PHY 221 Lab 1
(Fall 2003)
Position, Displacement, Average Velocity
Leader:
Critic:
Scribe:
PHY 211/221 is devoted to the description and explanation of motion. We start the course with the description of motion, a subject also known as kinematics.
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.
Meter sticks
Metal angle bracket
PC with ULI interface for measuring instruments
PASCO Motion Sensor (also known as a "sonic ranger")
PASCO cart on aluminum tracks (activity 3-5)
Pick a spot on your lab bench, just to the right of your PC, to be a reference point for your position measurements. Physicists and mathematicians call such a point the origin of coordinates.
Put down an angle bracket some distance away from the origin. Using a meter stick, measure the position of the angle bracket with respect to the origin (express your measurements in meters). Write it down here:
Now, move the angle bracket farther from the origin (along the direction defined by the origin and the initial position), 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 displacement?
2. Use of sonic ranger to measure static positions
Now you will make your first use of the computerized measuring equipment.
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 and that the box is on.
Next, click on the button labeled "Collect" near the top of the screen (or hit “Enter” key). When you hear a clicking sound, move your hand around near the front of the sonic ranger. Do you see a relationship between the position of your hand and the height of the blue line of the graph on the computer? What is the relationship?
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 from part 1.
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 bracket sitting at the second position? Indicate your answers on the graph above.
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 two positions?
For more accurate results, bring up the measurement cursor. Turn it on by clicking on the button labeled "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 measured positions of the angle bracket at position one and at position two?
Comment on the similarities and differences between the position measurements made with the sonic ranger, compared with those made with just a meter stick.
Does position measurement depend on the choice of the origin of coordinates?
What is the displacement of the angle bracket between the two positions measured with the sonic ranger?
Comment on the similarities and differences between the displacement measurement made with the sonic ranger, compared with the one made with just a meter stick.
Does displacement measurement depend on the choice of the origin of coordinates?
Put one of the aluminum tracks on your lab bench, and install a PASCO cart on it. Ensure that it moves freely on the track.
Try a measurement of the position of the cart as a function of time x(t), as it moves freely down the track (give it initial push and then let it go). Set up a meter stick alongside the track. Each student in a team of three has a key role to play here. The Leader sets the cart in motion, then calls out one-second intervals using her watch. The Critic reads the position of the cart along the meter stick at each second. The Scribe records the positions as they are called out. The Leader is responsible for ensuring that the cart does not fall off the track.
Make a graph of position vs. time:
How well does this procedure work? Is it accurate? Could you track complicated motions with such a procedure?
Hook your sonic ranger onto the end of your aluminum track. Push the cart along the track and collect some data. Fiddle with the angle-adjustment knob on the sonic ranger until you can see the cart all the way to the end of the track. (Tipped upwards a bit is probably best.) Ask your TA for help on this step if you need it.
Now, repeat the measurement of x(t) for a free moving cart, except using the sonic ranger instead of the meter stick.
Make a sketch of the graph that you see on the screen.
Compare and contrast the two methods for determining x(t) for a moving object. Which is easier? More accurate? Capable of tracking complicated motions?
5. Average velocity
Write down the position of the cart at t = 3 sec and at t = 5 sec. Use the measurement cursor to get accurate results.
What was the displacement of the cart during that time interval?
What was the average velocity during that time interval?
Now determine average velocity for time interval from t = 5 sec to t= 7 sec.
Compare average velocity in these two time intervals. Did it increase, decrease or stay the same? Any ideas why?