PSC 151 - Lab 3

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Apr 3, 2024

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Virtual Dynamics Track VPL Grapher PENCIL Physical Science Laboratory: PSC 151 Lab 3 Rev 12/19/18 Mod: 2/8/19 VPL Lab -Dynamics – Velocity – mod 1 Name: Date: Non-Constant Velocity Motion and Graphical Analysis II P URPOSE There are a number of useful ways of modeling (representing) motion. Graphing position, velocity, and acceleration vs. time is a good choice since the rise and fall and shape of a graph are analogous to the changes in these quantities. In this activity we’ll create velocity graphs of an object with constant velocity. At the end of this activity you should be able to  Observe a moving object and draw velocity vs. time ( v -t) graphs of its motion.  Look at a v - t graph and describe the motion that produced it.  Look at an x - t graph and draw the corresponding v -t graph. E QUIPMENT D ISCUSSION In the previous experiment, we bounced sound waves at different speeds and learned how to describe their motion with respect to time. We will extend the idea in this experiment. We will investigate how to take those same position-vs-time graphs and use them to find the velocity of the motion. To do this, we will need to use a new tool, the Grapher. Using Grapher – Graphs, best fit lines, slopes, areas, saving data The Dynamics Track data table contains position vs. time data. You’ll be using this with our Grapher tool. Let’s try it. Move your cart to the left end of the track. Adjust T max to 25 seconds. For the following, don’t stop until you’ve gone over and back twice as directed. If you run out of room try again. Turn on the motion sensor. Drag the cart to the right quickly, then back fairly slowly. Continue by doing the reverse – dragging to the right slowly, then returning to the left quickly. Turn off the motion sensor. Congratulations, you’ve made a capital M. (See Figure 1.) If not, give it another try. Hopefully the graph’s shape already means something to you but let’s go a bit further. Click the “Copy Data to Clipboard” button. Your data is now in your computer’s clipboard. You could paste it into a number of software programs such as Excel. We’ll use our Grapher Tool because it lets us manipulate the data in ways that are useful in physics. Open Grapher. Click in the box below “Click in the box below and hit Ctrl+V to paste data.” Type Ctrl+V. That is, hold down the Control key and type “v”. By convention the independent variable, time, appears in the x -column in the data table. The dependent variable, position, appears in the y -column. You’ll see what the other columns are for soon. You’ll see an “M” just like the one in the Dynamics Track graph. To adjust the scale of the two axes, click the “Man” button, short for manual scaling. Try 20, 0, 2, and 0. Click Submit, then Close. Edit the axis labels to “Position (m)” on the ordinate and “Time (s)” on the abscissa. (To save room, we don’t include titles in the graphs.) Let’s also shrink the graph a bit by clicking the check boxes beside the “2” next to the Graphs button. You can see that we can add a third graph but won’t need to in this lab.

Physical Science Laboratory: PSC 151 Lab 3 Rev 12/19/18 Mod: 2/8/19 VPL Lab -Dynamics – Velocity – mod 2 Let’s see what we can learn from our graph and data. Your M-graph should have four slanting segments. We want to find the slopes of the two segments inside the M .  In Grapher click at a point somewhere in the graph a bit to the right of the time when the first of the two inside segments begins. (See the left edge of the shaded area in the figure at about 5.3 seconds.)  Drag to the right. A gray box will appear. Continue dragging until you’re near the end of that segment and then release. (At about 12 seconds in the figure.) The vertical position of the mouse pointer is unimportant when you’re dragging horizontally.  By doing this you have also selected the data associated with this section of the graph. We can then use some other Grapher tools to analysis this data. Let’s try it. With the data still selected click the Linear Fit check box. Data will now appear in the Linear Fit data box. Grapher has drawn the line of best fit for that part of your graph in pink. The values for the M-graph shown in Figure 1 are displayed in Figure 1a. Now repeat for the next segment to the right, the rising segment inside the “M.” You now have a second line of best fit. Its data will appear in the text box as shown in Figure 3b. The two slopes, -0.271 m/s and 0.0265 m/s. These slopes are the average velocities, Δ x /Δ t , for these two segments. They are calculated using a mathematical technique called linear regression . Place below, your M graphs from the Dynamic Track and From the Grapher, showing the slopes of inner lines of the M Fig. 1 M graph from Dynamic Track Fig. 1b Left M graph from Grapher Fig. 1c Right M graph from Grapher 1b. Slope of left edge of M graph: m L = 1c. Slope of right edge of M graph: m R = A word of caution. You many have seen slopes appear that are way off. Right now I’m seeing -0.060 for example. What gives? Without clicking, move you mouse pointer up and down, crossing back and forth between graphs 1 and 2. A line of best fit is drawn for each graph. But the data displayed is for the highlighted graph, the one you have your Figure 1 – The “M” Figures 1a, 1b – Linear Fit Data

