Uniform Motion Lab

INTRODUCTION: In this experiment we will investigate motion without acceleration. Motion without acceleration is uniform (constant velocity) motion, which means it describes the motion of an object that has constant speed and constant direction. Accelerated motion is the motion of something with either a changing speed or a changing direction. In the next experiment, we will deal with changing speeds. CONSTANT VELOCITY MOTION: Our goal is to determine the relationship between the position and time for an object moving with a constant velocity. You can do this by simply noting the time for the object to reach certain positions. First however you must put an object into constant velocity motion. One way to do this is with a constant velocity motor. Many motor driven toys and model cars work this way. In this experiment however, you will use a non-motorized object. Unfortunately, most non-motorized objects don't move with a constant velocity because they slow down and stop after a relatively short period of time. In order to keep an object from slowing down, you must remove friction. Later you will learn that an object moving with no friction and no external forces acting on it will move forever with a constant velocity. To remove friction you will use an air-track which is a linear track that has many holes through which air blows, suspending a sliding sled. The sled moves along on a layer of air and does not actually touch the underlying track. The air-track is a one-dimensional version of the common air-hockey table which has a suspended puck free to move in two dimensions. The position equation for an object moving with a constant velocity is:

D vt= where D is the distance traveled, v is the constant velocity, and t is time. Since v is constant, this equation represents a proportional relationship between distance traveled and time. You will be using the Remote Web-based Science Lab (RWSL) facility In Denver, CO to perform this experiment. It is a real lab that you will access through the Internet using your computer. Your Instructor will let you know how to access this particular experiment. CAUTION: PLEASE DO NOT TURN OFF THE AIR SUPPLY TASKS: 1. LEVEL THE TRACK: The main advantage to using the RWSL for this experiment is that the track has been leveled for you already. Note from Figure 1 that you can raise or lower one end of the track by 1, 2 or 5 centimeters at a time. There is also a button that will return the track to the level position when It Is clicked. You should always make sure the track is level before you launch the sled in this experiment. 2. CONSTANT VELOCITY DATA (first data set): Once the track is level, turn on the air supply and place the sled onto the track. Click on one of the pre-programmed buttons to tell the robot arm to place the sled on the track. When the sled is loaded onto the track for the first time, the electromagnetic launcher is energized so it will hold onto the sled until you are ready to launch It. From the "Run Experiment" tab (Figure 2), make sure you have an empty data table displayed (all zeros) and then click "Launch Sled". This will cause the electromagnet to be turned off and a rubber band that Is mounted on the launcher will push the sled forward on the track. The photogates will be triggered as the sled passes by each one and the resulting times will be displayed in the data table. Each photogate will report two times for each run. All times are from when the sled was launched and the first time for each photogate indicates when the sled first arrived there. The second time for each photogate is when the back end of the sled has cleared the sensor. NOTE: You will also notice In Figure 1 that there is an option to put the sled onto the scale to obtain its mass. In this experiment, It is not necessary to know the mass of the sled, so we will not use this function. However, it will be used in some future experiments. NOTE: Unfortunately, the robot arm is not functioning correctly, so all the “buttons” for controlling the robot have been disabled and we will start the experiment with the sled on the track and the air supply turned on. CAUTION: PLEASE DO NOT TURN OFF THE AIR SUPPLY 3. CONSTANT VELOCITY DATA): The sled will be sitting at the end of the air-track. You will need to capture it onto the electromagnetic launcher and launch it to collect a set of data. Here are the steps to do this: a) Click the button labeled "Energize Launcher". b) Go to the Setup Experiment tab (Figure 1). c) Select the 1 cm button on the left side of the screen and click the down arrow to lower the left end of the track by 1 cm. CAUTION: DO NOT lower the end of the track more than 1 cm at this time. Doing so will cause the sled to impact the launcher too hard and may damage it. The other options (2 and 5 cm) will be used in future experiments.) d) The sled will move back down the track and will stick to the electromagnet, holding it in place. e) Return the track to the level position f) Go back to the Run Experiment tab (Figure 2) and make sure you have an empty data table. g) Click "Launch Sled" to release it from the electromagnet. 4. Finishing the experiment. After you are sure you have all your data, and have written it down in your notes, recapture the sled on the electromagnetic launcher as described above. However, after step e, click the button labeled "Sled to Storage" to tell the robot arm to move the sled off the track and place it back into the storage location. Now the equipment is ready for the next lab group.

