Straight Line Motion (Motion Sensor)

Transcription

1 Straight Line Motion (Motion Sensor) Name Section Theory An object which moves along a straight path is said to be executing linear motion. Such motion can be described with the use of the physical quantities: position, velocity, acceleration, and time. Galileo was the first natural philosopher to experimentally determine the relation between the above physical quantities. It is now well-known that the relationships are given by the following four equations x = 1 x v t at o + o + (1) vo + v x = t () v vo at (3) v o x o = v + a( x ) (4) where x is position (x o initial position), v is velocity (v o initial velocity), a acceleration, and t time. Different types of motion occur when acceleration is zero or a non-zero constant. By obtaining the position of a moving object at various times, one can determine the quantities in the equations. You will cause a cart to move along a horizontal track as well as down an inclined track, demonstrating zero and positive acceleration. In each case, a computer will record the position of the cart as a function of time. From these data, the Data Studio program will determine positions, velocities, and accelerations as functions of time, displaying it both in table and graph form. You will use these tables and graphs in your analysis of each motion. Apparatus Computer, Pasco 750 interface Motion sensor, Dynamics track, Frictionless cart, Wood block. Procedure If the Data Studio program is not up, start it (double-click the shortcut on the Windows desktop). From the Welcome screen, select Open Activity (the activity you want is Straight Line Motion). You are now ready to collect data. If you are taking over the apparatus from someone else or if you just want to get rid of data and start over go to the main menu within Data Studio. Select Experiment Delete Last Data Run (or Delete ALL Data Runs). Constant Velocity In this procedure, you will give the cart a push to get it started and then let it continue on its own at a constant velocity. The cart, although listed above as frictionless, does possess some friction that will slow it down over the length of the track. Therefore, you might want to incline the track slightly downward so that the velocity will remain constant over the entire length of track. You might want to practice a few times until you are sure that the velocity is as constant as it will get. Start with the cart near the motion timer that is clipped to one end of the track. Give the cart a push and then click the Start button on the toolbar (to the left of the Timer window). Make sure you click the Stop button before the cart reaches the end of the track. Look at the graph entitled Position vs. Time. Does this graph indicate that you were you able to make the cart move with a relatively constant velocity? How do you know this from the graph? Sp07 Page 1 of 6

2 Now click on the graph entitled Velocity vs. Time. Does this graph confirm your previous answer? What should this graph (the curve) look like if the cart really were moving at a constant velocity? There are some minimized windows at the bottom of the Data Studio window; these are tables of data that were used to plot the graphs. Open the window entitled Velocity. What do these values tell you about your success in achieving a constant velocity? Click the Sigma ( ) on the toolbar below the graph title. Record the mean velocity given If the cart did move at a constant velocity, what would its acceleration be? Look at the graph and table with the acceleration data and comment on them below. Open the table entitled Position and record the Times and Positions in Table 1. Time (s) Table 1 Position (m) Sp07 Page of 6

3 Positive Acceleration Put a piece of wood under the track so that the end with near the motion timer is elevated. You will release the cart from this end so that it accelerates down the track to the other end. The procedure is the same as before; release, click Start, then Stop before the cart reaches the opposite end of the track. You do not need to delete the previous data the tables and graphs will display the data from multiple runs. Comment on your graphs (and possibly your tables) position, velocity, and acceleration below. Are they what you expected? Why or why not? Record your Velocity table below. Time (s) Table Velocity (m/s) The track has distances marked on one side; pick points on this scale (at least 40.0cm apart). Use a rule and measure the height of the track (from the table) at both points. Use the same units for each measurement. Record all 4 values here: Sp07 Page 3 of 6

4 Analysis Plot the data from Table 1 (Position vs. Time). This is from the Constant Velocity procedure. Determine the slope of the curve plotted and record the value here, along with the appropriate units. Compare (percent error) this with the mean velocity that you recorded earlier in the experiment. Do you think these values should be the same? Why or why not? Did your graph have a y-intercept? What is the value (include units) and its significance? Plot the data from Table (Velocity vs. Time). This is from the Positive Acceleration procedure. Determine the slope of the curve plotted and record the value here, along with the appropriate units. The process of letting an object accelerate down an incline (rather than free-fall) has been called diluting gravity ; the object accelerates due only to the component of its weight parallel to the plane, as shown here This acceleration is a fraction of g, namely a=gsin (5) But the sine of an angle is defined as the ratio of the opposite side of a right triangle to its hypotenuse. Using the values you recorded in the procedure, determine the theoretical acceleration of the cart down the incline. difference in track heights a= difference in track distances g (6) How does your graphical value compare (percent error) to this value? Record the comparison and any thoughts here. Sp07 Page 4 of 6

5 Pre Lab: Straight Line Motion (Motion Sensor) Name Section 1. Consider Equations 1-4 and rewrite the results when the acceleration is zero.. Describe what happens to the velocity when the acceleration is zero. 3. Describe what happens to the velocity when the acceleration is positive. 4. Describe what happens to the velocity when the acceleration is negative. Sp07 Page 5 of 6

6 5. Given an initial velocity of m/s and an acceleration of 3 m/s, plot velocity versus time and position versus time for time t = 0s to t = 5s. 6. Given an initial velocity of m/s and an acceleration of -3 m/s, plot velocity versus time and position versus time for time t = 0s to t = 5s. Sp07 Page 6 of 6