1. Answers: 1. C 2. D READING QUIZ
1. Which one of the following is a scalar quantity?
A) Force B) Position C) Mass D) Velocity
2. For vector addition you have to use ______ law.
A) Newton’s Second
B) the arithmetic
C) Pascal’s
D) the parallelogram
Answers:
1. C
2. D
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

2. SCALARS AND VECTORS (Section 2.1)
Scalars Vectors
Examples: mass, volume force, velocity
Characteristics: It has a magnitude It has a magnitude
(positive or negative) and direction
Addition rule: Simple arithmetic Parallelogram law
Special Notation: None Bold font, a line, an
arrow or a “carrot”
In the PowerPoint presentation vector quantity is represented Like this (in bold, italics, and yellow).
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

3. VECTOR OPERATIONS (Section 2.2)
Scalar Multiplication
and Division
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

4. VECTOR ADDITION USING EITHER THE PARALLELOGRAM LAW OR TRIANGLE
Triangle method (always ‘tip to tail’):
How do you subtract a vector?
How can you add more than two concurrent vectors graphically ?
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

5. TOOLS FOR COMPUTATION: THE SINE LAW AND THE COSINE LAW

6. RESOLUTION OF A VECTOR
“Resolution” of a vector is breaking up a vector into components. It is kind of like using the parallelogram law in reverse.
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

7. Answers: 1. C 2. A CONCEPT QUIZ
1. Can you resolve a 2-D vector along two directions, which are not at 90° to each other?
A) Yes, but not uniquely.
B) No.
C) Yes, uniquely.
2. Can you resolve a 2-D vector along three directions (say at 0, 60, and 120°)?
A) Yes, but not uniquely.
B) No.
C) Yes, uniquely.
Answers:
1. C
2. A
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

8. EXAMPLE 1
Find the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis.
Plan:
Sketch the system and show vector addition using the parallelogram law.
Sketch a triangle showing head-to-tail addition.
Apply trig to find the missing information.
Apply the results to the original diagram to solve the problem.
Perform a check calculation.
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

9. Resolve the force F2 into components acting along the u and v axes.
EXAMPLE 2
Resolve the force F2 into components acting along the u and v axes.
Plan:
Sketch the system and show the components using the parallelogram law.
Sketch a triangle showing head-to-tail addition.
Apply trig to find the missing information.
Apply the results to the original diagram to solve the problem.
Perform a check calculation.
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

10. EXERCISE 1
Determine the magnitude of the resultant force FR = F1 + F2 and its direction, measured clockwise from the positive u axis.
Plan:
Sketch the system and show vector addition using the parallelogram law.
Sketch a triangle showing head-to-tail addition.
Apply trig to find the missing information.
Apply the results to the original diagram to solve the problem.
Perform a check calculation.
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

11. EXERCISE 2
2-15: Resolve the force F1 into components acting along the u and v axes.
2-16: Resolve the force F2 into components acting along the u and v axes.
Plan:
Sketch the system and show the components using the parallelogram law.
Sketch a triangle showing head-to-tail addition.
Apply trig to find the missing information.
Apply the results to the original diagram to solve the problem.
Perform a check calculation.
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

12. Example 1: FR = 72.1 lb, θ = 73.9° (measured CCW from +x axis)
ANSWERS
Example 1:  FR = 72.1 lb, θ = 73.9° (measured CCW from +x axis)
Example 2:  F2u = 86.6 lb, F2v = lb
Exercise 1:  FR = 605 N, θ = 85.4° (measured CW from +u axis)
Exercise 2:  F1u = 183 N, F1v = 129 N, F2u = 150 N, F2v = 77.6 N
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4