Uniformly Accelerated Motion Lab Please read over the lab prior to watching the lab video. Please note this is a video lab, you don't need to purchase any equipment. You take your measurements off the video. Overview: This lab is a learning lab in which you will determine the acceleration of a cart rolling down an incline. It is designed to help you understand the relationships between time, displacement, velocity, and acceleration through graphs. The data will be graphed in three ways and you will analyze the motion of the cart graphically. The first will be a position versus time graph, the second will be a velocity versus time graph and the third will be an acceleration vs time graph. These graphs represent three different views of the same data and motion. The graphs will allow you to see what the cart is doing as it rolls down the inclined plane, and to see how the three types of graphs are related. Objective: 1. To determine the acceleration of a cart rolling down an inclined plane. 2. To accurately graph a position vs time graph, a velocity vs time graph, and an acceleration vs time graph. 3. To calculate the slope of a linear graph and the slope of a tangent line to the curve. 4. To calculate the area under the curve for the velocity vs time graph and the acceleration vs time graph 5. To explain the relationships of position, velocity and acceleration using graphs. Materials: Ticker-timer (60 Hz) Power supply for ticker-timer Ticker-tape Carbon disk Masking tape Cart 1 m long ramp Ruler Procedure: 1. These first steps of the procedure will be carried out for you in the lab video. a. Slant the ramp to an approximate angle of 30 using textbooks b. Attach a length of Ticker-tape to the back of the cart using masking tape and place the cart at the top of the ramp. c. Start the Ticker-timer and release the cart so it rolls down the inclined plane. d. The ticker-timer produces 60 dots every second. Therefore, six dots are produced in a time of 0.1 seconds. e. Measure the distances dn (ie. d1, d2, d3... dn) as shown in Figure 1. Record the distances in Table 1. 1-1 Uniformly Accelerated Motion Lab Figure 1: d2 d Ad 2. Position vs Time Graph: a. Plot a graph of Position vs Time and sketch your curved line of best fit. (Take time to look over graph expectations for this lab). b. Calculate the AVERAGE VELOCITY (Vavg) on the Position vs Time graph for the time interval from 0.000s to 0.600s. The average velocity (Vavg) is equal to the slope for that time interval. c. Calculate the displacement dT = Vavg t d. Compare the value found in 2c (dT) with the position d6 in table 1 using percent difference (Remember experimental values are always compared using percent difference). e. Draw a tangent line (check the pre-lab video for a review on tangent lines) at the point at t= 0.350s on the Position vs Time graph. f. Select two points along the tangent line to determine the slope. This value represents the INSTANTANEOUS VELOCITY (Vins) at t=0.350s g. Using percent difference, compare the average velocity for the 0.000-0.600s time interval to the instantaneous velocity at t=0.350s. 3. Complete Table 1 by calculating the blank values and copy the average velocity over to Table 2. (Note that the average velocity occurs at the midway time interval, do not change the average velocity values) 4. Average Velocity vs Time Graph: a. Using Table 2, plot a graph of Average Velocity vs Time and sketch your straight line of best fit for the 0.000-0.600s time interval. b. Calculate the entire area under this line of best fit. c. Using percent difference, compare the calculate area with the total displacement (dT) measured on the Ticker-tape. d. Calculate the slope of your line of best fit. This represents the AVERAGE ACCELERATION for the total time interval. 5. Calculate the average acceleration between each successive time interval and record the values to complete Table 2. 6. Average Acceleration vs Time Graph: a. Using Table 2, plot a graph of Average Acceleration vs Time and sketch your straight line of best fit for the 0.000-0.600s time interval. b. Calculate the entire area under this line of best fit. This is the AVERAGE VELOCITY. c. Using percent difference, compare the average velocity calculated in 6b with the average velocity calculated in 2b. %diff = - |1st experimental value 2nd experimental value| 1/2(1st experimental value + 2nd experimetnal value) x 100% 1-2 Uniformly Accelerated Motion Lab Results: Data and Observations: Complete the tables while going through the video and procedure. Table 1: Positions, Displacement, and Velocity of the cart rolling down an inclined plane as measured by a Ticker-timer. Please take your measurements in mm. Time (s) Position Xn (mm) Displacement AX (mm) Average Velocity Vavg (mm/s) 0.000 do = = 0.100 d = (d1-do)= (d1-do)/0.100= 0.200 d2= (d2-d1)= (d2-d1)/0.100= 0.300 d3= (d3-d2)= (d3-d2)/0.100= 0.400 d4= (d4-d3)= (d4-d3)/0.100= 0.500 0.600 d5= d6= (d5-d4)= (d5-d4)/0.100= (d6-d5)= (d6-d5)/0.100= Table 2: Average velocity and average acceleration of the cart rolling down the inclined plane. Time (s) 0.0500 0.150 0.250 0.350 0.450 0.550 Average Velocity Copied from Table 1 (mm/s) Average Acceleration (mm/s) (v2-v1)/0.100= (v3-v2)/0.100= (v4-v3)/0.100= (v5-v4)/0.100= (v6-v5)/0.100= Graph paper for the three graphs is attached to the end of this lab report. Calculations: Show your work for each calculation on a separate piece of paper. Discussion Questions: 1. What shape of line do you expect for a cart rolling down an incline when plotted as a position time graph? Is this what you see on your position time graph? Why or why not? 2. What shape of line do you expect for a cart rolling down an incline when plotted as an average velocity vs time graph? Is this what you see on your velocity time graph? Why or why not? 1-3 Uniformly Accelerated Motion Lab 3. What shape of line do you expect for a cart rolling down an incline when plotted as an acceleration time graph? Was the motion of the cart uniformly accelerated motion? Why or why not? 4. How do you think the average velocity of the cart found in 2d would compare to the instantaneous velocity if we chose a different point on the displacement time graph? Explain. (For example: how would the slope of the tangent line be different at t = 0.1 s and t = 0.6 s). 