One good way to describe the motion of some object is to say where it was at what time. We can call this the "position as a function of time", usually written x(t). Another name for x(t) is the "trajectory" of the object.
In lab, we want to measure the things that we think about in physics. So, we start your lab course with the question of how we can measure where an object is at various times.
PC with ULI interface for measuring instruments
PASCO Motion Sensor (also known as a "sonic ranger")
Put down an angle bracket some distance away from the origin.
a meter stick, measure the position of the angle bracket with respect
the origin. Write it down here:
How precise is your measurement?
Now, move the angle bracket farther from the origin, and measure
its location again. What is its position now?
When you moved the angle bracket from the first position to the
second position, you caused a displacement. How big was the
First, follow the instructions in the Appendix to set up your computer to make measurements with the sonic ranger. (Computer booted up, application Logger Pro running, file Motion Detector opened, one graph displayed.) Also, check to be sure that the PASCO Motion Detector ("sonic ranger") is plugged into Port 2 of your ULI interface box.
Next, click on the button labeled "Collect" near the top of the
screen. When you hear a clicking sound, move your hand around near the
the sonic ranger. Do you see a relationship between the position of
hand and the height of the blue line of the graph on the computer? What
Now you are ready to try some real quantitative measurements of position and displacement using the sonic ranger. Set the sonic ranger at the spot you called your origin of coordinates, and leave the meter stick aligned as you had it before. Place the angle bracket at the first position from part 1., then click on the "Collect" button on the screen. After a few seconds, move the angle bracket to the second position.
Make a sketch of the graph that appears on the screen:
What part of the graph corresponds to the angle bracket sitting at
the first position? What part of the graph corresponds to the angle
sitting at the second position?
Now read off the positions of the angle bracket at the two
locations. For rough measurements, you can just read the graph by eye.
What are the
For more accurate results, bring up the measurement cursor. Turn it on by clicking on the button labelled "x=?" on the toolbar near the top of the screen. Then you should see a vertical line that will move across the graph as you move the mouse, and a little window near the top of the graph that reads the graph by giving the value of distance D as a function of the time corresponding to where you place the cursor.
What are the positions of the angle bracket at position one and at
What was the displacement of the angle bracket between the two
Comment on the similarities and differences between position and
displacement measurements made with the sonic ranger, compared with
those made with just a meter stick.
Now, try a measurement of the position of the cart as a function of time x(t), as it moves down the track. Set the cart in motion, so that it takes 6 or 7 seconds to reach the end of the track. (The Leader sets it in motion, and the Scribe prepares to catch the cart if it is in danger of falling off the end of the track.)
Make a sketch of the graph that you see on the screen.
After practicing a few times, measure the motion of dynamics cart
as it rolls along the tilted track. Make a graph of the position of the
cart as a function of time. Sketch the graph here:
What is the shape of the graph of x(t)? How does it differ
from what you saw before, from the cart rolling on the level track? Why
tilting the track make a difference?
How would you most simply describe the motion of the cart?
position? Constant velocity? Constant acceleration?
Switch the computer display to "Three panes". Set up the second
graph to display velocity of the cart, and the third graph to display
its acceleration. How are those kinematic quantities defined? How might
the program calculate them?
Sketch all three graphs here:
Next, think of what kind of motion corresponds to v = constant. Sketch the graphs of x(t), v(t), and a(t).
Now, think of what kind of motion corresponds to a = constant. Sketch the graphs of x(t), v(t), and a(t).