FORCES AND MOTION 2

PHYSICS 30

DESCRIBING MOTION WITH DIAGRAMS

• The two most commonly used types of diagrams used to describe the motion of objects are:

Ticker Tape Diagrams

Vector Diagrams

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.

TICKER TAPE DIAGRAMS

• 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 TAPE DIAGRAMS

• 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 TAPE DIAGRAMS• 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.

• Examples

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.

VECTOR DIAGRAMS

• 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.

POSITION-TIME GRAPHS

• Contrasting a Constant and a Changing Velocity

To begin, consider a car moving with a constant, rightward (+) velocity - say of +10 m/s.

GRAPH IT!

POSITION-TIME GRAPHS

POSITION-TIME GRAPHS

• Now consider a car moving with a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating.

• GRAPH IT!

POSITION-TIME GRAPHS

POSITION-TIME GRAPHS• COMPARE

POSITIVE VELOCITYPOSITIVE VELOCITY

CONSTANT VELOCITYCHANGING VELOCITY (ACCELERATION

POSITION-TIME GRAPHS

• What about SLOPE?

• "As the slope goes, so goes the velocity."

• Whatever characteristics the velocity has, the slope will exhibit the same (and vice versa).

• If the velocity is constant, then the slope is constant (i.e., a straight line). If the velocity is changing, then the slope is changing (i.e., a curved line). If the velocity is positive, then the slope is positive (i.e., moving upwards and to the right).

POSITION-TIME GRAPHS

• Contrasting a Slow and a Fast Motion, Positive and Negative, ALL CONSTANT VELOCITY

POSITION-TIME GRAPHS• Contrasting a Slow and a Fast Motion

Positive, Slow, Positive, Fast, Negative, Slow, Negative, Fast,

Constant Velocity Constant Velocity Constant Velocity Constant Velocity

POSITION-TIME GRAPHS

• Representing an Accelerated Motion

• Curved lines have changing slope – IN THIS CASE MEANS CHANGING VELOCITY a.k.a. ACCELERATION!!

POSITION-TIME GRAPHS• Representing an Accelerated Motion

• Curved lines have changing slope – IN THIS CASE MEANS CHANGING VELOCITY a.k.a. ACCELERATION!!

NEGATIVE VELOCITY NEGATIVE VELOCITY

SLOW to FAST VELOCITY FAST TO SLOW VELOCITY

NEGATIVE ACCELERATION POSITIVE ACCELERATION

POSITION-TIME GRAPHS

• Constant Rightward Velocity

• Constant Leftward Velocity

• Rightward Velocity with a Rightward Acceleration

• Rightward Velocity with a Leftward Acceleration

• Leftward Velocity with a Leftward Acceleration

• Leftward Velocity with a Rightward Acceleration

• Passing Lane - Position vs. Time Graph

ACTIVITY

• Graph that Motion

• Graphs and Ramps

CHECK

• In your description, be sure to include such information as the direction of the velocity vector (i.e., positive or negative), whether there is a constant velocity or an acceleration, and whether the object is moving slow, fast, from slow to fast or from fast to slow.

CHECKPractice A Practice B

Positive, Changing Velocity Negative, Changing Velocity

Slow to Fast Slow to Fast

Positive Acceleration Negative Acceleration

POSITION-TIME GRAPHS

• The Meaning of Slope for a p-t Graph

• The slope of a position vs. time graph reveals pertinent information about an object's velocity.

• For example, a small slope means a small velocity; a negative slope means a negative velocity; a constant slope (straight line) means a constant velocity; a changing slope (curved line) means a changing velocity. Thus the shape of the line on the graph (straight, curving, steeply sloped, mildly sloped, etc.) is descriptive of the object's motion.

• Determining the Slope on a p-t Graph

CHECK

CHECK

-3m/s

CHECK

CHECK

4m/s

VELOCITY – TIME GRAPH• Constant Velocity versus Changing Velocity

VELOCITY – TIME GRAPH• Constant Velocity versus Changing Velocity

VELOCITY – TIME GRAPH• Constant Velocity versus Changing Velocity

VELOCITY – TIME GRAPH• Constant Velocity versus Changing Velocity

VELOCITY – TIME GRAPH• Constant Velocity versus Changing Velocity

POSITIVE VELOCITY POSITIVE VELOCITY

ZERO ACCELERATION POSITIVE ACCELERATION

• The principle is that the slope of the line on a velocity-time graph reveals useful information about the acceleration of the object. • If the acceleration is zero, then the slope is zero (i.e., a horizontal line).

• If the acceleration is positive, then the slope is positive (i.e., an upward sloping line).

• If the acceleration is negative, then the slope is negative (i.e., a downward sloping line).

• Positive Velocity versus Negative Velocity

• a positive velocity means the object is moving in the positive direction; and a negative velocity means the object is moving in the negative direction. So one knows an object is moving in the positive direction if the line is located in the positive region of the graph (whether it is sloping up or sloping down). And one knows that an object is moving in the negative direction if the line is located in the negative region of the graph (whether it is sloping up or sloping down).

• Speeding Up versus Slowing Down

• Speeding up means that the magnitude (or numerical value) of the velocity is getting large. For instance, an object with a velocity changing from +3 m/s to + 9 m/s is speeding up. Similarly, an object with a velocity changing from -3 m/s to -9 m/s is also speeding up. In each case, the magnitude of the velocity (the number itself, not the sign or direction) is increasing; the speed is getting bigger.

• Passing Lane - Velocity vs. Time Graph

• The Stoplight

• Motion of a Two-Stage Rocket

CHECK• 1. Consider the graph at the right. The object whose motion is represented by this graph is ... (include all that

are true):

• moving in the positive direction.

• moving with a constant velocity.

• moving with a negative velocity.

• slowing down.

• changing directions.

• speeding up.

• moving with a positive acceleration.

• moving with a constant acceleration.

CHECK• 1. Consider the graph at the right. The object whose motion is represented by this graph is ... (include all that are true):

• Answers: a, d and h apply.

• a: TRUE since the line is in the positive region of the graph.

• b. FALSE since there is an acceleration (i.e., a changing velocity).

• c. FALSE since a negative velocity would be a line in the negative region (i.e., below the horizontal axis).

• d. TRUE since the line is approaching the 0-velocity level (the x-axis).

• e. FALSE since the line never crosses the axis.

• f. FALSE since the line is not moving away from x-axis.

• g. FALSE since the line has a negative or downward slope.

• h. TRUE since the line is straight (i.e, has a constant slope).