Motion in a line

 
 

Objectives

  • Define kinetics and kinematics
  • Distinguish between speed and velocity
  • Distinguish between velocity and acceleration

Our author begins with a discussion of speed. However, we will begin by laying a foundation before we confuse ourselves with common definitions. Since speed implies motion, we must be looking at things in motion. Technically, the topic is dynamics. The study of Dynamics is generally divided into two parts. Kinetics, which focuses on the forces causing the motion. While kinematics deals with the geometrical aspects of motion (Hibbeler, p. 1) or “which studies the motion of particles and bodies in motion, without concern for the forces that produce these motions.” (Shelley, p. 473)

Initially, during our investigation of kinematics we will be discounting or ignoring the forces causing or producing by the motion. In addition, the physical properties of interest will be limited to the object’s mass, speed, acceleration and direction of motion. Therefore, all physical objects will be viewed as particles.

  1. A particle is a physical body whose dimensions are vanishingly small.
  2. All non-particle objects of interest are modeled as “rigid bodies.” Therefore the object’s physical dimensions are unaffected by internal or external forces.
  3. All non-particle objects are replaced by particles with the object’s attributes of mass and motion. (all the mass of an object is concentrated at one point)

There are two general types of particle motion. Straight line or rectilinear motion wherein an object is constrained to move along a straight line (AB) and curved or curvilinear motion that permits only curved motion.

NumberLine14.03.21

A point on the number line


  A particle moving along a linear path can travel only two directions. The similarities between the path and a “number line” suggest that the direction of any particle can be indicated by the common positive (+) and negative (-) signs. Taking the analogy a step further, if all measurements are made from a point in space (zero on the number line) than any point in space can be located using two descriptors, the direction and the distance from the point. Clearly, a number does not completely and positively identify the position of a point on the number line.

Directional numbers

Sign indicates direction

A number does not completely and positively identify the position of a point on the number line. This is the foundation of the difference between distance and displacement, speed and velocity and more importantly, scalars and vectors. Scalars communicate the count, size or magnitude of a number. A vector provides more information because it includes a directional component.

 

Hibbeler, R. (1985). Mechanics for engineers statics and dynamics. NY,NY: Macmillan.

Shelley, J. F. (1980). Engineering mechanics, statics and dynamics. McGraw-Hill Inc.

 

 

No comments

Be the first one to leave a comment.

Post a Comment