Resultants by Rectangular Components

1
Lecture 7

• Resultants by Rectangular Components

2
2D Resultants
y

• For two dimensions

Fy2
F2
F1
Fy1
Fx3
x
Fx1
Fx2
Fy3
F3
3
2D Resultants
4
3D Resultants

• For three dimensions

5
3D Resultants
6
Example 1

• Problem
• Determine
• 1. The magnitude R of the resultant and,
• 2. The angle qx between the line of action of the
  resultant and the x-axis.

7
Example 1

• Solution
• 1. Determine the unit vectors for , , .

z
e3
k
e2
j
i
y
e1
x
8
Example 1

• 2. Express the three forces as Cartesian vectors.

3. Find the resultant, R.
9
Example 1

• 4. Find the magnitude of the resultant, R.

5. Find qx, qy, and qz.
10
Note

• If the vector is defined by horizontal and
  vertical angles, determine the rectangular
  components of Fx, Fy, and Fz by trigonometry.

11
Example 2

• Problem
• Determine the magnitude and direction (qx, qy,
  qz) of the resultant.

12
Example 2

• Solution
• (1) Determine the unit vectors for F1.

13
Example 2

• (2) Determine Fx, Fy and Fz for F2.

14
Example 2

• (3) Express F1 as a Cartesian vector.

(4) The resultant R F1 F2 F3
15
Example 2

• (5) Find the magnitude of R.

(6) Find the direction angles.
16
Example 2

• (7) Determine the rectangular component of the
  force F1 along the line of action of force F2.

17
Example 2
(8) Determine the angle a between F1 and F2.
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Additional Material

• Problems 2-85, 93, 98, 102, 110, 114, 123