8/19/2019 Chapter 2-Force Vector

1/16

1.  FORCE VECTOR

1.1  Distinguish scalars and vectors

1.1.1 

Differentiate between scalars and vectors

A scalar is any positive or negative physical quantity that can be completely specified by its

magnitude. Examples of scalar quantities include length, mass and time.

A vector is any physical quantity that requires both a magnitude and direction for its complete

description. Examples of vectors encountered in statics are force, position, and moment.

1.1.2  Distinguish between free vectors, sliding vectors, fixed vectors

Free vector is one which can be moves anywhere in the space maintaining magnitude direction

and its sense. In other words, this vector does not have a specified point of application. Thecomponent vectors of a couple are free vectors.

Sliding vectors is one which may be applied anywhere along its line of action maintaining

magnitude, direction and sense. The force acting on a rigid body is an example of a sliding

8/19/2019 Chapter 2-Force Vector

2/16

8/19/2019 Chapter 2-Force Vector

3/16

The resultant of the difference between two vectors A and B of the same type may be expressed

as R = A – B = A + (-B)

1.2.3 

Determine resolution of vectors

1.3  Explain rectangular components

When a force is resolved into two components along the x and y axes, the components are then

called rectangular components.

1.3.1  Explain two forces acting on a particle

1.4  Determine the resultant force of coplanar forces by addition

1.4.1 

Explain scalar notationThe rectangular components of force F are found using the parallelogram law, so that F = Fx +

Fy. Because these components form a right triangle, their magnitudes can be determined from

Fx = F cos Ɵ  andFy = F sin Ɵ 

8/19/2019 Chapter 2-Force Vector

4/16

 

8/19/2019 Chapter 2-Force Vector

5/16

 

1.4.2  Explain Cartesian vector notation

It is also possible to represent the x and y components of a force in terms of Cartesian unit vector

i and j. Each of these unit vectors has a dimensionless magnitude of one, and so they can be used

to designate the directions of the x and yaxes.

F = Fxi+Fy j 

8/19/2019 Chapter 2-Force Vector

6/16

 

1.4.3  Determine coplanar forces and resultant force using scalar notation and Cartesian

notation

1.4.3.1 Determine the resultant force of coplanar forces by addition

We can represent the components of the resultant force of any number of coplanar forces

symbolically by the algebraic sum of the x and y components of all the forces.

8/19/2019 Chapter 2-Force Vector

7/16

 

Once these components are determined, they may be sketched along the x and y axes with proper

sense of direction, and the resultant force can be determined from vector addition. From the

sketch, the magnitude of FR is then found from the Pythagorean theorem; that is

8/19/2019 Chapter 2-Force Vector

8/16

1.4.4  Explain position vectors and x, y, z coordinates

Position vector is important in formulating a Cartesian force vector directed between two points

in space. Position vector r, is defined as a fixed vector which located a point in space relative to

another point. For example, if r extends from the origin of coordinates, o, to point P(x, y, z), then

r can be expressed in Cartesian vector form as

r = xi + y j + zk

Or in more general case,

r = (xB-xA)i + (yB-yA) j + (zB-zA)k

8/19/2019 Chapter 2-Force Vector

9/16

8/19/2019 Chapter 2-Force Vector

10/16

 

8/19/2019 Chapter 2-Force Vector

11/16

 

1.5  Analyze the force vectors and x, y, z coordinates

8/19/2019 Chapter 2-Force Vector

12/16

 

8/19/2019 Chapter 2-Force Vector

13/16

1.5.1  Explain the force vector directed along the line

1.5.2  Determine the force vector directed along the line

1.6  EXERCISES

8/19/2019 Chapter 2-Force Vector

14/16

 

8/19/2019 Chapter 2-Force Vector

15/16

 

8/19/2019 Chapter 2-Force Vector

16/16