CHAPTER 2: FORCE VECTOR

2.1 Understand scalars and vectors 2.1.1 Differentiate between scalars and vectors

VECTORS • When comparing two vector

quantities of the same type, you have to compare both the magnitude and the direction. When doing any mathematical operation on a vector quantity (like adding, subtracting, multiplying ..) you have to consider both the magnitude and the direction. This makes dealing with vector quantities a little more complicated than scalars.

• For scalars, you only have to compare the magnitude.

SCALARS

• A vector is shown graphically by an arrow. The length of the arrow represents the magnitude of the vector, and the angle ᶿ between the vector and the fixed axis defines the direction of its line of action. The head or tip of the arrow indicates the sense of direction of the vector, Fig. 2-1

• Check Your Understanding

• 1. To test your understanding of this distinction, consider the following quantities listed below. Categorize each quantity as being either a vector or a scalar.

– a. 5 m

– b. 30 m/sec, East

– c. 5 mi., North

– d. 20 degrees Celsius

– e. 256 bytes

– f. 4000 Calories

2.1.2 Distinguish free vectors, sliding vectors, fixed vectors

2.2 Understand rectangular components 2.2.1 Explain two forces acting on a particle

2.3 Understand vectors and vector operations 2.3.1 Calculate addition of vectors

2.3.2 Calculate subtractions of vectors

• The process of determining the magnitude of a vector.

• The two methods of vector resolution that we will examine are

– the parallelogram method

– the trigonometric method

2.3.3 Determine resolutions of vectors

The parallelogram method

The above method is illustrated below for determining the components of the

force acting upon Fido. As the 60-Newton tension force acts upward and

rightward on Fido at an angle of 40 degrees, the components of this force can

be determined using trigonometric functions.

The trigonometric method

2.4 Understand the resultant force of coplanar forces by addition

2.5 Understand Cartesian vectors

2.7 Understand position vectors

and x, y, z coordinates

2.8 Understand the force vector

directed along the line

2.9 Understand the dot product