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Lect3_Statics Dr. ALI AL-SHATRI Che. Eng .pdf

Abu Hussein
Abu Hussein

Resultant force

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Statics Lecture 3 1
To express force and position in Cartesian vector form and explain how to determine the vectors magnitude and direction. Objective: 2 Lecture 3
Addition of a system of coplanar forces 3 When a force is resolved into two components along the x and y axes, the components are then called rectangular components. For analytical work we can represent these components in one of two ways, using either scalar or Cartesian vector notation. Scalar Notation. The rectangular components of force F shown in Fig. 215a are found using the parallelogram law, so that = + . Because these components form a right triangle, they can be determined from = =
Addition of a system of coplanar forces 4 Instead of using the angle , however, the direction of F can also be defined using a small slope triangle, as in the example shown in Fig. 215b. Since this triangle and the larger shaded triangle are similar, the proportional length of the sides gives
Addition of a system of coplanar forces 5 Cartesian Vector Notation. It is represented the x and y components of a force in terms of Cartesian unit vectors i and j. They are called unit vectors because they have a dimensionless magnitude of 1, and so they can be used to designate the directions of the x and y axes, respectively, Fig. 216. Since the magnitude of each component of F is always a positive quantity, which is represented by the (positive) scalars and , then we can express F as a Cartesian vector,
Coplanar force resultants: 6
7 Summary
8 Example 3.1
9 Example 3.1 = + = .
10 Example 3.2
11 Example 3.2
12 Example 3.3
13 Example 3.3

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Lect3_Statics Dr. ALI AL-SHATRI Che. Eng .pdf

  • 2. To express force and position in Cartesian vector form and explain how to determine the vectors magnitude and direction. Objective: 2 Lecture 3
  • 3. Addition of a system of coplanar forces 3 When a force is resolved into two components along the x and y axes, the components are then called rectangular components. For analytical work we can represent these components in one of two ways, using either scalar or Cartesian vector notation. Scalar Notation. The rectangular components of force F shown in Fig. 215a are found using the parallelogram law, so that = + . Because these components form a right triangle, they can be determined from = =
  • 4. Addition of a system of coplanar forces 4 Instead of using the angle , however, the direction of F can also be defined using a small slope triangle, as in the example shown in Fig. 215b. Since this triangle and the larger shaded triangle are similar, the proportional length of the sides gives
  • 5. Addition of a system of coplanar forces 5 Cartesian Vector Notation. It is represented the x and y components of a force in terms of Cartesian unit vectors i and j. They are called unit vectors because they have a dimensionless magnitude of 1, and so they can be used to designate the directions of the x and y axes, respectively, Fig. 216. Since the magnitude of each component of F is always a positive quantity, which is represented by the (positive) scalars and , then we can express F as a Cartesian vector,