Chapter Two Vectors 1 Vectors n n A

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Chapter Two Vectors 1

Chapter Two Vectors 1

Vectors n n A quantity consisting only of magnitude is called a scalar quantity.

Vectors n n A quantity consisting only of magnitude is called a scalar quantity. A quantity that has both magnitude and direction and obeys certain algebraic laws is called a vector quantity. 2

Vector Components n See Figure 2 -1. n or n See Figure 2 -2.

Vector Components n See Figure 2 -1. n or n See Figure 2 -2. East: North: n n 3

n 4

n 4

n See Figure 2 -3. n See Figures 2 -4, 2 -5, 2 -6,

n See Figure 2 -3. n See Figures 2 -4, 2 -5, 2 -6, 2 -7. 5

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n 6

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n 7

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n 9

Example 2 -1 n A box is pulled by two persons exerting the forces

Example 2 -1 n A box is pulled by two persons exerting the forces F 1 and F 2 shown in Fig. 2 -8, which F 1 is given as 50 lb. Two questions may now be asked. 1. What force F 2 must be applied so that the box moves only in the x direction? 2. What single force could replace F 1 and F 2 so that the box moves only in the x direction? 10

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n 11

Sol n See Figure 2 -9. Forces on x direction: n Forces on y

Sol n See Figure 2 -9. Forces on x direction: n Forces on y direction: n 12

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n 13

n If the object is going to move in the x direction, then n

n If the object is going to move in the x direction, then n Question 2 can be answered as 14

Unit Vectors n n See Figure 2 -10. See Figure 2 -11. 15

Unit Vectors n n See Figure 2 -10. See Figure 2 -11. 15

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n 16

Dot Product n n The dot product is defined as where on the right

Dot Product n n The dot product is defined as where on the right side A and B are the magnitude of each of the vectors and θ is the angle between them. See Figure 2 -12. 17

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n 18

Cross Product n n n If C is the cross product of A and

Cross Product n n n If C is the cross product of A and B, we have and See Figure 2 -13. The direction of C is perpendicular to both A and B and consequently perpendicular to the plane containing A and B (and obey the right-hand rule). See Figures 2 -14, 2 -15. Homework: 12, 16, 17. 19

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n 21