Figure 1 - RWSL Interface: Setup Experiment screen

Figure 2 - RWSL Interface: Run Experiment screen

Click here to turn on the Air Supply

Click on these arrows to change data tables. There are 10 data tables, numbered 0 through 9.

In order to determine the distance that the cart has moved for each time, you will need to use the cameras to determine the location of each photogate. Camera 1 should be used for the first photogate (Figure 3), camera 2 for the second, and so on. Select each camera and then click preset 2 to zoom in on the photogate and read its location from the centimeter scale on the side of the airtrack. Before it is launched, the front edge of the sled is located at 21.4 cm from the end of the airtrack.

Figure 3: Camera 1, preset #2, showing the location of Photogate #1 Data Collection:

Shows the location of photogate #1

The approach to the determination of the value of the constant velocity of the sled will be to generate a statistically significant set of data, and calculate the mean, the median and the mode of the sample distribution. The independent variable is the discrete distance between each photo gate. The dependent variable is the time of activation of the photo gate signal indicating the leading edge of the sled having reached this discrete pre-marked point in the linear travel along the air track. A total of ten "runs" will be made in which four discrete points in the linear path will be recorded. A ten by four matrix of data will be recorded. The row of data, i.e., time of the leading edge of the sled coinciding with the location of each of the four photo locations will be statistically analyzed. The median value of the discrete row will then be plotted against the measured distance to the gate.. The slope of this plot will then be determined yielding the value of the average constant velocity of the sled along the air track. Data Observations: Refer to Fig. 2: RWSL Interface. Incremental Time Values The timing data display consists of the eight numerical windows labeled " photo gate 1, 2, 3, 4". The first display is the time value in seconds that has elapsed since the sled was launched and the leading edge coincides with the prepositioned photo gate. The second window is the time in seconds that has elapsed since the leading edge of the sled initiated the signal and the trailing edge interrupted the signal. Thus the remaining three blocks of data provide the additional timing profile of the arrival of the sled at each of the designated points. We will be interested in the value of time that results when the leading edge of the sled coincides with the prepositioned photo gate. Refer to Figure 3: Camera 1 Preset 2 showing the location of photo gate #1 Incremental Distance Values The location of each photo gate is observed on the scale as described In the Figure 3 guidelines. It Is of cardinal importance to note that the leading edge of the sled is located 21.4 cm from the end of the track and not at zero. This is due to the launcher configuration. Thus this value represents a bias that must be subtracted from each camera reading to obtain the true distance traveled by the sled to each photo gate. Failure to account for this off set will invalidate the data and produce invalid results. The student will use the prepositioned cameras to read the measuring tape value which gives the location of the corresponding photo gates. See Figure 3 for an actual example of the expected video frame. Procedure: All operations are "mouse" controlled with cursor and right/left click as required-indicated. "Select", "Initiate" and similar commands involve placing the cursor over the indicated label, control or display and executing the command by normal click. Section1: Data Generation.

