LAB 03: The Equations of Uniform Motion

Transcription

1 LAB 03: The Equations of Uniform Motion This experiment uses a ramp and a low-friction cart. If you give the cart a gentle push up the ramp, the cart will roll upward, slow and stop, and then roll back down, speeding up. A graph of its velocity vs. time would show these changes. Is there a mathematical pattern to the changes in velocity? What is the accompanying pattern to the position vs. time graph? What would the acceleration vs. time graph look like? Is the acceleration constant? In this experiment, you will use a Motion Detector to collect position, velocity, and acceleration data for a cart rolling on flat ground and up and down a ramp. Analysis of the graphs of this motion will answer these questions and allow you to discover the mathematics that describes these types of motion. PURPOSE Collect position, velocity, and acceleration data for various motions. Analyze the position vs. time and velocity vs. time graphs. Determine the best fit equations for the position vs. time and velocity vs. time graphs. Compare and contrast the equations of different types of motion. Determine what meaning the coefficients have for the best fit equations. EQUIPMENT Windows PC LabPro Logger Pro Software Vernier Motion Detector Vernier Dynamics Track Vernier Dynamics Car ball PRELIMINARY QUESTIONS 1.) Consider the changes in motion a cart will undergo as it rolls up and down a ramp. Make a sketch of your prediction for the position vs. time graph. Describe in words what this graph means. Do you know any mathematical equations that tend to look like this graph? 2.) Make a sketch of your prediction for the velocity vs. time graph. Describe in words what this graph means. Do you know any mathematical equations that tend to look like this graph? 3.) Consider the changes in motion a ball will undergo as it is thrown up and down. Make a sketch of your prediction for the position vs. time graph. Describe in words what this graph means. Do you know any mathematical equations that tend to look like this graph? 4.) Make a sketch of your prediction for the velocity vs. time graph. Describe in words what this graph means. Do you know any mathematical equations that tend to look like this graph? Lab 03: The Equations of Uniform Motion 1/5

2 PROCEDURE Name: Class: Part l: Constant Velocity Motion 1.) Connect the Vernier Motion Detector to the DIG/SONIC 1 channel of the interface. If the Motion Detector has a switch, set it to Track. 2.) Make sure the track is lying flat on the lab table. Adjust the head of the detector so that it is pointing straight down the track, or angled up just a little. If you have a level, check that your track is as level as possible. 3.) Open the file 03 Cart on a Ramp from the Physics with Vernier folder located on your flash drive. 4.) Place the cart on the track on the end near the motion detector, about 20 cm away. Click to begin data collection. Wait about a second, and then briefly push the cart down the ramp, letting it roll freely up nearly to the end. Catch the cart as it nears the end stop. 5.) Examine the position vs. time graph. Repeat Step 4 if your position vs. time graph does not show an area of smoothly changing position. Check with your instructor if you are not sure. 6.) Once you are happy with you graph, save it on your group s flash drive. If there is not one created already, create a folder for your class, i.e. Honors-002, and create a folder in there representative of the lab, i.e. Lab03. Save the file as Lab03_Part1a. 7.) Repeat the experiment but this time push the cart harder (do not send it over the edge though). Save this file as Lab03_Part1b. Part 1 in Lab Analysis 1.) Sketch the two motion graphs for each type of motion in your lab notebook. The graphs you have recorded are fairly complex and it is important to identify different regions of each graph. Click the Examine button and move the mouse across any part of the graph to answer the following questions. Record your answers in your lab notebook, and mark up the graph where appropriate. Identify the region when the cart was being pushed by your hand. Identify the region where the cart is rolling freely. 2.) Analyze the motion graphically. Using the Tangent button, determine the velocity of the cart on the position vs. time graph. If the graph is noisy make sure your tangent lines up with the general slope of the graph. Using the Examine button, determine the velocity of the cart from the velocity vs. time plot. If your graph is a little jumpy, use the Stat button to get the mean of the horizontal section. 3.) Determine the equation of motion. If the track is flat, your cart should undergo constant velocity motion. LoggerPro allows you to attempt to fit curves to your data. (a.) Open your first trial and highlight the part of your position vs. time graph where the cart was rolling freely. Click the Curve Fit button to activate the Curve Fit dialog. Keep the fit type Automatic, Check Time Offset and try different equations to fit to your data. To try an equation, select an equation type then select Try Fit. Try to get the curve to fit as close to your data as possible. Lab 03: The Equations of Uniform Motion 2/5

