. What distance downstream does the boat reach the opposite shore?

40. Balanced & Unbalanced Forces
Equilibrium

41. Balanced? or Unbalanced?

42. Forces are in Equilibrium
Statics
Forces are in Equilibrium

43. Are these Objects are in Equilibrium?
Ceiling
5 kg
25 N
50 N
10 N
15 N
102 N

44. Solving Static Problems
The First Condition of Equilibrium: The upward forces must balance the downward forces, and the leftward forces must balance the rightward forces.
SFx = 0 SFy = 0 at equilibrium
Solution of Problems in Static's:
Isolate a body. What point or object are you going to talk about?
Draw the forces acting on the body you have isolated, and label them. (If their value is not know, give them a symbol such as F1, FP, T1, etc.) Remember…this is a free-body diag.

45. Solving Static Problems
Cont.
Split each of the forces into its x and y components, and label the components in terms of the symbols given in rule 2 and the proper sines and cosines.
4) Write down your summation equations for the first condition of equilibrium.
5) Solve the equations for the unknowns.

46. Equilibrium problem Solve for Fx & Fy? 300 N 10 kg Fx Fy
20º
10 kg Fx Fy
Ans: Fx = N Fy = N

47. Equilibrium problem 200 N Solve for F? 10 kg F 50 N ө
30º
50 N
Answer: F = º S of W

48. Tension Warm-up W
37º
45º
Find the tension in each rope if the weight (W) is 50 N.
Be sure to pick an appropriate point to draw your free-body-diagram. Then sum your x forces and then your y-forces.
Answers: T1= N, T2= N

49. Strongman
When the strongman suspends the 10N telephone book with the rope held vertically the tension in each strand of rope is 5 N. If the strongman could suspend the book from the strands pulled horizontally as shown, the tension in each strand would be:
About 5 N
About 10 N
About 20 N
More than a million Newtons... basically impossible.

50. Vector Addition of Forces

51. Components Warm-up
The two cars below are both accelerated by a 10 N force. Which car experiences the larger acceleration?
Car 1
Car 2
Both cars accelerate similarly.
Explain 10
VROOM! 1 10 2