This section will configure the air track for operation, load the sled on the track, travel along the path and generate the time/distance data. ( ) 1. 0.0 Assure no error messages are displayed on your computer screen. (This will confirm that a stable link with the RWSL server has been established and we are good to go for operation.) The sled is returned to the launcher by lowering the track on the launcher end. This will allow the sled to glide back to the launch position gravitationally. A step is provided to insure the sled does not impact the launcher with a high impulse that would damage the launcher mechanism. ( ) 1.1.0 From the SETUP EXPERIMENT panel (Ref. Figure 1)

( ) 1.1.1 Select ENERGIZE LAUNCHER ( ) 1.1.2 Make sure the 1-cm is lit up. Select LOWER TRACK

CAUTION/WARNING: INCREMENTAL TRACK LOWERING IS PRE-SET LIMITED TO A VALUE OF 1 CM. THIS WILL PREVENT OVER SPEEDING OF THE SLED ON THE RETURN TRAVEL. DO NOT DEFEAT THIS SETTNG OR DAMAGE WILL OCCURR TO THE LAUNCHER MECHANISM.

( ) 1.2.0 Use cameras to verify sled is captured by launcher electromagnet ( ) 1.3.0 Select the RUN EXPERIMENT panel (Reference Fig. 2-RWSL Interface)

( ) 1.3.1 Increment TRIAL NUMBER counter, if necessary, to get an empty data table ( ) 1.4.0 Pan area coverage camera, verify sled is In place and no obstacles are impacting the sled track ( ) 1.5.0 Select Preset 2 for each camera to view the respective photo gate positions Record these values here and in DATA TABLE #1:

Gate 1 ___________cm, Gate 2 __________cm Gate 3 ___________cm, Gate 4 __________cm Bias value for sled extension: 21.4 cm:

( ) 1.6.0 Select RUN EXPERIMENT (Reference Fig. 2-RWSL Interface)

1.6.1 Select LAUNCH SLED ( ) 1. 7.0 Pan the cameras as necessary to visually verify sled travels freely down the air track with a smooth motion ( ) 1. 8.0 From photo gate display panel record the following values here and In DATA TABLE #1 Photo gate 1 T(s) ___________ (top value for sled leading edge coincidence) Photo gate 2 T(s) ___________(top value for sled leading edge coincidence Photo gate 3 T(s) ___________(top value for sled leading edge coincidence Photo gate 4 T(s) ___________(top value for sled leading edge coincidence ( ) 1.9.0 Complete a total of ten runs as per the preceding procedure. Populate Data table #1 from this data.

Section 2 -Data Capture and Reduction A total of ten runs will comprise the data set for this experiment. Data table #1 will be populated with the discrete distance/time data generated by the successive runs. The mean and Standard deviation will be computed from this data. The distance measurements will be considered discrete and in the middle of the tolerance. The ten "run" values of time for each of the four distance points will be analyzed with the mean and standard deviation calculated. ( ) 2.1.0 Populate Data Table #1 from the ten separate runs

Table #1 (Raw Data) Run 1

time Run 2 time

Run 3 time

Run4 time Run 5 time

Run6 time

Run 7 time

Run 8 time

Run 9 Time

Run10 time

D1 cm

D2 cm

D3 cm

D4 Cm

( ) 2.2.0 Reduce the data according to the following D1 =Camera Reading minus 21.4 cm D2 = Camera Reading minus 21.4 cm D3 = Camera Reading minus 21.4 cm D4 = Camera Reading minus 21.4 cm n <tn> = 1/n ∑ tn I=1 Table # 2 Reduced Data D Position T Elapsed Time D1

T1

D2

T2

D3

T3

D4

T4

( ) 2.3.0 Using EXCEL, plot the data of Table 2 ( ) 2.4.0 Compute the value of the constant velocity of the sled by determining the slope of the plot Section 3-Analysis and Conclusions ( ) 3.1.0 What are possible and reasonable sources of error in the data? ( ) 3.2.0 If more than ten runs were made, would the true average value be better ascertained? Give the rationale for you’re answer. ( ) 3.3.0 Can each run be viewed as an independent event? If so what are the implications? ( ) 3.4.0 How would the addition of more discrete distance points aid in the determination of the average velocity? ( ) 3.5.0 The data display also yields the time of coincidence between both the leading and trailing edge of the sled it passes the discrete point. Describe how this data can give an approximation of the instantaneous velocity of the sled at these discrete points.