3 (d.) Repeat the process for your velocity vs. time graph, recording the best fit equation as well as any given Coefficients. (e.) Repeat the process for your other trial and develop two more equations. Part 2: Motion on an incline (a.) Use the books available to raise the end of your track with the motion detector attached to it. (b.) Position the cart near the detector (~20 cm from it), click, wait a second then release the cart and allow it to travel down the ramp, but catch it before it hits the end. (c.) Examine the position vs. time graph. Repeat step (b) if your position vs. time graph does not show an area of smoothly changing position. Check with your instructor if you are not sure whether you need to repeat data collection. (d.) Once you are happy with you graph, save it on your groups flash drive as Lab03_Part2a. (e.) Approximately double the height of the end (i.e. add more books) and repeat steps b d. Borrow books from another group or ask your teacher if necessary. (f.) Save the graph for the higher end as Lab03_Part2b. (g.) Now move the cart to the bottom of the ramp, and adjust the height as in step (a). Position the detector at the bottom of the ramp about 20 cm from the cart. (h.) Click wait a second then push the cart up the hill (make sure you do not crash it into the detector). Allow it to move up, and then back down the ramp. (i.) Once you get a good graph, save it on the flash drive as Lab03_Part2c. Part 2 in Lab Analysis 1.) Again print or sketch the two motion graphs for each motion. Click the Examine button and move the mouse across any part of the graph to answer the following questions. Determine where the cart had the maximum velocity on each graph. Use the Tangent button on the position vs. time graph to get the slope. Use the Examine button on the velocity vs. time graph. Record these values in your lab notebook. Determine the acceleration of the motion from the velocity vs. time graph by using the Tangent button. Make sure the tangent lines up with the overall slope of the graph. Repeat for your other two sets of graphs. 2.) Determine the equation of motion. If the track is slanted, your cart should undergo constant acceleration motion. LoggerPro allows you to attempt to fit curves to your data. (a.) Open your first trial and highlight the part of your position vs. time graph where the cart was rolling freely. Click the Curve Fit button to activate the Curve Fit dialog. Keep the fit type Automatic, Check Time Offset and try different equations to fit to your data. To try an equation, select an equation type then select Try Fit. Try to get the curve to fit as close to your data as possible. (d.) Repeat the process for your velocity vs. time graph, recording the best fit equation as well as any given Coefficients. (e.) Repeat the process for your other downhill trial and develop two more equations. (f.) Repeat the process for your up and down trial and develop two equations. Lab 03: The Equations of Uniform Motion 3/5

4 Part 3: Vertical Ball Toss (a.) Place the Motion Detector on the lab table and protect it by placing a wire basket over it. (b.) Open the file 06 Ball Toss from the Physics with Vernier folder on your flash drive. (c.) In this step, you will toss the ball straight upward above the Motion Detector and let it fall back toward the Motion Detector. This step may require some practice. Hold the ball directly above the Motion Detector. Click to begin data collection. Wait one second, and then toss the ball straight upward. Be sure to move your hands out of the way after you release it. A toss of 1 m above the Motion Detector works well. You will get best results if you catch and hold the ball above the Motion Detector. (d.) Examine the position vs. time graph. Repeat Step (c) if your position vs. time graph does not show an area of smoothly changing position. Check with your teacher if you are not sure whether you need to repeat the data collection. (e.) Once you get a good graph, save it on the flash drive as Lab03_Part3. Part 3 in Lab Analysis 1.) Again print or sketch the two motion graphs for each motion. Click the Examine button and move the mouse across any part of the graph to answer the following questions. Identify the region when the ball was and label it on each graph. stationary before you let it go moving upward stopped at top moving downward 2.) Determine the max velocity and acceleration Determine where the ball had the maximum velocity on each graph. Use the Tangent button on the position vs. time graph to get the slope. Use the Examine button on the velocity vs. time graph. Record these values in your lab notebook. Determine the acceleration of the motion from the velocity vs. time graph by using the Tangent button. Make sure the tangent lines up with the overall slope of the graph. 3.) Determine the equation of motion. (a.) Highlight the whole curve where the ball is in the air, going up and down. Click the Curve Fit button to activate the Curve Fit dialog. Keep the fit type Automatic, Check Time Offset and try different equations to fit to your data. To try an equation, select an equation type then select Try Fit. Try to get the curve to fit as close to your data as possible. Lab 03: The Equations of Uniform Motion 4/5

5 ANALYSIS Part 1 1.) What values did you determine for the velocity of the cart? 2.) What equations did you develop for the constant velocity motion from Part 1a? 3.) What equations did you develop for the constant velocity motion from Part 1b? 4.) How were these equations the same? How were they different? 5.) What do you think the different coefficients correspond to in the equation from the position vs. time graph? The velocity vs. time graph? Did they have any relation to your velocity? Part 2 6.) What values did you determine for the maximum velocity and acceleration? 7.) What equations did you develop for the motion from Part 2a? 8.) What equations did you develop for the motion from Part 2b? 9.) What equations did you develop for the motion from Part 2c? 10.) How were these equations the same? How were they different? 11.) What do you think the different coefficients correspond to in the equation from the position vs. time graph? The velocity vs. time graph? 12.) Did your equations have any relation to the velocity and acceleration you found? 13.) How did these equations differ from the ones from Part 1? 14.) Can you see any way that these equations are similar to the ones from Part 1? Part 3 15.) What equations did you develop for the motion from Part 3? 16.) What do you think the different coefficients correspond to in the equation from the position vs. time graph? The velocity vs. time graph? 17.) Did your equations have any relation to the velocity and acceleration you found? 18.) How is your equation from Part 3 similar to the equations from Part 2? How is it different? Lab 03: The Equations of Uniform Motion 5/5