Physical Science Laboratory: PSC 151 Lab 3 Rev 12/19/18 Mod: 2/8/19 VPL Lab -Dynamics – Velocity – mod 3 pointer over. PROCEDURE We’ve seen that our x - t graph is an analog, a model, of the motion itself. But, there’s more. The graph contains the data necessary to create the corresponding velocity vs. time graph . We’ll explore that now. IIA. Motion away from and then toward the motion sensor: Looking back at part IA from the last lab, we see that the cart moved slowly (IA1a), and then quickly (IA1b), away from the motion sensor. In part IB they did the same but toward the sensor. We’ll now create velocity-time graphs for these motions. 1. Set Recoil to 0. Recreate your first position-time graph by launching the cart with an initial velocity of 20 cm/s. Be sure to start quickly enough so that there is a horizontal section on both ends of the graph. One way to do that is to use the delay clock. Try it. It works like the Go→ button except there’s a 5 second delay before launch. If you click this button and wait until the clock is at about 11 o’clock and then turn on the sensor you’ll have what you need. 2. Using the Sketch Graph tool, create a velocity vs. time graph that looks like Graph IIA below. The dots are inserted to help you read the velocity scale. They’re located at approximately at ±0.6, ±0.3, and 0. Be sure to include them. You’ll use the Sketch tool and this v - t graph for the rest of this section. 3. Look at your just-created x - t graph to see the time when the cart started moving. You know that the velocity is 0.2 m/s at this time. Put a dot on the v - t graph representing the velocity at the time when the cart starts moving. That would be at (your start time, 0.2 m/s.) Add another dot for the last time when the cart is moving at 0.2 m/s just before it hits the bumper. Place below, your velocity-time sketch graphs created on the sketch pad from x-t motion graphs on the dynamic track

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Physical Science Laboratory: PSC 151 Lab 3 Rev 12/19/18 Mod: 2/8/19 VPL Lab -Dynamics – Velocity – mod 4 Fig. 2a v-t sketch graph for v o = 0.20 m/s Fig. 2b v-t sketch graph for v o = 0.50 m/s 4. What about the velocity between these two times? If the velocity is constant, then you’d have a succession of dots between your initial and final dots. A.k.a., a line. Add a horizontal line to indicate the cart’s motion at a constant 0.2 m/s. We’ll find the velocity line for 50 cm/s a different way.  With the dynamics track, launch the cart at 50 cm/s from the left end just as you did previously with 20 cm/s.  Copy Data to Clipboard.  Paste the data into Grapher as before using the Ctrl+V technique.  Check the box for Graph #2 to display it. Click the Manual scale button on the top graph. Adjust its graph scales to 8, 0, 2.0, and 0. Submit and Close. Click the Manual scale button on the bottom graph. Adjust its graph scales to 8, 0, .6, and -.6. Submit and Close. Label the axes appropriately for velocity vs. time, including units.

Physical Science Laboratory: PSC 151 Lab 3 Rev 12/19/18 Mod: 2/8/19 VPL Lab -Dynamics – Velocity – mod 5

Physical Science Laboratory: PSC 151 Lab 3 Rev 12/19/18 Mod: 2/8/19 VPL Lab -Dynamics – Velocity – mod 6 Both of these graphs hold the value of the cart’s velocity. Here’s how to find it. We could use any time interval but let’s use an approximately 2-second interval to examine each graph. Perhaps from 2 to 4 seconds, or 2.5 to 4.5 seconds. Just pick one. I’ll use 2 to 4 seconds in my example. a) In the x - t graph, click anywhere along the vertical graph grid line at 2 seconds. Drag to the right until you reach the 4 second line and release the mouse button. Click the linear fit check box. This will produce a straight line and populate the data box. b) Do the same thing for the v- t graph except this time click the “Stats” checkbox. This will populate the Stats data box. Roll over (put your pointer in) the top graph and check the slope of that graph in the Linear Fit data box. Then roll over the bottom graph and note the mean value of that graph in the Stats box. They should both say approximately .50. The slope of the x - t graph, Δ x /Δt, is ~.50, the average velocity. The average value of the v - t graph, ~.50, is the average for what is plotted for our 2-second interval on that graph, also the velocity. 5. The slope of the position-time graph, including its sign, and the mean value of the velocity-time graph, (the height of the line), including its sign are both measures of 6. Note that the line on the v - t graph in Grapher is just what you need to add to Graph IIA that you’re building with Sketch Graph. Be sure to draw this line for the same time interval as the one in the Grapher graph. This should be more than 2 seconds. A bit less than 4 seconds. Now for the trip back to the left. 7. Repeat the necessary steps above to create the third graph line using -20 cm/s. Use the slope of the position-time graph. 8. Repeat the necessary steps above to create the fourth graph line using -50 cm/s. Use the mean value of the velocity- time graph. 9. Take a Screenshot of the four line graph, save it as “Vel_IIA.png”, print it out, and attach it below.

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Physical Science Laboratory: PSC 151 Lab 3 Rev 12/19/18 Mod: 2/8/19 VPL Lab -Dynamics – Velocity – mod 7 Place below, the x-t and v-t graphs plotted on the Grapher for v o = 0.20 m/s; v o = 0.50 m/s; v o = -0.20 m/s v o = -0.50 m/s

Physical Science Laboratory: PSC 151 Lab 3 Rev 12/19/18 Mod: 2/8/19 VPL Lab -Dynamics – Velocity – mod 8 IIA. Observations: Slow away, fast away; slow toward, fast toward 10. What is similar about the 4 graphs? (Not the motions, the graphs.) All graphs are straight 11. What is different about the graphs for 20 cm/s and 50 cm/s (other than their lengths)? The slopes of the two graphs are different 12. What about the motion does a horizontal segment on a velocity-time graph indicate? Velocity is constant if the line is horizontal 13. What about the motion does the height of a horizontal straight-line v - t graph indicate? The height tell you the position changes as well as how fast . the steeper the line faster the motion 14. How is the direction of motion indicated by a velocity-time graph? On a velocity- time graph, motion shows by the line not being straight. If the line moves up or down then the direction changes

PSC 151 - Lab 3

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