PART 1. Object moving away from the motion sensor.

Run 1. Make sure the track is level (press “Set θ = 0°), the “Recoil” feature is set to 0 and the “Brakes” are off. Select Tmax = 15 s. Move the cart to the left end of track (close to the motion sensor).

Start the motion sensor and push the cart relatively slowly to the right. If you have problems releasing the cart with a push, set the “V0?” to # 5 and press “Go➔ ” button situated next to V0? . Stop the recording at 15 seconds. Copy the data to clipboard and paste it into Logger Pro. Label the columns adequately and enter proper units. In the data table (or from the position vs time graph) choose two points far apart from each other (from the portion of your recording where the cart’s position was changing).

a) In Table 1, clearly state the selected time values, t1 and t2, and the corresponding positions, x1 and x2. Find distance and displacement that the cart traveled between t1 and t2. Calculate the average speed and the average velocity in time interval ∆t = t2 – t1.

b) Now select two consecutive data points of time and position, somewhere at the beginning of cart’s movement. Report them in Table 1, and then calculate the instantaneous velocity at that instant.

c) Repeat the same calculation for a different instant of time but close to the right end of track where the cart was still moving. Report all the data in Table 1. 

Compare two instantaneous velocities (found in b and c) to the average velocity (found in a)? According to the theoey about constant velocity motion, should those values agree with one another? Can you conclude that during time interval t1 → t2 the cart was moving with constant velocity? Provide the evidence to your answer based on your calculations.

Now we will compare average velocity to the value of the slope of the position-time graph. On the position vs. time graph in GA highlight (drag around with the computer cursor) part of the plot corresponding to the cart moving along the track and apply linear fit. The shaded area contains the selected data upon which the linear fit will be calculated. If a region is not selected, the linear fit will be calculated for all data displayed in the graph.

In Table 2, report the slope and y-intercept of position vs time graph. In Discussion section be sure to address how the slope value of the linear fit compares to your calculated average velocity. Write also the equation of the cart’s motion (5) using the value of the slope as the true value of the average velocity.

Add a new calculated column to the data table for the velocity. Remember to label the column and add proper units.

Display the velocity vs. time graph in a new graph window (Insert → Graph).

Carefully highlight the part of this plot in the time interval that corresponds to the one used to obtain the slope of the position vs time graph. The velocity vs time graph is a steady horizontal non-zero line. Apply statistics to the selected part.

Re-size both graph windows, position vs. time and velocity vs. time, to fit them on one page.  

In Table 3 report the mean value of velocity and standard deviation from the velocity vs time graph. In Discussion section be sure to address how the mean value from the displayed statistics compare to the slope of position vs. time plot.

Run 2. Bring the cart back to the left end of track and record a new run for a case when you push the cart a little harder, still away from the motion sensor (or use V0? Set to # 6). Copy the new data and add it to the same Logger Pro file (as a new data set).

You can display the new data in the existing graph windows you’ve created for run 1. Just click the label of the vertical axis on the graph, select “More” and check the appropriate box in the YAxis Options window.

Report all further data in tables 4 and 5. Apply linear fit to the relevant portion of the new plot of position vs. time (where the cart was moving). Record the slope value and its uncertainty. From the new graph of position vs. time how can you tell that the cart was moving faster? From the new graph of position vs. time how can you conclude that the cart was moving with constant velocity?

Make a plot velocity vs time as in run 1. What was the average (mean) velocity of the moving cart in run 2? How does its value compare to the average velocity of the first run? What graphical attribute signifies cart’s speed? Write the equation of the cart’s motion (5) using the value of the slope as the true value of the average velocity.

Save the Logger Pro file for future reference.

Organize your graph windows so they fit on one page, capture the screen and paste it into a Word file – you will have to insert it into your lab report.

lab-manualconstant-velocity-motion-in-one-dimension