5. Use the words bank to answer the following questions (words can be used more than once if necessary): a. Position Displacement Distance Average velocity Instantaneous velocity Average acceleration What does the slope on the position vs time graph represent? b. What does the slope on the average velocity vs time graph represent? C. What does the area under the average velocity vs time graph represent? d. What does the area under the average acceleration vs time graph represent? 6. Consider the following velocity-time graph for a cyclist: VELOCITY 0 P Q R S TIME a) Why is the cyclist's acceleration greatest between points P and Q? b) Why is the cyclist's displacement greatest between points R and S? c) The cyclist is traveling at constant velocity between points Q and R. How can you tell? 1-4 Uniformly Accelerated Motion Lab 7. Consider the following displacement-time graphs: a) L b) d) I. e) Which graph shows a negative velocity? Explain your reasoning. c) II. III. Which graph shows that the object isn't moving? Explain your reasoning. Which graph represents a decrease in velocity? Explain your reasoning. 8. Choose the correct sketch that represents the following scenario: Joni left their house at 6am for their daily jog. They jogged at a steady pace for 20minutes, then took a 5minute break. After the break, they turned around and began running back home, while gradually increasing speed for the next 10 minutes. At this point, Joni experienced a tightening of their hamstring and slowed down gradually for the remaining 5 minutes it took her to reach home. d d t t C. b. a. d. t f. E t 9. In this lab we only did one trial with the cart rolling down the inclined plane. This was done to reduce the number of calculations in this lab. How can you change this lab to achieve higher accuracy and precision (make it a fairer test)? 10. Why do we use percent difference rather than percent error in this lab? 11. What new questions do you have after doing this lab? If you could extend this lab what else would you like to find out using this equipment? What new hypothesis could be tested? Conclusion: In two or three short sentences, summarize the key findings of the lab. 1-5 Uniformly Accelerated Motion Lab 1 Block = 1/4" Math-Aids.Com 1-7 Uniformly Accelerated Motion Lab 1 Block 1/4" +- Math-Aids.Com 1-8 Uniformly Accelerated Motion Lab Evaluation: Your lab worksheet will be marked using this rubric: Data table completed (for results that could Missing criteria 0 points Data tabulated but Data tabulated but Data tabulated some data is there are errors in be observed) missing. DISPLACEMENT TIME 2 points Missing graph 0 points Graph contains major errors or is All criteria met. some criteria or 4 points missing important criteria. minor errors. 3 points the data. 4 points Graph is missing and presented correctly. 6 points GRAPH --graph is neat, hand drawn on graph paper. --Axes are labelled and units are included. --graph has a meaningful title -- independent variable is on the x-axis and dependent is on the y- axis unless otherwise directed. --graph covers at least 2/3 of the page. --scale is equal and properly labelled. --line of best fit is used to show trend of graph and calculate slope. 2 points 1-9 64 Uniformly Accelerated Motion Lab Missing graph Graph contains major errors or is missing important criteria. 2 points VELOCITY TIME GRAPH --graph is neat, hand drawn on graph paper. --Axes are labelled and units are included. --graph has a meaningful title -- independent variable is on the x-axis and dependent is on the y- axis unless otherwise directed. --graph covers at least 2/3 of the page. --scale is equal and properly labelled. --line of best fit is used to show 0 points trend of graph and calculate slope. ACCELERATION TIME Graph is missing some criteria or minor errors. 3 points All criteria met. 4 points Missing graph Graph contains major errors or is missing important criteria. Graph is missing some criteria or minor errors. 3 points 2 points GRAPH --graph is neat, 0 points hand drawn on graph paper. --Axes are labelled and units are included. --graph has a meaningful title -- independent variable is on the x-axis and dependent is on the y- axis unless otherwise directed. --graph covers at least 2/3 of the page. --scale is equal and properly labelled. --line of best fit is used to show trend of graph and calculate slope. Discussion Questions from Lab Answered All criteria met. 4 points Questions not answered. 0 points Questions answered mostly incorrectly or Questions Questions answered mostly correctly. answered correctly; answers partially answered. 8 points demonstrate a 4 points solid understanding. 12 points 1-10 Uniformly Accelerated Motion Lab Conclusion: Missing Unclear Conclusion Provides conclusion: a stated but 0 points short, clear lengthy does not statement(s) restatement clearly of the key findings (what you know for sure of the results summarize provided. the key 1 points findings of as a result of the lab. 2 points the lab). Conclusion stated; clearly summarizes the key findings of the lab. 3 points 1-11