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Lab- Comparing Constant Velocity and Uniformly Accelerated Motion Purpose: Compare the motion of a toy car and a ball rolling down a ramp. Construct distance/time graphs for an object moving at a constant velocity and an object moving with constant acceleration. Construct velocity/time graphs for an object moving at a constant velocity and an object moving with constant acceleration. Explore relationships between distance/time and velocity/time graphs. Convert a distance/time graph for uniformly accelerated motion into a linear graph. Calculate acceleration using a distance/time^2 graph and a velocity /time graph and compare. Materials: Constant Velocity Car - reduced speed Ball Bearing Ramp with Groove Stop Watch Masking Tape Pencil Meter Stick 2 x 4 Block Procedure: 1. Remove the battery cover of your car and remove one of the batteries. Replace the battery with a wooden dowel that is covered with aluminum foil. This will reduce the speed of the car. 2. Make a ramp using the wooden ramp and the 2 x 4 block. The end of the board labeled zero should be on top of the block. 3. On the surface of the table apply a piece of masking tape that runs parallel to the ramp. The tape should be at least as long as the ramp and there should be about 15 cm between the ramp and the tape. 4. Draw a line on the tape that is even with the edge of the board that is on top of the 2 x 4 block. From this line measure and label every 10 cm. The tape should look like the edge of the board. 5. The car in this lab travels with uniform velocity where as the ball accelerates as it roles down the ramp. If the car and ball are released at the same time, the car should jump out in front, but the ball should catch the car as it gains speed. Run a few trial runs to make sure the ball passes the car between 30 and 60 cm. It is critical that both the car and ball “start” at the zero point at the same time. It might be easier to do this if the car starts behind the line and the ball is released as the car crosses the line. Make sure the car runs parallel to the ramp. 6. Measure the distance from the table to the top surface of the ramp where the ramp meets the 2 x 4 block. Record this in the data section. Joseph Cox Meadowcreek High School July 21, 2004 7. Begin collecting data by timing how long it takes the car to go from zero to the 10 cm mark. Time this five times and average. Now time how long it takes to go from 0 to the 20 cm mark, then from zero to the 30 cm mark, etc. Record in the data table for the car distance and time data. 8. Repeat the previous step for the ball and the ramp. 9. Clean up your work station. Data Height of Ramp _________________ Table 1 Car (Constant Velocity) – Distance and Time Data. Distance Trial 1 (s) Trial 2 (s) Trial 3 (s) Trial 4 (s) (cm) 0 0 0 0 0 10 20 30 40 50 60 70 80 Trial 5 (s) 0 Average (s) 0 Table 2 Ball (Uniform Acceleration) – Distance and Time Data Distance Trial 1 (s) Trial 2 (s) Trial 3 (s) Trial 4 (s) Trial 5 (s) (cm) 0 0 0 0 0 0 10 20 30 40 50 60 70 80 Average (s) 0 Analysis: 1. On the same graph plot the points for the distance and time data for both the car and the ball. For all graphs make sure you include a legend, title, and labels for both axes. 2. Compare and contrast the pattern of the points for both the car and the ball. In your description use mathematical words such as slope, constant, variable, decreasing, increasing, linear, parabolic. Remember you are looking at experimental data; small variations will be present. You are looking more for the general pattern. 3. Based on what you said in your answer to the previous question draw the best fit curve or line for both sets of data. Joseph Cox Meadowcreek High School July 21, 2004 4. At what time and distance does the ball pass the car? Describe the slope of each graph at this point. 5. What does the slope of a distance time graph indicate about the speed of an object? 6. Using the formula and definition of average velocity calculate the average velocity of both the ball and the car during each interval. Interval one is from 0- 10 cm, interval two is from 10-20 cm, etc. Display your results in a table. 7. Calculate the midpoint time of each interval. For example if interval two last from .50 to 1.0 s the mid point time is .75s. You should make separate tables which shows the mid point time and average velocity for each interval for both the car and the ball. 8. Before making a velocity/time graph for both the car and ball you need to decide if (0,0) should be used as a data point for one or both of the graphs. Write a statement giving your reason for using this or not using this data point for each graph. 9. Make a graph of velocity vs. time for both the car and the ball on the same graph. Each value for average velocity should be plotted at the time, which is at the mid point of the interval. Draw the best-fit lines. 10. Calculate the slope of the best-fit line for the distance/time graph of the car. This should be related to the velocity/time graph of the car. What is the relationship? 11. Compare the shape of the distance/time graph of the car to the shape of the velocity/time graph of the car. There is a relationship; what is it? 12. Compare the shape of the distance/time graph of the ball with the velocity/time graph of the car. What is the relationship? 13. Calculate the area under each velocity/time graph at the time when the ball passed the car indicated as in number four. Using the distance value from number four as your “accepted” value and the area each velocity-time graph as your “experimental” value, calculate a percent error for both the ball and the car. 14. What does the area under a velocity time graph represent? 15. Calculate the slope of the velocity/time graph for both the ball and the car. 16. Look at the units of the slope in the previous question. These are the units of what familiar quantity? 17. What does the slope of the velocity / time graph for both the car and the ball tell you about their motion? Analysis of Error: 1. In step 1 of the procedure a battery was removed to reduce the speed of the car. Explain how this helps to reduce error. 2. In step 5 of the procedure you were warned to make sure the car runs parallel to the ramp. Why is this important? Feel free to include a quick sketch as part of your answer. 3. Please identify at least one other source of error and the effect it has on the results. Extention- Using an equation to make a linear graph. As you know, the graph of distance/time for the ball is not linear, but it is possible to make a graph that relates distance and time for accelerated motion that is linear. Consider the following equation: d = vot + ½ at2 Joseph Cox Meadowcreek High School July 21, 2004 In this lab the initial velocity of the ball equals zero so the equation simplifies to: d = ½ at2 This equation can be rewritten as: d/t2 = ½ a From algebra I you will remember that the most basic definition for slope is rise over run. Rise is measured along the y-axis and run is measured along the x-axis. Using this definition if d is plotted on the y-axis and t2 is plotted on the x-axis the slope of this line should be ½ a. Make a data table and then a graph of d vs. t2 and use its slope to calculate acceleration. Use a percent difference to compare this value for the acceleration of the ball to the acceleration calculated in number 15. *This lab is an extention of the Going Shopping/Sloping Lab developed by Daniela Taylor and Kaye Elsner-McCall. Joseph Cox Meadowcreek High School July 21, 2004