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Constant Acceleration Lab Introduction In this lab you will compare two objects that are undergoing constant acceleration. Objectives Collect position, velocity, and acceleration data as a ball travels straight up and down and for a fan cart moving away and back. Analyze the position vs. time, velocity vs. time, and acceleration vs. time graphs. Determine the best fit equations for the position vs. time and velocity vs. time graphs. Determine the mean acceleration from the acceleration vs. time graph. Materials computer Vernier computer interface Logger Pro Horizontal ramp Vernier Motion Detector volleyball or basketball wire basket Fan Cart Procedure Part 1 : Ball Toss 1. Connect the Vernier Motion Detector to the DIG/SONIC 1 channel of the interface. 2. Place the Motion Detector on the floor and protect it by placing a wire basket over it. Make sure that the motion detector is placed away from the table as far as possible so to reduce any interference with the coned shaped ultrasonic beam. 3. Open the file “06 Ball Toss” from the Physics with Computers folder. 4. 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 and about 0.5 m from the Motion Detector. Click to begin data collection. You will notice a clicking sound from the Motion Detector. Wait one second, then toss the ball straight upward. Be sure to move your hands out of the way after you release it. A toss of 0.5 m above the Motion Detector works well. You will get best results if you catch and hold the ball when it is about 0.5 m above the Motion Detector. 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 Mr. Fawcett if you are not sure whether you need to repeat the data collection. Analysis 2 1. The motion of an object in free fall is modeled by y = v0t + ½ gt , where y is the vertical 2 position, v0 is the initial velocity, t is time, and g is the acceleration due to gravity (9.8 m/s ). This is a quadratic equation whose graph is a parabola. Your graph of position vs. time should be parabolic. To fit a quadratic equation to your data, click and drag the mouse across the portion of the position vs. time graph that is parabolic, highlighting the free-fall portion. Do not include the part where the ball is in your hands being thrown or caught. Click the Curve Fit button, , select Quadratic fit from the list of models and click . Examine the fit of the curve to your data and click to return to the main graph. How 2 closely does the coefficient of the t term in the curve fit compare to ½ g? 2. The graph of velocity vs. time should be linear. To fit a line to this data, click and drag the mouse across the free-fall region of the motion. Click the Linear Fit button, . How closely does the coefficient of the t term in the fit compare to the accepted value for g? 3. The graph of acceleration vs. time should appear to be more or less constant. Click and drag the mouse across the free-fall section of the motion and click the Statistics button, . How closely does the mean acceleration value compare to the values of g found in Steps 1 and 2? 4. Title your graphs “ball toss” and put your group members names on them before printing. Make sure that you have completed steps 1 through 3 before doing this. 5. List some reasons why your values for the ball’s acceleration may be different from the accepted value for g. Part 2: Fan Cart 1. Set the motion detector on the end of a horizontal ramp positioned on blocks to raise it above the computers. Angle the head of the motion detector so that it will pick up the full motion of the cart down the ramp. You might have to play around with this at first. 2. Position the cart at least 0.5 m from the motion detector and turn it on with the low setting and the fan pushing the cart towards you. Do not leave the cart running for long or you will wear the batteries down! 3. Use the Logger Pro Ball Toss file but you will have to resize the axes to better represent your data. Click to begin data collection. Push the cart away from you so that the cart moves down the ramp and then comes back to you under its own power. Be careful not to push it too hard!. Turn the fan off after it comes back to you. Now zoom in on the part of your graphs that represents the motion of the cart after it has left your hand until just before you catch it again. This is especially important for the a-t graph. 4. Repeat the part 1 analysis questions 1-3 but don’t compare with g 5. Title your graphs “Fan Cart” and put your group members names on them before printing. Make sure that you have completed the analysis steps 1 through 3 before doing this. Analysis Questions 6. In what way(s) is the fan cart motion similar to the ball toss motion? 7. In what ways(s) is the fan cart motion different to the ball toss motion? 8. Label on the ball toss v-t graph the point where the ball has reached maximum height. What is its speed and acceleration at this point? 9. Label on the fan cart v-t graph the point where the cart has traveled the furthest distance from the motion detector. What is it speed and acceleration at this point? 10. When the ball’s or carts velocity is zero, is its acceleration zero? Explain why or why not! 11. Could you produce the same shaped graphs by driving in a car? Explain! Constant Acceleration Lab Scoring Rubric Name(s) _______________________________________________ Class____ Part 1: Ball Toss 1. Three motion graphs 2. Compared: d-t graph with quadratic fit v-t graph with linear fit a-t graph with statistics box d-t - t2 coefficient to ½ g v-t - t coefficient to g a-t - mean acceleration to g 3. Accounted for differences with actual value for g _________ 10 pts _________ 6 pts _________ 2 pts Part 2: Fan Cart 4. Three motion graphs d-t graph with quadratic fit v-t graph with linear fit a-t graph with statistics box _________ 10 pts Analysis Questions 5. Explained how the fan cart’s motion is similar to the ball toss motion __________ 2 pts 6. Explained how the fan cart’s motion is different to the ball toss motion __________ 2 pts 7. Labeled ball toss v-t graph at highest point Described the speed and acceleration at this point __________ 4 pts 8. Labeled fan cart v-t graph at furthest point Described the speed and acceleration at this point __________ 4 pts 9. Explained acceleration when velocity is zero __________ 2 pts 10. Explained if could reproduce the graphs using a car __________ 2 pts Total ___________ 44 pts