Wed 9  SEP:

 

Key Concept(s) Today: Acceleration & Graphs

 

Journal:

 

Examples:

1.   If you travel 10m/s due east for 20 s, what is your:

a)   Speed

b)   Displacement

c)   Velocity

 

2.   If you travel 10m/s due east for 20 s, then you travel 20m/s for 20s due south, what is your:

a)   Speed

b)   Displacement

c)   Velocity

 

3.   If you travel 10m/s due east for 20 s, then you travel 20m/s for 20s due south, then you travel 10m/s due west for 20s, what is your:

a)   Speed

b)   Displacement

c)   Velocity

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.

a)   Speed (Dist/time) = 200m/20s = 10m

b)   Displacement  200m due east or 00

c)   Velocity = (Disp/time  & Dir) = 200m/20s = 10m @00

 

2.

a)   Speed (Dist/time) = 200m/20s = 10m

b)   Displacement  200m due east or 00

c)   Velocity = (Disp/time  & Dir) = 200m/20s = 10m @00

3.

 

a)   Speed (Dist/time) = 200m/20s = 10m

b)   Displacement  200m due east or 00

c)   Velocity = (Disp/time  & Dir) = 200m/20s = 10m @00

 

 

 

 

 

 

 

 DEMO:

 

 

 

 

 

 

1. Draw a free Body Diagram of this ball on an incline plane.

 

2. Draw graphs (Pos vs Time, Vel vs Time, & Acceleration vs Time) for a ball rolling down an incline plane

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

     x

                                               t

 

 

 

 

                    v

 

                          

                            t

 

 

 

 

 

 

                                a

 

 

 

 

                                                                                                                                                t

 

 

 

Graphs:

 

Describing Motion with Position vs. Time Graphs

The Meaning of Shape for a p-t Graph

The specific features of the motion of objects are demonstrated by the shape and the slope of the lines on a position vs. time graph.

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

car in motion
 

position vs. time graphThe resulting graph would look like the graph at the right. Note that a motion with constant, positive velocity results in a line of constant and positive slope.

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

car in motion

position vs. time graph

The resulting graph would look like the graph at the right. Note that a motion with changing, positive velocity results in a line of changing and positive slope.

The Principle of Slope for a p–t Graph reveals useful information about the velocity of the object.

Positive Velocity Constant Velocity Positive Velocity Changing Velocity (acceleration)
graph graph

 

If the velocity is constant, then the slope is constant. If the velocity is non-constant (i.e., an acceleration +/-) then the slope is a curve.

Example

Leftward (–) Velocity; Slow to Fast Leftward (–) Velocity; Fast to Slow
graph graph
 

 

 

 

 

The Velocity- Time (V-T) Graph

If the slopes on V-T graphs are a straight line, the +/- acceleration is constant. If the slopes are curved, the acceleration is not constant.

 

car in motion

 

velocity graph

 

car in motion

graph
 

car in motion

 

graph


 

Questions:

1.   Does speed have a direction?

2.   Does velocity have a direction?

3.   What three things can one do to change velocity?

4.   Does acceleration have a direction?

5.   If acceleration is “0” is it moving?

6.   If velocity is “0” is it moving?

7.   If velocity is “0” can it be accelerating?

8.   Fill in table below

 

Vi (m/s)

Vf (m/s)

Time (s)

Acceleration

(m/s2)

10.0

31.0

7.0

 

0.0

0.0

10.0

 

5.0

5.0

10.0

 

5.0

-5.0

2.0

 

 

100.0

5.0

10.0

 

 

 

1.        +40 m/s/s. (The line rises +40 m/s for every 1 second of run)

2.        +20 m/s/s. The line rises +60 m/s for 3 seconds of run. The rise/run ratio is +20 m/s/s.

3.        -20 m/s/s. The line rises -160 m/s for 8 seconds of run. The rise/run ratio is -20 m/s/s.

4.        20m                        

5.        250m                      

6.        (20 + 250 + 90 + 120 ) = 480m

7.        -250m                     

8.        230m

 

 

 

Formulas:

 

·       Speed = dist/time

 

·       VelAvg = Vf  + Vi  /2

 

·       Vel =  Dx (or displacement) /time

 

·       Acc = Vf  – Vi /time     or   DV /time

 

Motion equations:

·       Vf  = Vi  + (a)(t)

 

·       Vf 2 - Vi2  = 2(a)(Dx)

 

·       Position (x) = Vi (t) + 1/2(a)(t2)

 

 

 

 

 

 

 

Graphs:

 

Applet:

http://www.physics.gatech.edu/academics/classes/2211_fall2000/main/demos/VectorAddition/vectortest.htm

Show how vectors are added #1

Show components of vectors #2

 

Vector Activity:

 

 

The head-to-tail method involves drawing a vector to scale on a sheet of paper beginning at a designated starting position. Where the head of this first vector ends, the tail of the second vector begins (thus, head-to-tail method). The process is repeated for all vectors which are being added. Once all the vectors have been added head-to-tail, the resultant is then drawn from the tail of the first vector to the head of the last vector; i.e., from start to finish. Once the resultant is drawn, its length can be measured and converted to real units using the given scale. The direction of the resultant can be determined by using a

  1. Choose a scale and indicate it on a sheet of paper
  2. Pick a starting location and draw the first vector to scale in the indicated direction.
  3. Starting from where the head of the first vector ends, draw the second vector to scale in the indicated direction.
  4. Label the magnitude and direction of this vector on the diagram.
  5. Repeat steps 2 and 3 for all vectors which are to be added
  6. Draw the resultant from the tail of the first vector to the head of the last vector. Label this vector as Resultant or simply R.
  7. Using a ruler, measure the length of the resultant and determine its magnitude by converting to real units using the scale (4.4 cm x 20 m/1 cm = 88 m).
  8. Measure the direction of the resultant using the counterclockwise convention discussed