Describing Motion with Diagrams(1-D Kinematics)

Introduction to Diagrams

Throughout The Physics Classroom Tutorial, there is a persistent appeal to your ability to represent physical concepts in a visual manner. You will quickly notice that this effort to provide visual representation of physical concepts permeates much of the discussion in The Physics Classroom Tutorial. The world that we study in physics is a physical world - a world that we can see. And if we can see it, we certainly ought to visualize it. And if we seek to understand it, then that understanding ought to involve visual representations. So as you continue your pursuit of physics understanding, always be mindful of your ability (or lack of ability) to visually represent it. Monitor your study and learning habits, asking if your knowledge has become abstracted to a series of vocabulary words that have (at least in your own mind) no relation to the physical world which it seeks to describe. Your understanding of physics should be intimately tied to the physical world as demonstrated by your visual images. Like the study of all of physics, our study of 1-dimensional kinematics will be concerned with the multiple means by which the motion of objects can be represented. Such means include the use of words, the use of graphs, the use of numbers, the use of equations, and the use of diagrams. Lesson 2 focuses on the use of diagrams to describe motion. The two most commonly used types of diagrams used to describe the motion of objects are:

• Ticker Tape Diagrams
• Vector Diagrams

Begin cultivating your visualization skills early in the course. Spend some time on the rest of Lesson 2, seeking to connect the visuals and graphics with the words and the physical reality. And as you proceed through the remainder of the unit 1 lessons, continue to make these same connections.

Ticker Tape Diagrams

A common way of analyzing the motion of objects in physics labs is to perform a ticker tape analysis. A long tape is attached to a moving object and threaded through a device that places a tick upon the tape at regular intervals of time - say every 0.10 second. As the object moves, it drags the tape through the "ticker," thus leaving a trail of dots. The trail of dots provides a history of the object's motion and therefore a representation of the object's motion.

The distance between dots on a ticker tape represents the object's position change during that time interval. A large distance between dots indicates that the object was moving fast during that time interval. A small distance between dots means the object was moving slow during that time interval. Ticker tapes for a fast- and slow-moving object are depicted below.

The analysis of a ticker tape diagram will also reveal if the object is moving with a constant velocity or accelerating. A changing distance between dots indicates a changing velocity and thus an acceleration. A constant distance between dots represents a constant velocity and therefore no acceleration. Ticker tapes for objects moving with a constant velocity and with an accelerated motion are shown below.

And so ticker tape diagrams provide one more means of representing various features of the motion of objects.

 

Check Your Understanding

Ticker tape diagrams are sometimes referred to as oil drop diagrams. Imagine a car with a leaky engine that drips oil at a regular rate. As the car travels through town, it would leave a trace of oil on the street. That trace would reveal information about the motion of the car. Renatta Oyle owns such a car and it leaves a signature of Renatta's motion wherever she goes. Analyze the three traces of Renatta's ventures as shown below. Assume Renatta is traveling from left to right. Describe Renatta's motion characteristics during each section of the diagram.

1.

ANS:  Renatta decelerates from a high speed to low speed until she is finally stopped. She remains at rest for a while and then gradually accelerates until the trace ends.

 

2.

ANS:  Renatta travels at a constant speed during the first time interval and then gradually accelerates until the trace ends.

 

3.

ANS:  Renatta moves with a constant speed in the first time interval. She then abruptly decelerates to a stop. She remains at rest for sometime and then moves with a constant speed, slower than the first speed.

Vector Diagrams

Vector diagrams are diagrams that depict the direction and relative magnitude of a vector quantity by a vector arrow. Vector diagrams can be used to describe the velocity of a moving object during its motion. For example, a vector diagram could be used to represent the motion of a car moving down the road.

In a vector diagram, the magnitude of a vector quantity is represented by the size of the vector arrow. If the size of the arrow in each consecutive frame of the vector diagram is the same, then the magnitude of that vector is constant. The diagrams below depict the velocity of a car during its motion. In the top diagram, the size of the velocity vector is constant, so the diagram is depicting a motion of constant velocity. In the bottom diagram, the size of the velocity vector is increasing, so the diagram is depicting a motion with increasing velocity - i.e., an acceleration.

Vector diagrams can be used to represent any vector quantity. In future studies, vector diagrams will be used to represent a variety of physical quantities such as acceleration, force, and momentum. Be familiar with the concept of using a vector arrow to represent the direction and relative size of a quantity. It will become a very important representation of an object's motion as we proceed further in our studies of the physics of motion.